%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU674^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed May 29 17:54:37 EDT 2024

% Result   : Theorem 35.72s 36.01s
% Output   : Proof 35.72s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SEU674^2 : TPTP v8.2.0. Released v3.7.0.
% 0.13/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n005.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon May 27 09:28:54 EDT 2024
% 0.20/0.35  % CPUTime    : 
% 0.21/0.50  %----Proving TH0
% 35.72/36.01  --- Run --ho-elim --full-saturate-quant at 10...
% 35.72/36.01  --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 35.72/36.01  --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 35.72/36.01  --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 35.72/36.01  --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 35.72/36.01  % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.i7bA4aCD2h/cvc5---1.0.5_21460.smt2
% 35.72/36.01  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.i7bA4aCD2h/cvc5---1.0.5_21460.smt2
% 35.72/36.01  (assume a0 (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))
% 35.72/36.01  (assume a1 (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))
% 35.72/36.01  (assume a2 (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B)))))
% 35.72/36.01  (assume a3 (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))))
% 35.72/36.01  (assume a4 (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B)))))))
% 35.72/36.01  (assume a5 (= tptp.ap (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf)))))))
% 35.72/36.01  (assume a6 (not (=> tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B))))))))
% 35.72/36.01  (assume a7 true)
% 35.72/36.01  (step t1 (cl (not (= (not (=> tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B))))))) (not (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf))))) B))))))) (not (not (=> tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B)))))))) (not (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf))))) B)))))) :rule equiv_pos2)
% 35.72/36.01  (step t2 (cl (= tptp.apProp tptp.apProp)) :rule refl)
% 35.72/36.01  (anchor :step t3 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (Xf $$unsorted) (:= Xf Xf)))
% 35.72/36.01  (step t3.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t3.t2 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t3.t3 (cl (= Xf Xf)) :rule refl)
% 35.72/36.01  (step t3.t4 (cl (= (@ (@ (@ tptp.func A) B) Xf) (@ (@ (@ tptp.func A) B) Xf))) :rule refl)
% 35.72/36.01  (step t3.t5 (cl (= (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B))))) :rule all_simplify)
% 35.72/36.01  (step t3.t6 (cl (= (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B)))) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B)))))) :rule cong :premises (t3.t4 t3.t5))
% 35.72/36.01  (step t3 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B))))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B))))))) :rule bind)
% 35.72/36.01  (step t4 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B))))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B))))))) :rule all_simplify)
% 35.72/36.01  (step t5 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B))))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (or (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_795)) B)))))) :rule all_simplify)
% 35.72/36.01  (anchor :step t6 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (Xf $$unsorted) (:= Xf Xf) (BOUND_VARIABLE_795 $$unsorted) (:= BOUND_VARIABLE_795 BOUND_VARIABLE_795)))
% 35.72/36.01  (step t6.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t6.t2 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t6.t3 (cl (= Xf Xf)) :rule refl)
% 35.72/36.01  (step t6.t4 (cl (= BOUND_VARIABLE_795 BOUND_VARIABLE_795)) :rule refl)
% 35.72/36.01  (step t6.t5 (cl (= (or (not (@ (@ (@ tptp.func A) B) Xf)) (or (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_795)) B))) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_795)) B)))) :rule all_simplify)
% 35.72/36.01  (step t6 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (or (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_795)) B)))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_795)) B))))) :rule bind)
% 35.72/36.01  (step t7 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B))))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_795)) B))))) :rule trans :premises (t5 t6))
% 35.72/36.01  (step t8 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B))))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_795)) B))))) :rule trans :premises (t4 t7))
% 35.72/36.01  (step t9 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B))))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_795)) B))))) :rule trans :premises (t3 t8))
% 35.72/36.01  (step t10 (cl (= (=> tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B)))))) (=> tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_795)) B)))))) :rule cong :premises (t2 t9))
% 35.72/36.01  (step t11 (cl (= (not (=> tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B))))))) (not (=> tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_795)) B))))))) :rule cong :premises (t10))
% 35.72/36.01  (step t12 (cl (and (= tptp.ap (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf)))))) (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)))) (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))))))))))) (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B)))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) (not (= tptp.ap (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))))) (not (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))))) (not (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))))) (not (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))))) (not (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))) (not (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) :rule and_neg)
% 35.72/36.01  (step t13 (cl (not (= (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)))) (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)))))) (not (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))))) (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))))) :rule equiv_pos2)
% 35.72/36.01  (step t14 (cl (= tptp.apProp tptp.apProp)) :rule refl)
% 35.72/36.01  (anchor :step t15 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (Xf $$unsorted) (:= Xf Xf) (BOUND_VARIABLE_759 $$unsorted) (:= BOUND_VARIABLE_759 BOUND_VARIABLE_759)))
% 35.72/36.01  (step t15.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t15.t2 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t15.t3 (cl (= Xf Xf)) :rule refl)
% 35.72/36.01  (step t15.t4 (cl (= BOUND_VARIABLE_759 BOUND_VARIABLE_759)) :rule refl)
% 35.72/36.01  (step t15.t5 (cl (and (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))))))))))) (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B)))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) (not (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))))) (not (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))))) (not (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))) (not (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) :rule and_neg)
% 35.72/36.01  (step t15.t6 (cl (not (= (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))) (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))))))))))))) (not (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))))) (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))))) :rule equiv_pos2)
% 35.72/36.01  (step t15.t7 (cl (= tptp.func tptp.func)) :rule refl)
% 35.72/36.01  (anchor :step t15.t8 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (R $$unsorted) (:= R R)))
% 35.72/36.01  (step t15.t8.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t15.t8.t2 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t15.t8.t3 (cl (= R R)) :rule refl)
% 35.72/36.01  (step t15.t8.t4 (cl (and (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B)))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) (not (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))))) (not (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))) (not (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) :rule and_neg)
% 35.72/36.01  (step t15.t8.t5 (cl (not (= (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))))) (not (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))) :rule equiv_pos2)
% 35.72/36.01  (step t15.t8.t6 (cl (= tptp.ex1 tptp.ex1)) :rule refl)
% 35.72/36.01  (anchor :step t15.t8.t7 :args ((A $$unsorted) (:= A A) (Xphi (-> $$unsorted Bool)) (:= Xphi Xphi)))
% 35.72/36.01  (step t15.t8.t7.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t15.t8.t7.t2 (cl (= Xphi Xphi)) :rule refl)
% 35.72/36.01  (step t15.t8.t7.t3 (cl (not (= (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) (not (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule equiv_pos2)
% 35.72/36.01  (step t15.t8.t7.t4 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 35.72/36.01  (anchor :step t15.t8.t7.t5 :args ((A $$unsorted) (:= A A)))
% 35.72/36.01  (step t15.t8.t7.t5.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t15.t8.t7.t5.t2 (cl (= (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (not (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule all_simplify)
% 35.72/36.01  (step t15.t8.t7.t5.t3 (cl (= (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) :rule all_simplify)
% 35.72/36.01  (step t15.t8.t7.t5.t4 (cl (= (not (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule cong :premises (t15.t8.t7.t5.t3))
% 35.72/36.01  (step t15.t8.t7.t5.t5 (cl (= (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule trans :premises (t15.t8.t7.t5.t2 t15.t8.t7.t5.t4))
% 35.72/36.01  (step t15.t8.t7.t5 (cl (= (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule bind)
% 35.72/36.01  (step t15.t8.t7.t6 (cl (= (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) :rule cong :premises (t15.t8.t7.t4 t15.t8.t7.t5))
% 35.72/36.01  (step t15.t8.t7.t7 (cl (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule resolution :premises (t15.t8.t7.t3 t15.t8.t7.t6 a0))
% 35.72/36.01  (step t15.t8.t7.t8 (cl (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) :rule refl)
% 35.72/36.01  (step t15.t8.t7.t9 (cl (= (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) :rule cong :premises (t15.t8.t7.t7 t15.t8.t7.t8))
% 35.72/36.01  (step t15.t8.t7 (cl (= (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) :rule bind)
% 35.72/36.01  (step t15.t8.t8 (cl (= (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) :rule cong :premises (t15.t8.t6 t15.t8.t7))
% 35.72/36.01  (step t15.t8.t9 (cl (= tptp.ex1 tptp.ex1)) :rule refl)
% 35.72/36.01  (anchor :step t15.t8.t10 :args ((A $$unsorted) (:= A A) (Xphi (-> $$unsorted Bool)) (:= Xphi Xphi)))
% 35.72/36.01  (step t15.t8.t10.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t15.t8.t10.t2 (cl (= Xphi Xphi)) :rule refl)
% 35.72/36.01  (step t15.t8.t10.t3 (cl (= (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule all_simplify)
% 35.72/36.01  (anchor :step t15.t8.t10.t4 :args ((Xx $$unsorted) (:= Xx Xx)))
% 35.72/36.01  (step t15.t8.t10.t4.t1 (cl (= Xx Xx)) :rule refl)
% 35.72/36.01  (step t15.t8.t10.t4.t2 (cl (= (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) :rule refl)
% 35.72/36.01  (step t15.t8.t10.t4.t3 (cl (= (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) :rule all_simplify)
% 35.72/36.01  (step t15.t8.t10.t4.t4 (cl (= (not (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) :rule cong :premises (t15.t8.t10.t4.t3))
% 35.72/36.01  (step t15.t8.t10.t4.t5 (cl (= (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) :rule cong :premises (t15.t8.t10.t4.t2 t15.t8.t10.t4.t4))
% 35.72/36.01  (step t15.t8.t10.t4 (cl (= (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) :rule bind)
% 35.72/36.01  (step t15.t8.t10.t5 (cl (= (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))) :rule cong :premises (t15.t8.t10.t4))
% 35.72/36.01  (step t15.t8.t10.t6 (cl (= (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))) :rule trans :premises (t15.t8.t10.t3 t15.t8.t10.t5))
% 35.72/36.01  (step t15.t8.t10 (cl (= (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))) :rule bind)
% 35.72/36.01  (step t15.t8.t11 (cl (= (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))))) :rule cong :premises (t15.t8.t9 t15.t8.t10))
% 35.72/36.01  (step t15.t8.t12 (cl (= (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))))) :rule trans :premises (t15.t8.t8 t15.t8.t11))
% 35.72/36.01  (step t15.t8.t13 (cl (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))) :rule resolution :premises (t15.t8.t5 t15.t8.t12 a1))
% 35.72/36.01  (step t15.t8.t14 (cl (not (= (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) (not (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule equiv_pos2)
% 35.72/36.01  (step t15.t8.t15 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 35.72/36.01  (anchor :step t15.t8.t16 :args ((A $$unsorted) (:= A A)))
% 35.72/36.01  (step t15.t8.t16.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t15.t8.t16.t2 (cl (= (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (not (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule all_simplify)
% 35.72/36.01  (step t15.t8.t16.t3 (cl (= (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) :rule all_simplify)
% 35.72/36.01  (step t15.t8.t16.t4 (cl (= (not (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule cong :premises (t15.t8.t16.t3))
% 35.72/36.01  (step t15.t8.t16.t5 (cl (= (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule trans :premises (t15.t8.t16.t2 t15.t8.t16.t4))
% 35.72/36.01  (step t15.t8.t16 (cl (= (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule bind)
% 35.72/36.01  (step t15.t8.t17 (cl (= (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) :rule cong :premises (t15.t8.t15 t15.t8.t16))
% 35.72/36.01  (step t15.t8.t18 (cl (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule resolution :premises (t15.t8.t14 t15.t8.t17 a0))
% 35.72/36.01  (step t15.t8.t19 (cl (and (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B)))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) :rule resolution :premises (t15.t8.t4 a2 t15.t8.t13 t15.t8.t18))
% 35.72/36.01  (step t15.t8.t20 (cl (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))))) :rule and :premises (t15.t8.t19))
% 35.72/36.01  (step t15.t8.t21 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t15.t8.t22 (cl (= (@ tptp.breln A) (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A))) :rule cong :premises (t15.t8.t20 t15.t8.t21))
% 35.72/36.01  (step t15.t8.t23 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t15.t8.t24 (cl (= (@ (@ tptp.breln A) B) (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B))) :rule cong :premises (t15.t8.t22 t15.t8.t23))
% 35.72/36.01  (step t15.t8.t25 (cl (= R R)) :rule refl)
% 35.72/36.01  (step t15.t8.t26 (cl (= (@ (@ (@ tptp.breln A) B) R) (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) R))) :rule cong :premises (t15.t8.t24 t15.t8.t25))
% 35.72/36.01  (anchor :step t15.t8.t27 :args ((Xx $$unsorted) (:= Xx Xx)))
% 35.72/36.01  (step t15.t8.t27.t1 (cl (= Xx Xx)) :rule refl)
% 35.72/36.01  (step t15.t8.t27.t2 (cl (= (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in Xx) A)))) :rule refl)
% 35.72/36.01  (step t15.t8.t27.t3 (cl (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))) :rule and :premises (t15.t8.t19))
% 35.72/36.01  (step t15.t8.t27.t4 (cl (= (@ tptp.ex1 B) (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B))) :rule cong :premises (t15.t8.t27.t3 t15.t8.t23))
% 35.72/36.01  (step t15.t8.t27.t5 (cl (= (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))) :rule refl)
% 35.72/36.01  (step t15.t8.t27.t6 (cl (= (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))) :rule cong :premises (t15.t8.t27.t4 t15.t8.t27.t5))
% 35.72/36.01  (step t15.t8.t27.t7 (cl (= (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))) (or (not (@ (@ tptp.in Xx) A)) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))) :rule cong :premises (t15.t8.t27.t2 t15.t8.t27.t6))
% 35.72/36.01  (step t15.t8.t27 (cl (= (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))) :rule bind)
% 35.72/36.01  (step t15.t8.t28 (cl (= (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))) (and (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))) :rule cong :premises (t15.t8.t26 t15.t8.t27))
% 35.72/36.01  (step t15.t8 (cl (= (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))) (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))))) :rule bind)
% 35.72/36.01  (step t15.t9 (cl (= (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))) (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))))) :rule cong :premises (t15.t7 t15.t8))
% 35.72/36.01  (step t15.t10 (cl (= tptp.func tptp.func)) :rule refl)
% 35.72/36.01  (anchor :step t15.t11 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (R $$unsorted) (:= R R)))
% 35.72/36.01  (step t15.t11.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t15.t11.t2 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t15.t11.t3 (cl (= R R)) :rule refl)
% 35.72/36.01  (step t15.t11.t4 (cl (= (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) (lambda ((B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))))) :rule all_simplify)
% 35.72/36.01  (step t15.t11.t5 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t15.t11.t6 (cl (= (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) (@ (lambda ((B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) B))) :rule cong :premises (t15.t11.t4 t15.t11.t5))
% 35.72/36.01  (step t15.t11.t7 (cl (= (@ (lambda ((B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) B) (lambda ((C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))))) :rule all_simplify)
% 35.72/36.01  (step t15.t11.t8 (cl (= (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) (lambda ((C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))))) :rule trans :premises (t15.t11.t6 t15.t11.t7))
% 35.72/36.01  (step t15.t11.t9 (cl (= R R)) :rule refl)
% 35.72/36.01  (step t15.t11.t10 (cl (= (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) R) (@ (lambda ((C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) R))) :rule cong :premises (t15.t11.t8 t15.t11.t9))
% 35.72/36.01  (step t15.t11.t11 (cl (= (@ (lambda ((C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) R) (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)))) :rule all_simplify)
% 35.72/36.01  (step t15.t11.t12 (cl (= (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) R) (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)))) :rule trans :premises (t15.t11.t10 t15.t11.t11))
% 35.72/36.01  (anchor :step t15.t11.t13 :args ((Xx $$unsorted) (:= Xx Xx)))
% 35.72/36.01  (step t15.t11.t13.t1 (cl (= Xx Xx)) :rule refl)
% 35.72/36.01  (step t15.t11.t13.t2 (cl (= (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in Xx) A)))) :rule refl)
% 35.72/36.01  (step t15.t11.t13.t3 (cl (= (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))) :rule all_simplify)
% 35.72/36.01  (step t15.t11.t13.t4 (cl (= (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))) :rule refl)
% 35.72/36.01  (step t15.t11.t13.t5 (cl (= (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))) (@ (lambda ((Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))) :rule cong :premises (t15.t11.t13.t3 t15.t11.t13.t4))
% 35.72/36.01  (step t15.t11.t13.t6 (cl (= (@ (lambda ((Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx)))))))))) :rule all_simplify)
% 35.72/36.01  (anchor :step t15.t11.t13.t7 :args ((Xx $$unsorted) (:= Xx Xx)))
% 35.72/36.01  (step t15.t11.t13.t7.t1 (cl (= Xx Xx)) :rule refl)
% 35.72/36.01  (step t15.t11.t13.t7.t2 (cl (= (@ tptp.in Xx) (@ tptp.in Xx))) :rule refl)
% 35.72/36.01  (step t15.t11.t13.t7.t3 (cl (= (@ tptp.dsetconstr B) (@ tptp.dsetconstr B))) :rule refl)
% 35.72/36.01  (anchor :step t15.t11.t13.t7.t4 :args ((Xx $$unsorted) (:= Xx Xx)))
% 35.72/36.01  (step t15.t11.t13.t7.t4.t1 (cl (= Xx Xx)) :rule refl)
% 35.72/36.01  (step t15.t11.t13.t7.t4.t2 (cl (= (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))) :rule all_simplify)
% 35.72/36.01  (step t15.t11.t13.t7.t4 (cl (= (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx)) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))) :rule bind)
% 35.72/36.01  (step t15.t11.t13.t7.t5 (cl (= (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx))) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) :rule cong :premises (t15.t11.t13.t7.t3 t15.t11.t13.t7.t4))
% 35.72/36.01  (step t15.t11.t13.t7.t6 (cl (= (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx)))) (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))) :rule cong :premises (t15.t11.t13.t7.t2 t15.t11.t13.t7.t5))
% 35.72/36.01  (step t15.t11.t13.t7.t7 (cl (= (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx))))) (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))))) :rule cong :premises (t15.t11.t13.t7.t6))
% 35.72/36.01  (step t15.t11.t13.t7.t8 (cl (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.setadjoin Xx) tptp.emptyset))) :rule refl)
% 35.72/36.01  (step t15.t11.t13.t7.t9 (cl (= (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx)))) (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))) :rule cong :premises (t15.t11.t13.t7.t8 t15.t11.t13.t7.t5))
% 35.72/36.01  (step t15.t11.t13.t7.t10 (cl (= (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))))) :rule cong :premises (t15.t11.t13.t7.t9))
% 35.72/36.01  (step t15.t11.t13.t7.t11 (cl (= (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx)))))) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))) :rule cong :premises (t15.t11.t13.t7.t7 t15.t11.t13.t7.t10))
% 35.72/36.01  (step t15.t11.t13.t7 (cl (= (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx))))))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))))))) :rule bind)
% 35.72/36.01  (step t15.t11.t13.t8 (cl (= (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx)))))))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))) :rule cong :premises (t15.t11.t13.t7))
% 35.72/36.01  (step t15.t11.t13.t9 (cl (= (@ (lambda ((Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))) :rule trans :premises (t15.t11.t13.t6 t15.t11.t13.t8))
% 35.72/36.01  (step t15.t11.t13.t10 (cl (= (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))) :rule trans :premises (t15.t11.t13.t5 t15.t11.t13.t9))
% 35.72/36.01  (step t15.t11.t13.t11 (cl (= (or (not (@ (@ tptp.in Xx) A)) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))))))))) :rule cong :premises (t15.t11.t13.t2 t15.t11.t13.t10))
% 35.72/36.01  (step t15.t11.t13 (cl (= (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) :rule bind)
% 35.72/36.01  (step t15.t11.t14 (cl (= (and (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))))))))))) :rule cong :premises (t15.t11.t12 t15.t11.t13))
% 35.72/36.01  (step t15.t11 (cl (= (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))) (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))))) :rule bind)
% 35.72/36.01  (step t15.t12 (cl (= (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))) (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))))))))))))) :rule cong :premises (t15.t10 t15.t11))
% 35.72/36.01  (step t15.t13 (cl (= (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))) (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))))))))))))) :rule trans :premises (t15.t9 t15.t12))
% 35.72/36.01  (step t15.t14 (cl (not (= (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))) (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))))) (not (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))))) (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))))) :rule equiv_pos2)
% 35.72/36.01  (anchor :step t15.t15 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (R $$unsorted) (:= R R)))
% 35.72/36.01  (step t15.t15.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t15.t15.t2 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t15.t15.t3 (cl (= R R)) :rule refl)
% 35.72/36.01  (step t15.t15.t4 (cl (= (@ (@ (@ tptp.breln A) B) R) (@ (@ (@ tptp.breln A) B) R))) :rule refl)
% 35.72/36.01  (step t15.t15.t5 (cl (= (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))) :rule all_simplify)
% 35.72/36.01  (step t15.t15.t6 (cl (= (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))) :rule cong :premises (t15.t15.t4 t15.t15.t5))
% 35.72/36.01  (step t15.t15 (cl (= (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))) (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))))) :rule bind)
% 35.72/36.01  (step t15.t16 (cl (= (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))) (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))))) :rule cong :premises (t15.t10 t15.t15))
% 35.72/36.01  (step t15.t17 (cl (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))))) :rule resolution :premises (t15.t14 t15.t16 a3))
% 35.72/36.01  (step t15.t18 (cl (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))))) :rule resolution :premises (t15.t6 t15.t13 t15.t17))
% 35.72/36.01  (step t15.t19 (cl (not (= (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))))) (not (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))) :rule equiv_pos2)
% 35.72/36.01  (step t15.t20 (cl (= tptp.ex1 tptp.ex1)) :rule refl)
% 35.72/36.01  (anchor :step t15.t21 :args ((A $$unsorted) (:= A A) (Xphi (-> $$unsorted Bool)) (:= Xphi Xphi)))
% 35.72/36.01  (step t15.t21.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t15.t21.t2 (cl (= Xphi Xphi)) :rule refl)
% 35.72/36.01  (step t15.t21.t3 (cl (not (= (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) (not (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule equiv_pos2)
% 35.72/36.01  (step t15.t21.t4 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 35.72/36.01  (anchor :step t15.t21.t5 :args ((A $$unsorted) (:= A A)))
% 35.72/36.01  (step t15.t21.t5.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t15.t21.t5.t2 (cl (= (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (not (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule all_simplify)
% 35.72/36.01  (step t15.t21.t5.t3 (cl (= (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) :rule all_simplify)
% 35.72/36.01  (step t15.t21.t5.t4 (cl (= (not (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule cong :premises (t15.t21.t5.t3))
% 35.72/36.01  (step t15.t21.t5.t5 (cl (= (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule trans :premises (t15.t21.t5.t2 t15.t21.t5.t4))
% 35.72/36.01  (step t15.t21.t5 (cl (= (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule bind)
% 35.72/36.01  (step t15.t21.t6 (cl (= (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) :rule cong :premises (t15.t21.t4 t15.t21.t5))
% 35.72/36.01  (step t15.t21.t7 (cl (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule resolution :premises (t15.t21.t3 t15.t21.t6 a0))
% 35.72/36.01  (step t15.t21.t8 (cl (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) :rule refl)
% 35.72/36.01  (step t15.t21.t9 (cl (= (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) :rule cong :premises (t15.t21.t7 t15.t21.t8))
% 35.72/36.01  (step t15.t21 (cl (= (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) :rule bind)
% 35.72/36.01  (step t15.t22 (cl (= (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) :rule cong :premises (t15.t20 t15.t21))
% 35.72/36.01  (step t15.t23 (cl (= tptp.ex1 tptp.ex1)) :rule refl)
% 35.72/36.01  (anchor :step t15.t24 :args ((A $$unsorted) (:= A A) (Xphi (-> $$unsorted Bool)) (:= Xphi Xphi)))
% 35.72/36.01  (step t15.t24.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t15.t24.t2 (cl (= Xphi Xphi)) :rule refl)
% 35.72/36.01  (step t15.t24.t3 (cl (= (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule all_simplify)
% 35.72/36.01  (anchor :step t15.t24.t4 :args ((Xx $$unsorted) (:= Xx Xx)))
% 35.72/36.01  (step t15.t24.t4.t1 (cl (= Xx Xx)) :rule refl)
% 35.72/36.01  (step t15.t24.t4.t2 (cl (= (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) :rule refl)
% 35.72/36.01  (step t15.t24.t4.t3 (cl (= (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) :rule all_simplify)
% 35.72/36.01  (step t15.t24.t4.t4 (cl (= (not (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) :rule cong :premises (t15.t24.t4.t3))
% 35.72/36.01  (step t15.t24.t4.t5 (cl (= (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) :rule cong :premises (t15.t24.t4.t2 t15.t24.t4.t4))
% 35.72/36.01  (step t15.t24.t4 (cl (= (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) :rule bind)
% 35.72/36.01  (step t15.t24.t5 (cl (= (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))) :rule cong :premises (t15.t24.t4))
% 35.72/36.01  (step t15.t24.t6 (cl (= (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))) :rule trans :premises (t15.t24.t3 t15.t24.t5))
% 35.72/36.01  (step t15.t24 (cl (= (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))) :rule bind)
% 35.72/36.01  (step t15.t25 (cl (= (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))))) :rule cong :premises (t15.t23 t15.t24))
% 35.72/36.01  (step t15.t26 (cl (= (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))))) :rule trans :premises (t15.t22 t15.t25))
% 35.72/36.01  (step t15.t27 (cl (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))) :rule resolution :premises (t15.t19 t15.t26 a1))
% 35.72/36.01  (step t15.t28 (cl (not (= (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) (not (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule equiv_pos2)
% 35.72/36.01  (step t15.t29 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 35.72/36.01  (anchor :step t15.t30 :args ((A $$unsorted) (:= A A)))
% 35.72/36.01  (step t15.t30.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t15.t30.t2 (cl (= (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (not (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule all_simplify)
% 35.72/36.01  (step t15.t30.t3 (cl (= (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) :rule all_simplify)
% 35.72/36.01  (step t15.t30.t4 (cl (= (not (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule cong :premises (t15.t30.t3))
% 35.72/36.01  (step t15.t30.t5 (cl (= (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule trans :premises (t15.t30.t2 t15.t30.t4))
% 35.72/36.01  (step t15.t30 (cl (= (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule bind)
% 35.72/36.01  (step t15.t31 (cl (= (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) :rule cong :premises (t15.t29 t15.t30))
% 35.72/36.01  (step t15.t32 (cl (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule resolution :premises (t15.t28 t15.t31 a0))
% 35.72/36.01  (step t15.t33 (cl (and (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))))))))))) (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B)))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) :rule resolution :premises (t15.t5 t15.t18 a2 t15.t27 t15.t32))
% 35.72/36.01  (step t15.t34 (cl (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))))) :rule and :premises (t15.t33))
% 35.72/36.01  (step t15.t35 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t15.t36 (cl (= (@ tptp.func A) (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A))) :rule cong :premises (t15.t34 t15.t35))
% 35.72/36.01  (step t15.t37 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t15.t38 (cl (= (@ (@ tptp.func A) B) (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B))) :rule cong :premises (t15.t36 t15.t37))
% 35.72/36.01  (step t15.t39 (cl (= Xf Xf)) :rule refl)
% 35.72/36.01  (step t15.t40 (cl (= (@ (@ (@ tptp.func A) B) Xf) (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf))) :rule cong :premises (t15.t38 t15.t39))
% 35.72/36.01  (step t15.t41 (cl (= (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf)))) :rule cong :premises (t15.t40))
% 35.72/36.01  (step t15.t42 (cl (= (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)))) :rule refl)
% 35.72/36.01  (step t15.t43 (cl (= (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) :rule refl)
% 35.72/36.01  (step t15.t44 (cl (= (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)) (or (not (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)))) :rule cong :premises (t15.t41 t15.t42 t15.t43))
% 35.72/36.01  (step t15 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))))) :rule bind)
% 35.72/36.01  (step t16 (cl (= (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)))) (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)))))) :rule cong :premises (t14 t15))
% 35.72/36.01  (anchor :step t17 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (Xf $$unsorted) (:= Xf Xf) (BOUND_VARIABLE_759 $$unsorted) (:= BOUND_VARIABLE_759 BOUND_VARIABLE_759)))
% 35.72/36.01  (step t17.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t17.t2 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t17.t3 (cl (= Xf Xf)) :rule refl)
% 35.72/36.01  (step t17.t4 (cl (= BOUND_VARIABLE_759 BOUND_VARIABLE_759)) :rule refl)
% 35.72/36.01  (step t17.t5 (cl (= (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) (lambda ((B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))))) :rule all_simplify)
% 35.72/36.01  (step t17.t6 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t17.t7 (cl (= (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) (@ (lambda ((B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) B))) :rule cong :premises (t17.t5 t17.t6))
% 35.72/36.01  (step t17.t8 (cl (= (@ (lambda ((B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) B) (lambda ((R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))))) :rule all_simplify)
% 35.72/36.01  (step t17.t9 (cl (= (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) (lambda ((R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))))) :rule trans :premises (t17.t7 t17.t8))
% 35.72/36.01  (step t17.t10 (cl (= Xf Xf)) :rule refl)
% 35.72/36.01  (step t17.t11 (cl (= (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf) (@ (lambda ((R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) Xf))) :rule cong :premises (t17.t9 t17.t10))
% 35.72/36.01  (step t17.t12 (cl (= (@ (lambda ((R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) Xf) (and (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))))) :rule all_simplify)
% 35.72/36.01  (step t17.t13 (cl (= (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf) (and (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))))) :rule trans :premises (t17.t11 t17.t12))
% 35.72/36.01  (step t17.t14 (cl (= (not (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf)) (not (and (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf)))))))))))))) :rule cong :premises (t17.t13))
% 35.72/36.01  (step t17.t15 (cl (= (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)))) :rule refl)
% 35.72/36.01  (step t17.t16 (cl (= (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) :rule refl)
% 35.72/36.01  (step t17.t17 (cl (= (or (not (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)) (or (not (and (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf)))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)))) :rule cong :premises (t17.t14 t17.t15 t17.t16))
% 35.72/36.01  (step t17 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (and (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf)))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))))) :rule bind)
% 35.72/36.01  (step t18 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (and (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf)))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))))) :rule all_simplify)
% 35.72/36.01  (step t19 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))))) :rule trans :premises (t17 t18))
% 35.72/36.01  (step t20 (cl (= (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)))) (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)))))) :rule cong :premises (t2 t19))
% 35.72/36.01  (step t21 (cl (= (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)))) (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)))))) :rule trans :premises (t16 t20))
% 35.72/36.01  (step t22 (cl (not (= (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B)))))) (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)))))) (not (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B))))))) (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))))) :rule equiv_pos2)
% 35.72/36.01  (anchor :step t23 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (Xf $$unsorted) (:= Xf Xf)))
% 35.72/36.01  (step t23.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t23.t2 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t23.t3 (cl (= Xf Xf)) :rule refl)
% 35.72/36.01  (step t23.t4 (cl (= (@ (@ (@ tptp.func A) B) Xf) (@ (@ (@ tptp.func A) B) Xf))) :rule refl)
% 35.72/36.01  (step t23.t5 (cl (= (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B))))) :rule all_simplify)
% 35.72/36.01  (step t23.t6 (cl (= (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B)))) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B)))))) :rule cong :premises (t23.t4 t23.t5))
% 35.72/36.01  (step t23 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B))))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B))))))) :rule bind)
% 35.72/36.01  (step t24 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B))))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B))))))) :rule all_simplify)
% 35.72/36.01  (step t25 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B))))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (or (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)))))) :rule all_simplify)
% 35.72/36.01  (anchor :step t26 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (Xf $$unsorted) (:= Xf Xf) (BOUND_VARIABLE_759 $$unsorted) (:= BOUND_VARIABLE_759 BOUND_VARIABLE_759)))
% 35.72/36.01  (step t26.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t26.t2 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t26.t3 (cl (= Xf Xf)) :rule refl)
% 35.72/36.01  (step t26.t4 (cl (= BOUND_VARIABLE_759 BOUND_VARIABLE_759)) :rule refl)
% 35.72/36.01  (step t26.t5 (cl (= (or (not (@ (@ (@ tptp.func A) B) Xf)) (or (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)))) :rule all_simplify)
% 35.72/36.01  (step t26 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (or (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))))) :rule bind)
% 35.72/36.01  (step t27 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B))))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))))) :rule trans :premises (t25 t26))
% 35.72/36.01  (step t28 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B))))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))))) :rule trans :premises (t24 t27))
% 35.72/36.01  (step t29 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B))))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))))) :rule trans :premises (t23 t28))
% 35.72/36.01  (step t30 (cl (= (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B)))))) (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)))))) :rule cong :premises (t2 t29))
% 35.72/36.01  (step t31 (cl (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))))) :rule resolution :premises (t22 t30 a4))
% 35.72/36.01  (step t32 (cl (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))))) :rule resolution :premises (t13 t21 t31))
% 35.72/36.01  (step t33 (cl (not (= (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))) (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))))))))))))) (not (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))))) (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))))) :rule equiv_pos2)
% 35.72/36.01  (step t34 (cl (= tptp.func tptp.func)) :rule refl)
% 35.72/36.01  (anchor :step t35 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (R $$unsorted) (:= R R)))
% 35.72/36.01  (step t35.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t35.t2 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t35.t3 (cl (= R R)) :rule refl)
% 35.72/36.01  (step t35.t4 (cl (and (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B)))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) (not (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))))) (not (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))) (not (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) :rule and_neg)
% 35.72/36.01  (step t35.t5 (cl (not (= (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))))) (not (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))) :rule equiv_pos2)
% 35.72/36.01  (step t35.t6 (cl (= tptp.ex1 tptp.ex1)) :rule refl)
% 35.72/36.01  (anchor :step t35.t7 :args ((A $$unsorted) (:= A A) (Xphi (-> $$unsorted Bool)) (:= Xphi Xphi)))
% 35.72/36.01  (step t35.t7.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t35.t7.t2 (cl (= Xphi Xphi)) :rule refl)
% 35.72/36.01  (step t35.t7.t3 (cl (not (= (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) (not (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule equiv_pos2)
% 35.72/36.01  (step t35.t7.t4 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 35.72/36.01  (anchor :step t35.t7.t5 :args ((A $$unsorted) (:= A A)))
% 35.72/36.01  (step t35.t7.t5.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t35.t7.t5.t2 (cl (= (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (not (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule all_simplify)
% 35.72/36.01  (step t35.t7.t5.t3 (cl (= (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) :rule all_simplify)
% 35.72/36.01  (step t35.t7.t5.t4 (cl (= (not (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule cong :premises (t35.t7.t5.t3))
% 35.72/36.01  (step t35.t7.t5.t5 (cl (= (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule trans :premises (t35.t7.t5.t2 t35.t7.t5.t4))
% 35.72/36.01  (step t35.t7.t5 (cl (= (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule bind)
% 35.72/36.01  (step t35.t7.t6 (cl (= (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) :rule cong :premises (t35.t7.t4 t35.t7.t5))
% 35.72/36.01  (step t35.t7.t7 (cl (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule resolution :premises (t35.t7.t3 t35.t7.t6 a0))
% 35.72/36.01  (step t35.t7.t8 (cl (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) :rule refl)
% 35.72/36.01  (step t35.t7.t9 (cl (= (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) :rule cong :premises (t35.t7.t7 t35.t7.t8))
% 35.72/36.01  (step t35.t7 (cl (= (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) :rule bind)
% 35.72/36.01  (step t35.t8 (cl (= (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) :rule cong :premises (t35.t6 t35.t7))
% 35.72/36.01  (step t35.t9 (cl (= tptp.ex1 tptp.ex1)) :rule refl)
% 35.72/36.01  (anchor :step t35.t10 :args ((A $$unsorted) (:= A A) (Xphi (-> $$unsorted Bool)) (:= Xphi Xphi)))
% 35.72/36.01  (step t35.t10.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t35.t10.t2 (cl (= Xphi Xphi)) :rule refl)
% 35.72/36.01  (step t35.t10.t3 (cl (= (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule all_simplify)
% 35.72/36.01  (anchor :step t35.t10.t4 :args ((Xx $$unsorted) (:= Xx Xx)))
% 35.72/36.01  (step t35.t10.t4.t1 (cl (= Xx Xx)) :rule refl)
% 35.72/36.01  (step t35.t10.t4.t2 (cl (= (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) :rule refl)
% 35.72/36.01  (step t35.t10.t4.t3 (cl (= (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) :rule all_simplify)
% 35.72/36.01  (step t35.t10.t4.t4 (cl (= (not (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) :rule cong :premises (t35.t10.t4.t3))
% 35.72/36.01  (step t35.t10.t4.t5 (cl (= (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) :rule cong :premises (t35.t10.t4.t2 t35.t10.t4.t4))
% 35.72/36.01  (step t35.t10.t4 (cl (= (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) :rule bind)
% 35.72/36.01  (step t35.t10.t5 (cl (= (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))) :rule cong :premises (t35.t10.t4))
% 35.72/36.01  (step t35.t10.t6 (cl (= (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))) :rule trans :premises (t35.t10.t3 t35.t10.t5))
% 35.72/36.01  (step t35.t10 (cl (= (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))) :rule bind)
% 35.72/36.01  (step t35.t11 (cl (= (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))))) :rule cong :premises (t35.t9 t35.t10))
% 35.72/36.01  (step t35.t12 (cl (= (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))))) :rule trans :premises (t35.t8 t35.t11))
% 35.72/36.01  (step t35.t13 (cl (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))) :rule resolution :premises (t35.t5 t35.t12 a1))
% 35.72/36.01  (step t35.t14 (cl (not (= (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) (not (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule equiv_pos2)
% 35.72/36.01  (step t35.t15 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 35.72/36.01  (anchor :step t35.t16 :args ((A $$unsorted) (:= A A)))
% 35.72/36.01  (step t35.t16.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t35.t16.t2 (cl (= (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (not (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule all_simplify)
% 35.72/36.01  (step t35.t16.t3 (cl (= (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) :rule all_simplify)
% 35.72/36.01  (step t35.t16.t4 (cl (= (not (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule cong :premises (t35.t16.t3))
% 35.72/36.01  (step t35.t16.t5 (cl (= (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule trans :premises (t35.t16.t2 t35.t16.t4))
% 35.72/36.01  (step t35.t16 (cl (= (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule bind)
% 35.72/36.01  (step t35.t17 (cl (= (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) :rule cong :premises (t35.t15 t35.t16))
% 35.72/36.01  (step t35.t18 (cl (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule resolution :premises (t35.t14 t35.t17 a0))
% 35.72/36.01  (step t35.t19 (cl (and (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B)))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) :rule resolution :premises (t35.t4 a2 t35.t13 t35.t18))
% 35.72/36.01  (step t35.t20 (cl (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))))) :rule and :premises (t35.t19))
% 35.72/36.01  (step t35.t21 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t35.t22 (cl (= (@ tptp.breln A) (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A))) :rule cong :premises (t35.t20 t35.t21))
% 35.72/36.01  (step t35.t23 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t35.t24 (cl (= (@ (@ tptp.breln A) B) (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B))) :rule cong :premises (t35.t22 t35.t23))
% 35.72/36.01  (step t35.t25 (cl (= R R)) :rule refl)
% 35.72/36.01  (step t35.t26 (cl (= (@ (@ (@ tptp.breln A) B) R) (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) R))) :rule cong :premises (t35.t24 t35.t25))
% 35.72/36.01  (anchor :step t35.t27 :args ((Xx $$unsorted) (:= Xx Xx)))
% 35.72/36.01  (step t35.t27.t1 (cl (= Xx Xx)) :rule refl)
% 35.72/36.01  (step t35.t27.t2 (cl (= (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in Xx) A)))) :rule refl)
% 35.72/36.01  (step t35.t27.t3 (cl (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))) :rule and :premises (t35.t19))
% 35.72/36.01  (step t35.t27.t4 (cl (= (@ tptp.ex1 B) (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B))) :rule cong :premises (t35.t27.t3 t35.t23))
% 35.72/36.01  (step t35.t27.t5 (cl (= (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))) :rule refl)
% 35.72/36.01  (step t35.t27.t6 (cl (= (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))) :rule cong :premises (t35.t27.t4 t35.t27.t5))
% 35.72/36.01  (step t35.t27.t7 (cl (= (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))) (or (not (@ (@ tptp.in Xx) A)) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))) :rule cong :premises (t35.t27.t2 t35.t27.t6))
% 35.72/36.01  (step t35.t27 (cl (= (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))) :rule bind)
% 35.72/36.01  (step t35.t28 (cl (= (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))) (and (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))) :rule cong :premises (t35.t26 t35.t27))
% 35.72/36.01  (step t35 (cl (= (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))) (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))))) :rule bind)
% 35.72/36.01  (step t36 (cl (= (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))) (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))))) :rule cong :premises (t34 t35))
% 35.72/36.01  (step t37 (cl (= tptp.func tptp.func)) :rule refl)
% 35.72/36.01  (anchor :step t38 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (R $$unsorted) (:= R R)))
% 35.72/36.01  (step t38.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t38.t2 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t38.t3 (cl (= R R)) :rule refl)
% 35.72/36.01  (step t38.t4 (cl (= (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) (lambda ((B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))))) :rule all_simplify)
% 35.72/36.01  (step t38.t5 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t38.t6 (cl (= (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) (@ (lambda ((B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) B))) :rule cong :premises (t38.t4 t38.t5))
% 35.72/36.01  (step t38.t7 (cl (= (@ (lambda ((B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) B) (lambda ((C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))))) :rule all_simplify)
% 35.72/36.01  (step t38.t8 (cl (= (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) (lambda ((C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))))) :rule trans :premises (t38.t6 t38.t7))
% 35.72/36.01  (step t38.t9 (cl (= R R)) :rule refl)
% 35.72/36.01  (step t38.t10 (cl (= (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) R) (@ (lambda ((C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) R))) :rule cong :premises (t38.t8 t38.t9))
% 35.72/36.01  (step t38.t11 (cl (= (@ (lambda ((C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) R) (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)))) :rule all_simplify)
% 35.72/36.01  (step t38.t12 (cl (= (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) R) (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)))) :rule trans :premises (t38.t10 t38.t11))
% 35.72/36.01  (anchor :step t38.t13 :args ((Xx $$unsorted) (:= Xx Xx)))
% 35.72/36.01  (step t38.t13.t1 (cl (= Xx Xx)) :rule refl)
% 35.72/36.01  (step t38.t13.t2 (cl (= (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in Xx) A)))) :rule refl)
% 35.72/36.01  (step t38.t13.t3 (cl (= (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))) :rule all_simplify)
% 35.72/36.01  (step t38.t13.t4 (cl (= (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))) :rule refl)
% 35.72/36.01  (step t38.t13.t5 (cl (= (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))) (@ (lambda ((Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))) :rule cong :premises (t38.t13.t3 t38.t13.t4))
% 35.72/36.01  (step t38.t13.t6 (cl (= (@ (lambda ((Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx)))))))))) :rule all_simplify)
% 35.72/36.01  (anchor :step t38.t13.t7 :args ((Xx $$unsorted) (:= Xx Xx)))
% 35.72/36.01  (step t38.t13.t7.t1 (cl (= Xx Xx)) :rule refl)
% 35.72/36.01  (step t38.t13.t7.t2 (cl (= (@ tptp.in Xx) (@ tptp.in Xx))) :rule refl)
% 35.72/36.01  (step t38.t13.t7.t3 (cl (= (@ tptp.dsetconstr B) (@ tptp.dsetconstr B))) :rule refl)
% 35.72/36.01  (anchor :step t38.t13.t7.t4 :args ((Xx $$unsorted) (:= Xx Xx)))
% 35.72/36.01  (step t38.t13.t7.t4.t1 (cl (= Xx Xx)) :rule refl)
% 35.72/36.01  (step t38.t13.t7.t4.t2 (cl (= (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))) :rule all_simplify)
% 35.72/36.01  (step t38.t13.t7.t4 (cl (= (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx)) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))) :rule bind)
% 35.72/36.01  (step t38.t13.t7.t5 (cl (= (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx))) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) :rule cong :premises (t38.t13.t7.t3 t38.t13.t7.t4))
% 35.72/36.01  (step t38.t13.t7.t6 (cl (= (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx)))) (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))) :rule cong :premises (t38.t13.t7.t2 t38.t13.t7.t5))
% 35.72/36.01  (step t38.t13.t7.t7 (cl (= (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx))))) (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))))) :rule cong :premises (t38.t13.t7.t6))
% 35.72/36.01  (step t38.t13.t7.t8 (cl (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.setadjoin Xx) tptp.emptyset))) :rule refl)
% 35.72/36.01  (step t38.t13.t7.t9 (cl (= (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx)))) (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))) :rule cong :premises (t38.t13.t7.t8 t38.t13.t7.t5))
% 35.72/36.01  (step t38.t13.t7.t10 (cl (= (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))))) :rule cong :premises (t38.t13.t7.t9))
% 35.72/36.01  (step t38.t13.t7.t11 (cl (= (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx)))))) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))) :rule cong :premises (t38.t13.t7.t7 t38.t13.t7.t10))
% 35.72/36.01  (step t38.t13.t7 (cl (= (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx))))))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))))))) :rule bind)
% 35.72/36.01  (step t38.t13.t8 (cl (= (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)) Xx)))))))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))) :rule cong :premises (t38.t13.t7))
% 35.72/36.01  (step t38.t13.t9 (cl (= (@ (lambda ((Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))) :rule trans :premises (t38.t13.t6 t38.t13.t8))
% 35.72/36.01  (step t38.t13.t10 (cl (= (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))) :rule trans :premises (t38.t13.t5 t38.t13.t9))
% 35.72/36.01  (step t38.t13.t11 (cl (= (or (not (@ (@ tptp.in Xx) A)) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))))))))) :rule cong :premises (t38.t13.t2 t38.t13.t10))
% 35.72/36.01  (step t38.t13 (cl (= (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) :rule bind)
% 35.72/36.01  (step t38.t14 (cl (= (and (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))))))))))) :rule cong :premises (t38.t12 t38.t13))
% 35.72/36.01  (step t38 (cl (= (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))) (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))))) :rule bind)
% 35.72/36.01  (step t39 (cl (= (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))) A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))) (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))))))))))))) :rule cong :premises (t37 t38))
% 35.72/36.01  (step t40 (cl (= (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))) (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))))))))))))) :rule trans :premises (t36 t39))
% 35.72/36.01  (step t41 (cl (not (= (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))) (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))))) (not (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))))) (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))))) :rule equiv_pos2)
% 35.72/36.01  (anchor :step t42 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (R $$unsorted) (:= R R)))
% 35.72/36.01  (step t42.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t42.t2 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t42.t3 (cl (= R R)) :rule refl)
% 35.72/36.01  (step t42.t4 (cl (= (@ (@ (@ tptp.breln A) B) R) (@ (@ (@ tptp.breln A) B) R))) :rule refl)
% 35.72/36.01  (step t42.t5 (cl (= (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))) :rule all_simplify)
% 35.72/36.01  (step t42.t6 (cl (= (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))) :rule cong :premises (t42.t4 t42.t5))
% 35.72/36.01  (step t42 (cl (= (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))) (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))))) :rule bind)
% 35.72/36.01  (step t43 (cl (= (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))) (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))))) :rule cong :premises (t37 t42))
% 35.72/36.01  (step t44 (cl (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))))) :rule resolution :premises (t41 t43 a3))
% 35.72/36.01  (step t45 (cl (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))))) :rule resolution :premises (t33 t40 t44))
% 35.72/36.01  (step t46 (cl (not (= (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))))) (not (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))) :rule equiv_pos2)
% 35.72/36.01  (step t47 (cl (= tptp.ex1 tptp.ex1)) :rule refl)
% 35.72/36.01  (anchor :step t48 :args ((A $$unsorted) (:= A A) (Xphi (-> $$unsorted Bool)) (:= Xphi Xphi)))
% 35.72/36.01  (step t48.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t48.t2 (cl (= Xphi Xphi)) :rule refl)
% 35.72/36.01  (step t48.t3 (cl (not (= (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) (not (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule equiv_pos2)
% 35.72/36.01  (step t48.t4 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 35.72/36.01  (anchor :step t48.t5 :args ((A $$unsorted) (:= A A)))
% 35.72/36.01  (step t48.t5.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t48.t5.t2 (cl (= (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (not (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule all_simplify)
% 35.72/36.01  (step t48.t5.t3 (cl (= (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) :rule all_simplify)
% 35.72/36.01  (step t48.t5.t4 (cl (= (not (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule cong :premises (t48.t5.t3))
% 35.72/36.01  (step t48.t5.t5 (cl (= (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule trans :premises (t48.t5.t2 t48.t5.t4))
% 35.72/36.01  (step t48.t5 (cl (= (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule bind)
% 35.72/36.01  (step t48.t6 (cl (= (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) :rule cong :premises (t48.t4 t48.t5))
% 35.72/36.01  (step t48.t7 (cl (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule resolution :premises (t48.t3 t48.t6 a0))
% 35.72/36.01  (step t48.t8 (cl (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) :rule refl)
% 35.72/36.01  (step t48.t9 (cl (= (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) :rule cong :premises (t48.t7 t48.t8))
% 35.72/36.01  (step t48 (cl (= (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) :rule bind)
% 35.72/36.01  (step t49 (cl (= (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) :rule cong :premises (t47 t48))
% 35.72/36.01  (step t50 (cl (= tptp.ex1 tptp.ex1)) :rule refl)
% 35.72/36.01  (anchor :step t51 :args ((A $$unsorted) (:= A A) (Xphi (-> $$unsorted Bool)) (:= Xphi Xphi)))
% 35.72/36.01  (step t51.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t51.t2 (cl (= Xphi Xphi)) :rule refl)
% 35.72/36.01  (step t51.t3 (cl (= (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule all_simplify)
% 35.72/36.01  (anchor :step t51.t4 :args ((Xx $$unsorted) (:= Xx Xx)))
% 35.72/36.01  (step t51.t4.t1 (cl (= Xx Xx)) :rule refl)
% 35.72/36.01  (step t51.t4.t2 (cl (= (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) :rule refl)
% 35.72/36.01  (step t51.t4.t3 (cl (= (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) :rule all_simplify)
% 35.72/36.01  (step t51.t4.t4 (cl (= (not (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) :rule cong :premises (t51.t4.t3))
% 35.72/36.01  (step t51.t4.t5 (cl (= (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) :rule cong :premises (t51.t4.t2 t51.t4.t4))
% 35.72/36.01  (step t51.t4 (cl (= (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) :rule bind)
% 35.72/36.01  (step t51.t5 (cl (= (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))) :rule cong :premises (t51.t4))
% 35.72/36.01  (step t51.t6 (cl (= (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))) :rule trans :premises (t51.t3 t51.t5))
% 35.72/36.01  (step t51 (cl (= (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))) :rule bind)
% 35.72/36.01  (step t52 (cl (= (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))))) :rule cong :premises (t50 t51))
% 35.72/36.01  (step t53 (cl (= (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))))) :rule trans :premises (t49 t52))
% 35.72/36.01  (step t54 (cl (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))) :rule resolution :premises (t46 t53 a1))
% 35.72/36.01  (step t55 (cl (not (= (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) (not (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule equiv_pos2)
% 35.72/36.01  (step t56 (cl (= tptp.singleton tptp.singleton)) :rule refl)
% 35.72/36.01  (anchor :step t57 :args ((A $$unsorted) (:= A A)))
% 35.72/36.01  (step t57.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t57.t2 (cl (= (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (not (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule all_simplify)
% 35.72/36.01  (step t57.t3 (cl (= (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) :rule all_simplify)
% 35.72/36.01  (step t57.t4 (cl (= (not (forall ((Xx $$unsorted)) (not (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule cong :premises (t57.t3))
% 35.72/36.01  (step t57.t5 (cl (= (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) :rule trans :premises (t57.t2 t57.t4))
% 35.72/36.01  (step t57 (cl (= (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule bind)
% 35.72/36.01  (step t58 (cl (= (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) :rule cong :premises (t56 t57))
% 35.72/36.01  (step t59 (cl (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) :rule resolution :premises (t55 t58 a0))
% 35.72/36.01  (step t60 (cl (and (= tptp.ap (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf)))))) (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)))) (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))))))))))) (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B)))) (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))) (= tptp.singleton (lambda ((A $$unsorted)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) :rule resolution :premises (t12 a5 t32 t45 a2 t54 t59))
% 35.72/36.01  (step t61 (cl (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))))) :rule and :premises (t60))
% 35.72/36.01  (anchor :step t62 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (Xf $$unsorted) (:= Xf Xf) (BOUND_VARIABLE_795 $$unsorted) (:= BOUND_VARIABLE_795 BOUND_VARIABLE_795)))
% 35.72/36.01  (step t62.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t62.t2 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t62.t3 (cl (= Xf Xf)) :rule refl)
% 35.72/36.01  (step t62.t4 (cl (= BOUND_VARIABLE_795 BOUND_VARIABLE_795)) :rule refl)
% 35.72/36.01  (step t62.t5 (cl (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))))) :rule and :premises (t60))
% 35.72/36.01  (step t62.t6 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t62.t7 (cl (= (@ tptp.func A) (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A))) :rule cong :premises (t62.t5 t62.t6))
% 35.72/36.01  (step t62.t8 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t62.t9 (cl (= (@ (@ tptp.func A) B) (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B))) :rule cong :premises (t62.t7 t62.t8))
% 35.72/36.01  (step t62.t10 (cl (= Xf Xf)) :rule refl)
% 35.72/36.01  (step t62.t11 (cl (= (@ (@ (@ tptp.func A) B) Xf) (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf))) :rule cong :premises (t62.t9 t62.t10))
% 35.72/36.01  (step t62.t12 (cl (= (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf)))) :rule cong :premises (t62.t11))
% 35.72/36.01  (step t62.t13 (cl (= (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)))) :rule refl)
% 35.72/36.01  (step t62.t14 (cl (= tptp.in tptp.in)) :rule refl)
% 35.72/36.01  (step t62.t15 (cl (= tptp.ap (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))))) :rule and :premises (t60))
% 35.72/36.01  (step t62.t16 (cl (= (@ tptp.ap A) (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A))) :rule cong :premises (t62.t15 t62.t6))
% 35.72/36.01  (step t62.t17 (cl (= (@ (@ tptp.ap A) B) (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B))) :rule cong :premises (t62.t16 t62.t8))
% 35.72/36.01  (step t62.t18 (cl (= (@ (@ (@ tptp.ap A) B) Xf) (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) Xf))) :rule cong :premises (t62.t17 t62.t10))
% 35.72/36.01  (step t62.t19 (cl (= BOUND_VARIABLE_795 BOUND_VARIABLE_795)) :rule refl)
% 35.72/36.01  (step t62.t20 (cl (= (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_795) (@ (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) Xf) BOUND_VARIABLE_795))) :rule cong :premises (t62.t18 t62.t19))
% 35.72/36.01  (step t62.t21 (cl (= (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_795)) (@ tptp.in (@ (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) Xf) BOUND_VARIABLE_795)))) :rule cong :premises (t62.t14 t62.t20))
% 35.72/36.01  (step t62.t22 (cl (= (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_795)) B) (@ (@ tptp.in (@ (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) Xf) BOUND_VARIABLE_795)) B))) :rule cong :premises (t62.t21 t62.t8))
% 35.72/36.01  (step t62.t23 (cl (= (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_795)) B)) (or (not (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) Xf) BOUND_VARIABLE_795)) B)))) :rule cong :premises (t62.t12 t62.t13 t62.t22))
% 35.72/36.01  (step t62 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_795)) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) Xf) BOUND_VARIABLE_795)) B))))) :rule bind)
% 35.72/36.01  (step t63 (cl (= (=> tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_795)) B)))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) Xf) BOUND_VARIABLE_795)) B)))))) :rule cong :premises (t61 t62))
% 35.72/36.01  (step t64 (cl (= (not (=> tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_795)) B))))) (not (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) Xf) BOUND_VARIABLE_795)) B))))))) :rule cong :premises (t63))
% 35.72/36.01  (step t65 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))))) :rule refl)
% 35.72/36.01  (anchor :step t66 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (Xf $$unsorted) (:= Xf Xf) (BOUND_VARIABLE_795 $$unsorted) (:= BOUND_VARIABLE_795 BOUND_VARIABLE_795)))
% 35.72/36.01  (step t66.t1 (cl (= A A)) :rule refl)
% 35.72/36.01  (step t66.t2 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t66.t3 (cl (= Xf Xf)) :rule refl)
% 35.72/36.01  (step t66.t4 (cl (= BOUND_VARIABLE_795 BOUND_VARIABLE_795)) :rule refl)
% 35.72/36.01  (step t66.t5 (cl (= (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) (lambda ((B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))))) :rule all_simplify)
% 35.72/36.01  (step t66.t6 (cl (= B B)) :rule refl)
% 35.72/36.01  (step t66.t7 (cl (= (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) (@ (lambda ((B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) B))) :rule cong :premises (t66.t5 t66.t6))
% 35.72/36.01  (step t66.t8 (cl (= (@ (lambda ((B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) B) (lambda ((R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))))) :rule all_simplify)
% 35.72/36.01  (step t66.t9 (cl (= (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) (lambda ((R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))))) :rule trans :premises (t66.t7 t66.t8))
% 35.72/36.01  (step t66.t10 (cl (= Xf Xf)) :rule refl)
% 35.72/36.01  (step t66.t11 (cl (= (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf) (@ (lambda ((R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) Xf))) :rule cong :premises (t66.t9 t66.t10))
% 35.72/36.01  (step t66.t12 (cl (= (@ (lambda ((R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) Xf) (and (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))))) :rule all_simplify)
% 35.72/36.01  (step t66.t13 (cl (= (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf) (and (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))))) :rule trans :premises (t66.t11 t66.t12))
% 35.72/36.01  (step t66.t14 (cl (= (not (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf)) (not (and (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf)))))))))))))) :rule cong :premises (t66.t13))
% 35.72/36.01  (step t66.t15 (cl (= (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)))) :rule refl)
% 35.72/36.01  (step t66.t16 (cl (= tptp.in tptp.in)) :rule refl)
% 35.72/36.01  (step t66.t17 (cl (= (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) (lambda ((B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))))) :rule all_simplify)
% 35.72/36.01  (step t66.t18 (cl (= (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) (@ (lambda ((B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B))) :rule cong :premises (t66.t17 t66.t6))
% 35.72/36.01  (step t66.t19 (cl (= (@ (lambda ((B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B) (lambda ((Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))))) :rule all_simplify)
% 35.72/36.01  (step t66.t20 (cl (= (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) (lambda ((Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))))) :rule trans :premises (t66.t18 t66.t19))
% 35.72/36.01  (step t66.t21 (cl (= (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) Xf) (@ (lambda ((Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) Xf))) :rule cong :premises (t66.t20 t66.t10))
% 35.72/36.01  (step t66.t22 (cl (= (@ (lambda ((Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) Xf) (lambda ((Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))))) :rule all_simplify)
% 35.72/36.01  (step t66.t23 (cl (= (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) Xf) (lambda ((Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))))) :rule trans :premises (t66.t21 t66.t22))
% 35.72/36.01  (step t66.t24 (cl (= BOUND_VARIABLE_795 BOUND_VARIABLE_795)) :rule refl)
% 35.72/36.01  (step t66.t25 (cl (= (@ (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) Xf) BOUND_VARIABLE_795) (@ (lambda ((Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) BOUND_VARIABLE_795))) :rule cong :premises (t66.t23 t66.t24))
% 35.72/36.01  (step t66.t26 (cl (= (@ (lambda ((Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) BOUND_VARIABLE_795) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf)))))) :rule all_simplify)
% 35.72/36.01  (step t66.t27 (cl (= (@ (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) Xf) BOUND_VARIABLE_795) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf)))))) :rule trans :premises (t66.t25 t66.t26))
% 35.72/36.01  (step t66.t28 (cl (= (@ tptp.in (@ (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) Xf) BOUND_VARIABLE_795)) (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf))))))) :rule cong :premises (t66.t16 t66.t27))
% 35.72/36.01  (step t66.t29 (cl (= (@ (@ tptp.in (@ (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) Xf) BOUND_VARIABLE_795)) B) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf))))) B))) :rule cong :premises (t66.t28 t66.t6))
% 35.72/36.01  (step t66.t30 (cl (= (or (not (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) Xf) BOUND_VARIABLE_795)) B)) (or (not (and (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf)))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf))))) B)))) :rule cong :premises (t66.t14 t66.t15 t66.t29))
% 35.72/36.01  (step t66 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) Xf) BOUND_VARIABLE_795)) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (and (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf)))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf))))) B))))) :rule bind)
% 35.72/36.01  (step t67 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (and (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf)))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf))))) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf))))) B))))) :rule all_simplify)
% 35.72/36.01  (step t68 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) Xf) BOUND_VARIABLE_795)) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf))))) B))))) :rule trans :premises (t66 t67))
% 35.72/36.01  (step t69 (cl (= (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) Xf) BOUND_VARIABLE_795)) B)))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf))))) B)))))) :rule cong :premises (t65 t68))
% 35.72/36.01  (step t70 (cl (= (not (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B)) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) R)))))))))))) A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (Xx $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) A) B) Xf) BOUND_VARIABLE_795)) B))))) (not (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf))))) B))))))) :rule cong :premises (t69))
% 35.72/36.01  (step t71 (cl (= (not (=> tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_795)) B))))) (not (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf))))) B))))))) :rule trans :premises (t64 t70))
% 35.72/36.01  (step t72 (cl (= (not (=> tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B))))))) (not (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf))))) B))))))) :rule trans :premises (t11 t71))
% 35.72/36.01  (step t73 (cl (not (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf))))) B)))))) :rule resolution :premises (t1 t72 a6))
% 35.72/36.01  (step t74 (cl (not (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf))))) B))))) :rule not_implies2 :premises (t73))
% 35.72/36.01  (step t75 (cl (= (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf))))) B))))) :rule hole :args ((forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))) (= B B) (= Xy Xy) (= BOUND_VARIABLE_759 BOUND_VARIABLE_795) (= Xf Xf) (= Xx Xx) (= Xx Xx) (= Xx Xx) (= A A)))
% 35.72/36.01  (step t76 (cl (not (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)))) (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf))))) B)))) :rule equiv1 :premises (t75))
% 35.72/36.01  (step t77 (cl (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf))))) B))) (not (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B))))) :rule reordering :premises (t76))
% 35.72/36.01  (step t78 (cl (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_759 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_759) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_759) Xy)) Xf))))) B)))) :rule not_implies1 :premises (t73))
% 35.72/36.01  (step t79 (cl (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_795 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_795) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_795) Xy)) Xf))))) B)))) :rule resolution :premises (t77 t78))
% 35.72/36.01  (step t80 (cl) :rule resolution :premises (t74 t79))
% 35.72/36.01  
% 35.72/36.01  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.i7bA4aCD2h/cvc5---1.0.5_21460.smt2
% 35.72/36.01  % cvc5---1.0.5 exiting
% 35.72/36.01  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------