TSTP Solution File: SET047^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET047^1 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n029.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 17:43:51 EDT 2024
% Result : Theorem 0.23s 0.57s
% Output : Proof 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SET047^1 : TPTP v8.2.0. Released v8.1.0.
% 0.07/0.16 % Command : do_cvc5 %s %d
% 0.17/0.37 % Computer : n029.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Tue May 28 10:56:54 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.23/0.54 %----Proving TH0
% 0.23/0.57 --- Run --ho-elim --full-saturate-quant at 10...
% 0.23/0.57 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.3uSzS6FaKb/cvc5---1.0.5_29965.smt2
% 0.23/0.57 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.3uSzS6FaKb/cvc5---1.0.5_29965.smt2
% 0.23/0.57 (assume a0 (= tptp.mlocal (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual))))
% 0.23/0.57 (assume a1 (= tptp.mnot (lambda ((A (-> tptp.mworld Bool)) (W tptp.mworld)) (not (@ A W)))))
% 0.23/0.57 (assume a2 (= tptp.mand (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (and (@ A W) (@ B W)))))
% 0.23/0.57 (assume a3 (= tptp.mor (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (or (@ A W) (@ B W)))))
% 0.23/0.57 (assume a4 (= tptp.mimplies (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (=> (@ A W) (@ B W)))))
% 0.23/0.57 (assume a5 (= tptp.mequiv (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W)))))
% 0.23/0.57 (assume a6 (= tptp.mbox (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (=> (@ (@ tptp.mrel W) V) (@ Phi V))))))
% 0.23/0.57 (assume a7 (= tptp.mdia (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (exists ((V tptp.mworld)) (and (@ (@ tptp.mrel W) V) (@ Phi V))))))
% 0.23/0.57 (assume a8 (= tptp.mforall_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W)))))
% 0.23/0.57 (assume a9 (= tptp.mexists_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (exists ((X $$unsorted)) (@ (@ A X) W)))))
% 0.23/0.57 (assume a10 (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.set_equal X) Y)) (@ tptp.mforall_di (lambda ((Z $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.element Z) X)) (@ (@ tptp.element Z) Y)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.57 (assume a11 (not (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0))))))
% 0.23/0.57 (assume a12 true)
% 0.23/0.57 (step t1 (cl (not (= (not (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0))))) false)) (not (not (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0)))))) false) :rule equiv_pos2)
% 0.23/0.57 (step t2 (cl (and (= tptp.mexists_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (not (forall ((X $$unsorted)) (not (@ (@ A X) W)))))) (= tptp.mforall_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W)))) (= tptp.mdia (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (not (forall ((V tptp.mworld)) (or (not (@ (@ tptp.mrel W) V)) (not (@ Phi V))))))) (= tptp.mbox (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (or (not (@ (@ tptp.mrel W) V)) (@ Phi V))))) (= tptp.mequiv (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W)))) (= tptp.mimplies (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (=> (@ A W) (@ B W)))) (= tptp.mor (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (or (@ A W) (@ B W)))) (= tptp.mand (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (and (@ A W) (@ B W)))) (= tptp.mnot (lambda ((A (-> tptp.mworld Bool)) (W tptp.mworld)) (not (@ A W)))) (= tptp.mlocal (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual)))) (not (= tptp.mexists_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (not (forall ((X $$unsorted)) (not (@ (@ A X) W))))))) (not (= tptp.mforall_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))))) (not (= tptp.mdia (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (not (forall ((V tptp.mworld)) (or (not (@ (@ tptp.mrel W) V)) (not (@ Phi V)))))))) (not (= tptp.mbox (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (or (not (@ (@ tptp.mrel W) V)) (@ Phi V)))))) (not (= tptp.mequiv (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))))) (not (= tptp.mimplies (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (=> (@ A W) (@ B W))))) (not (= tptp.mor (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (or (@ A W) (@ B W))))) (not (= tptp.mand (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (and (@ A W) (@ B W))))) (not (= tptp.mnot (lambda ((A (-> tptp.mworld Bool)) (W tptp.mworld)) (not (@ A W))))) (not (= tptp.mlocal (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual))))) :rule and_neg)
% 0.23/0.57 (step t3 (cl (not (= (= tptp.mexists_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (exists ((X $$unsorted)) (@ (@ A X) W)))) (= tptp.mexists_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (not (forall ((X $$unsorted)) (not (@ (@ A X) W)))))))) (not (= tptp.mexists_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (exists ((X $$unsorted)) (@ (@ A X) W))))) (= tptp.mexists_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (not (forall ((X $$unsorted)) (not (@ (@ A X) W))))))) :rule equiv_pos2)
% 0.23/0.57 (step t4 (cl (= tptp.mexists_di tptp.mexists_di)) :rule refl)
% 0.23/0.57 (anchor :step t5 :args ((A (-> $$unsorted tptp.mworld Bool)) (:= A A) (W tptp.mworld) (:= W W)))
% 0.23/0.57 (step t5.t1 (cl (= A A)) :rule refl)
% 0.23/0.57 (step t5.t2 (cl (= W W)) :rule refl)
% 0.23/0.57 (step t5.t3 (cl (= (exists ((X $$unsorted)) (@ (@ A X) W)) (not (forall ((X $$unsorted)) (not (@ (@ A X) W)))))) :rule all_simplify)
% 0.23/0.57 (step t5 (cl (= (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (exists ((X $$unsorted)) (@ (@ A X) W))) (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (not (forall ((X $$unsorted)) (not (@ (@ A X) W))))))) :rule bind)
% 0.23/0.57 (step t6 (cl (= (= tptp.mexists_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (exists ((X $$unsorted)) (@ (@ A X) W)))) (= tptp.mexists_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (not (forall ((X $$unsorted)) (not (@ (@ A X) W)))))))) :rule cong :premises (t4 t5))
% 0.23/0.57 (step t7 (cl (= tptp.mexists_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (not (forall ((X $$unsorted)) (not (@ (@ A X) W))))))) :rule resolution :premises (t3 t6 a9))
% 0.23/0.57 (step t8 (cl (not (= (= tptp.mdia (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (exists ((V tptp.mworld)) (and (@ (@ tptp.mrel W) V) (@ Phi V))))) (= tptp.mdia (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (not (forall ((V tptp.mworld)) (or (not (@ (@ tptp.mrel W) V)) (not (@ Phi V))))))))) (not (= tptp.mdia (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (exists ((V tptp.mworld)) (and (@ (@ tptp.mrel W) V) (@ Phi V)))))) (= tptp.mdia (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (not (forall ((V tptp.mworld)) (or (not (@ (@ tptp.mrel W) V)) (not (@ Phi V)))))))) :rule equiv_pos2)
% 0.23/0.57 (step t9 (cl (= tptp.mdia tptp.mdia)) :rule refl)
% 0.23/0.57 (anchor :step t10 :args ((Phi (-> tptp.mworld Bool)) (:= Phi Phi) (W tptp.mworld) (:= W W)))
% 0.23/0.57 (step t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.23/0.57 (step t10.t2 (cl (= W W)) :rule refl)
% 0.23/0.57 (step t10.t3 (cl (= (exists ((V tptp.mworld)) (and (@ (@ tptp.mrel W) V) (@ Phi V))) (not (forall ((V tptp.mworld)) (not (and (@ (@ tptp.mrel W) V) (@ Phi V))))))) :rule all_simplify)
% 0.23/0.57 (step t10.t4 (cl (= (forall ((V tptp.mworld)) (not (and (@ (@ tptp.mrel W) V) (@ Phi V)))) (forall ((V tptp.mworld)) (or (not (@ (@ tptp.mrel W) V)) (not (@ Phi V)))))) :rule all_simplify)
% 0.23/0.57 (step t10.t5 (cl (= (not (forall ((V tptp.mworld)) (not (and (@ (@ tptp.mrel W) V) (@ Phi V))))) (not (forall ((V tptp.mworld)) (or (not (@ (@ tptp.mrel W) V)) (not (@ Phi V))))))) :rule cong :premises (t10.t4))
% 0.23/0.57 (step t10.t6 (cl (= (exists ((V tptp.mworld)) (and (@ (@ tptp.mrel W) V) (@ Phi V))) (not (forall ((V tptp.mworld)) (or (not (@ (@ tptp.mrel W) V)) (not (@ Phi V))))))) :rule trans :premises (t10.t3 t10.t5))
% 0.23/0.57 (step t10 (cl (= (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (exists ((V tptp.mworld)) (and (@ (@ tptp.mrel W) V) (@ Phi V)))) (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (not (forall ((V tptp.mworld)) (or (not (@ (@ tptp.mrel W) V)) (not (@ Phi V)))))))) :rule bind)
% 0.23/0.57 (step t11 (cl (= (= tptp.mdia (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (exists ((V tptp.mworld)) (and (@ (@ tptp.mrel W) V) (@ Phi V))))) (= tptp.mdia (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (not (forall ((V tptp.mworld)) (or (not (@ (@ tptp.mrel W) V)) (not (@ Phi V))))))))) :rule cong :premises (t9 t10))
% 0.23/0.57 (step t12 (cl (= tptp.mdia (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (not (forall ((V tptp.mworld)) (or (not (@ (@ tptp.mrel W) V)) (not (@ Phi V)))))))) :rule resolution :premises (t8 t11 a7))
% 0.23/0.57 (step t13 (cl (not (= (= tptp.mbox (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (=> (@ (@ tptp.mrel W) V) (@ Phi V))))) (= tptp.mbox (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (or (not (@ (@ tptp.mrel W) V)) (@ Phi V))))))) (not (= tptp.mbox (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (=> (@ (@ tptp.mrel W) V) (@ Phi V)))))) (= tptp.mbox (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (or (not (@ (@ tptp.mrel W) V)) (@ Phi V)))))) :rule equiv_pos2)
% 0.23/0.57 (step t14 (cl (= tptp.mbox tptp.mbox)) :rule refl)
% 0.23/0.57 (anchor :step t15 :args ((Phi (-> tptp.mworld Bool)) (:= Phi Phi) (W tptp.mworld) (:= W W)))
% 0.23/0.57 (step t15.t1 (cl (= Phi Phi)) :rule refl)
% 0.23/0.57 (step t15.t2 (cl (= W W)) :rule refl)
% 0.23/0.57 (step t15.t3 (cl (= (forall ((V tptp.mworld)) (=> (@ (@ tptp.mrel W) V) (@ Phi V))) (forall ((V tptp.mworld)) (or (not (@ (@ tptp.mrel W) V)) (@ Phi V))))) :rule all_simplify)
% 0.23/0.57 (step t15 (cl (= (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (=> (@ (@ tptp.mrel W) V) (@ Phi V)))) (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (or (not (@ (@ tptp.mrel W) V)) (@ Phi V)))))) :rule bind)
% 0.23/0.57 (step t16 (cl (= (= tptp.mbox (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (=> (@ (@ tptp.mrel W) V) (@ Phi V))))) (= tptp.mbox (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (or (not (@ (@ tptp.mrel W) V)) (@ Phi V))))))) :rule cong :premises (t14 t15))
% 0.23/0.57 (step t17 (cl (= tptp.mbox (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (or (not (@ (@ tptp.mrel W) V)) (@ Phi V)))))) :rule resolution :premises (t13 t16 a6))
% 0.23/0.57 (step t18 (cl (and (= tptp.mexists_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (not (forall ((X $$unsorted)) (not (@ (@ A X) W)))))) (= tptp.mforall_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W)))) (= tptp.mdia (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (not (forall ((V tptp.mworld)) (or (not (@ (@ tptp.mrel W) V)) (not (@ Phi V))))))) (= tptp.mbox (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (or (not (@ (@ tptp.mrel W) V)) (@ Phi V))))) (= tptp.mequiv (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W)))) (= tptp.mimplies (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (=> (@ A W) (@ B W)))) (= tptp.mor (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (or (@ A W) (@ B W)))) (= tptp.mand (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (and (@ A W) (@ B W)))) (= tptp.mnot (lambda ((A (-> tptp.mworld Bool)) (W tptp.mworld)) (not (@ A W)))) (= tptp.mlocal (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual))))) :rule resolution :premises (t2 t7 a8 t12 t17 a5 a4 a3 a2 a1 a0))
% 0.23/0.57 (step t19 (cl (= tptp.mlocal (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual)))) :rule and :premises (t18))
% 0.23/0.57 (step t20 (cl (= tptp.mforall_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))))) :rule and :premises (t18))
% 0.23/0.57 (anchor :step t21 :args ((X $$unsorted) (:= X X) (__flatten_var_0 tptp.mworld) (:= __flatten_var_0 __flatten_var_0)))
% 0.23/0.57 (step t21.t1 (cl (= X X)) :rule refl)
% 0.23/0.57 (step t21.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.23/0.57 (anchor :step t21.t3 :args ((Y $$unsorted) (:= Y Y) (__flatten_var_0 tptp.mworld) (:= __flatten_var_0 __flatten_var_0)))
% 0.23/0.57 (step t21.t3.t1 (cl (= Y Y)) :rule refl)
% 0.23/0.57 (step t21.t3.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.23/0.57 (step t21.t3.t3 (cl (= tptp.mequiv (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))))) :rule and :premises (t18))
% 0.23/0.57 (step t21.t3.t4 (cl (= (@ (@ tptp.set_equal X) Y) (@ (@ tptp.set_equal X) Y))) :rule refl)
% 0.23/0.57 (step t21.t3.t5 (cl (= (@ tptp.mequiv (@ (@ tptp.set_equal X) Y)) (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)))) :rule cong :premises (t21.t3.t3 t21.t3.t4))
% 0.23/0.57 (step t21.t3.t6 (cl (= (@ (@ tptp.set_equal Y) X) (@ (@ tptp.set_equal Y) X))) :rule refl)
% 0.23/0.57 (step t21.t3.t7 (cl (= (@ (@ tptp.mequiv (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)))) :rule cong :premises (t21.t3.t5 t21.t3.t6))
% 0.23/0.57 (step t21.t3.t8 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.23/0.57 (step t21.t3.t9 (cl (= (@ (@ (@ tptp.mequiv (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0) (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) :rule cong :premises (t21.t3.t7 t21.t3.t8))
% 0.23/0.57 (step t21.t3 (cl (= (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0)) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0)))) :rule bind)
% 0.23/0.57 (step t21.t4 (cl (= (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))))) :rule cong :premises (t20 t21.t3))
% 0.23/0.57 (step t21.t5 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.23/0.57 (step t21.t6 (cl (= (@ (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0) (@ (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0))) :rule cong :premises (t21.t4 t21.t5))
% 0.23/0.57 (step t21 (cl (= (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0)) (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0)))) :rule bind)
% 0.23/0.57 (step t22 (cl (= (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0))) (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0))))) :rule cong :premises (t20 t21))
% 0.23/0.57 (step t23 (cl (= (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0)))) (@ (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual)) (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0)))))) :rule cong :premises (t19 t22))
% 0.23/0.57 (step t24 (cl (= (not (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0))))) (not (@ (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual)) (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0))))))) :rule cong :premises (t23))
% 0.23/0.57 (step t25 (cl (= (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual)) (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual)))) :rule refl)
% 0.23/0.57 (step t26 (cl (= (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))))) :rule refl)
% 0.23/0.57 (anchor :step t27 :args ((X $$unsorted) (:= X X) (__flatten_var_0 tptp.mworld) (:= __flatten_var_0 __flatten_var_0)))
% 0.23/0.57 (step t27.t1 (cl (= X X)) :rule refl)
% 0.23/0.57 (step t27.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.23/0.57 (anchor :step t27.t3 :args ((Y $$unsorted) (:= Y Y) (__flatten_var_0 tptp.mworld) (:= __flatten_var_0 __flatten_var_0)))
% 0.23/0.57 (step t27.t3.t1 (cl (= Y Y)) :rule refl)
% 0.23/0.57 (step t27.t3.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.23/0.57 (step t27.t3.t3 (cl (= (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (lambda ((B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ (@ (@ tptp.set_equal X) Y) W) (@ B W))))) :rule all_simplify)
% 0.23/0.57 (anchor :step t27.t3.t4 :args ((B (-> tptp.mworld Bool)) (:= B B) (W tptp.mworld) (:= W W)))
% 0.23/0.57 (step t27.t3.t4.t1 (cl (= B B)) :rule refl)
% 0.23/0.57 (step t27.t3.t4.t2 (cl (= W W)) :rule refl)
% 0.23/0.57 (step t27.t3.t4.t3 (cl (= (= (@ (@ (@ tptp.set_equal X) Y) W) (@ B W)) (= (@ B W) (@ (@ (@ tptp.set_equal X) Y) W)))) :rule all_simplify)
% 0.23/0.57 (step t27.t3.t4 (cl (= (lambda ((B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ (@ (@ tptp.set_equal X) Y) W) (@ B W))) (lambda ((B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ B W) (@ (@ (@ tptp.set_equal X) Y) W))))) :rule bind)
% 0.23/0.57 (step t27.t3.t5 (cl (= (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (lambda ((B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ B W) (@ (@ (@ tptp.set_equal X) Y) W))))) :rule trans :premises (t27.t3.t3 t27.t3.t4))
% 0.23/0.57 (step t27.t3.t6 (cl (= (@ (@ tptp.set_equal Y) X) (@ (@ tptp.set_equal Y) X))) :rule refl)
% 0.23/0.57 (step t27.t3.t7 (cl (= (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) (@ (lambda ((B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ B W) (@ (@ (@ tptp.set_equal X) Y) W))) (@ (@ tptp.set_equal Y) X)))) :rule cong :premises (t27.t3.t5 t27.t3.t6))
% 0.23/0.57 (step t27.t3.t8 (cl (= (@ (lambda ((B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ B W) (@ (@ (@ tptp.set_equal X) Y) W))) (@ (@ tptp.set_equal Y) X)) (lambda ((W tptp.mworld)) (= (@ (@ (@ tptp.set_equal Y) X) W) (@ (@ (@ tptp.set_equal X) Y) W))))) :rule all_simplify)
% 0.23/0.57 (anchor :step t27.t3.t9 :args ((W tptp.mworld) (:= W W)))
% 0.23/0.57 (step t27.t3.t9.t1 (cl (= W W)) :rule refl)
% 0.23/0.57 (step t27.t3.t9.t2 (cl (= (= (@ (@ (@ tptp.set_equal Y) X) W) (@ (@ (@ tptp.set_equal X) Y) W)) (= (@ (@ (@ tptp.set_equal X) Y) W) (@ (@ (@ tptp.set_equal Y) X) W)))) :rule all_simplify)
% 0.23/0.57 (step t27.t3.t9 (cl (= (lambda ((W tptp.mworld)) (= (@ (@ (@ tptp.set_equal Y) X) W) (@ (@ (@ tptp.set_equal X) Y) W))) (lambda ((W tptp.mworld)) (= (@ (@ (@ tptp.set_equal X) Y) W) (@ (@ (@ tptp.set_equal Y) X) W))))) :rule bind)
% 0.23/0.57 (step t27.t3.t10 (cl (= (@ (lambda ((B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ B W) (@ (@ (@ tptp.set_equal X) Y) W))) (@ (@ tptp.set_equal Y) X)) (lambda ((W tptp.mworld)) (= (@ (@ (@ tptp.set_equal X) Y) W) (@ (@ (@ tptp.set_equal Y) X) W))))) :rule trans :premises (t27.t3.t8 t27.t3.t9))
% 0.23/0.57 (step t27.t3.t11 (cl (= (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) (lambda ((W tptp.mworld)) (= (@ (@ (@ tptp.set_equal X) Y) W) (@ (@ (@ tptp.set_equal Y) X) W))))) :rule trans :premises (t27.t3.t7 t27.t3.t10))
% 0.23/0.57 (step t27.t3.t12 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.23/0.57 (step t27.t3.t13 (cl (= (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0) (@ (lambda ((W tptp.mworld)) (= (@ (@ (@ tptp.set_equal X) Y) W) (@ (@ (@ tptp.set_equal Y) X) W))) __flatten_var_0))) :rule cong :premises (t27.t3.t11 t27.t3.t12))
% 0.23/0.57 (step t27.t3.t14 (cl (= (@ (lambda ((W tptp.mworld)) (= (@ (@ (@ tptp.set_equal X) Y) W) (@ (@ (@ tptp.set_equal Y) X) W))) __flatten_var_0) (= (@ (@ (@ tptp.set_equal X) Y) __flatten_var_0) (@ (@ (@ tptp.set_equal Y) X) __flatten_var_0)))) :rule all_simplify)
% 0.23/0.57 (step t27.t3.t15 (cl (= (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0) (= (@ (@ (@ tptp.set_equal X) Y) __flatten_var_0) (@ (@ (@ tptp.set_equal Y) X) __flatten_var_0)))) :rule trans :premises (t27.t3.t13 t27.t3.t14))
% 0.23/0.57 (step t27.t3 (cl (= (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0)) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (= (@ (@ (@ tptp.set_equal X) Y) __flatten_var_0) (@ (@ (@ tptp.set_equal Y) X) __flatten_var_0))))) :rule bind)
% 0.23/0.57 (step t27.t4 (cl (= (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (= (@ (@ (@ tptp.set_equal X) Y) __flatten_var_0) (@ (@ (@ tptp.set_equal Y) X) __flatten_var_0)))))) :rule cong :premises (t26 t27.t3))
% 0.23/0.57 (step t27.t5 (cl (= (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (= (@ (@ (@ tptp.set_equal X) Y) __flatten_var_0) (@ (@ (@ tptp.set_equal Y) X) __flatten_var_0)))) (lambda ((W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (= (@ (@ (@ tptp.set_equal X) Y) __flatten_var_0) (@ (@ (@ tptp.set_equal Y) X) __flatten_var_0))) X) W))))) :rule all_simplify)
% 0.23/0.57 (anchor :step t27.t6 :args ((W tptp.mworld) (:= W W)))
% 0.23/0.57 (step t27.t6.t1 (cl (= W W)) :rule refl)
% 0.23/0.57 (anchor :step t27.t6.t2 :args ((X $$unsorted) (:= X X)))
% 0.23/0.57 (step t27.t6.t2.t1 (cl (= X X)) :rule refl)
% 0.23/0.57 (step t27.t6.t2.t2 (cl (= (@ (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (= (@ (@ (@ tptp.set_equal X) Y) __flatten_var_0) (@ (@ (@ tptp.set_equal Y) X) __flatten_var_0))) X) (lambda ((__flatten_var_0 tptp.mworld)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0))))) :rule all_simplify)
% 0.23/0.57 (step t27.t6.t2.t3 (cl (= W W)) :rule refl)
% 0.23/0.57 (step t27.t6.t2.t4 (cl (= (@ (@ (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (= (@ (@ (@ tptp.set_equal X) Y) __flatten_var_0) (@ (@ (@ tptp.set_equal Y) X) __flatten_var_0))) X) W) (@ (lambda ((__flatten_var_0 tptp.mworld)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0))) W))) :rule cong :premises (t27.t6.t2.t2 t27.t6.t2.t3))
% 0.23/0.57 (step t27.t6.t2.t5 (cl (= (@ (lambda ((__flatten_var_0 tptp.mworld)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0))) W) (= (@ (@ (@ tptp.set_equal X) X) W) (@ (@ (@ tptp.set_equal X) X) W)))) :rule all_simplify)
% 0.23/0.57 (step t27.t6.t2.t6 (cl (= (@ (@ (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (= (@ (@ (@ tptp.set_equal X) Y) __flatten_var_0) (@ (@ (@ tptp.set_equal Y) X) __flatten_var_0))) X) W) (= (@ (@ (@ tptp.set_equal X) X) W) (@ (@ (@ tptp.set_equal X) X) W)))) :rule trans :premises (t27.t6.t2.t4 t27.t6.t2.t5))
% 0.23/0.57 (step t27.t6.t2 (cl (= (forall ((X $$unsorted)) (@ (@ (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (= (@ (@ (@ tptp.set_equal X) Y) __flatten_var_0) (@ (@ (@ tptp.set_equal Y) X) __flatten_var_0))) X) W)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) W) (@ (@ (@ tptp.set_equal X) X) W))))) :rule bind)
% 0.23/0.57 (step t27.t6 (cl (= (lambda ((W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (= (@ (@ (@ tptp.set_equal X) Y) __flatten_var_0) (@ (@ (@ tptp.set_equal Y) X) __flatten_var_0))) X) W))) (lambda ((W tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) W) (@ (@ (@ tptp.set_equal X) X) W)))))) :rule bind)
% 0.23/0.57 (step t27.t7 (cl (= (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (= (@ (@ (@ tptp.set_equal X) Y) __flatten_var_0) (@ (@ (@ tptp.set_equal Y) X) __flatten_var_0)))) (lambda ((W tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) W) (@ (@ (@ tptp.set_equal X) X) W)))))) :rule trans :premises (t27.t5 t27.t6))
% 0.23/0.57 (step t27.t8 (cl (= (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) (lambda ((W tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) W) (@ (@ (@ tptp.set_equal X) X) W)))))) :rule trans :premises (t27.t4 t27.t7))
% 0.23/0.57 (step t27.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.23/0.57 (step t27.t10 (cl (= (@ (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0) (@ (lambda ((W tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) W) (@ (@ (@ tptp.set_equal X) X) W)))) __flatten_var_0))) :rule cong :premises (t27.t8 t27.t9))
% 0.23/0.57 (step t27.t11 (cl (= (@ (lambda ((W tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) W) (@ (@ (@ tptp.set_equal X) X) W)))) __flatten_var_0) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0))))) :rule all_simplify)
% 0.23/0.57 (step t27.t12 (cl (= (@ (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0))))) :rule trans :premises (t27.t10 t27.t11))
% 0.23/0.57 (step t27 (cl (= (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0)) (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0)))))) :rule bind)
% 0.23/0.57 (step t28 (cl (= (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0))) (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0))))))) :rule cong :premises (t26 t27))
% 0.23/0.57 (step t29 (cl (= (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0))))) (lambda ((W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0)))) X) W))))) :rule all_simplify)
% 0.23/0.57 (anchor :step t30 :args ((W tptp.mworld) (:= W W)))
% 0.23/0.57 (step t30.t1 (cl (= W W)) :rule refl)
% 0.23/0.57 (anchor :step t30.t2 :args ((X $$unsorted) (:= X X)))
% 0.23/0.57 (step t30.t2.t1 (cl (= X X)) :rule refl)
% 0.23/0.57 (step t30.t2.t2 (cl (= (@ (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0)))) X) (lambda ((__flatten_var_0 tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0)))))) :rule all_simplify)
% 0.23/0.57 (anchor :step t30.t2.t3 :args ((__flatten_var_0 tptp.mworld) (:= __flatten_var_0 __flatten_var_0)))
% 0.23/0.57 (step t30.t2.t3.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.23/0.57 (anchor :step t30.t2.t3.t2 :args ((X $$unsorted) (:= X X)))
% 0.23/0.57 (step t30.t2.t3.t2.t1 (cl (= X X)) :rule refl)
% 0.23/0.57 (step t30.t2.t3.t2.t2 (cl (= (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0)) true)) :rule all_simplify)
% 0.23/0.57 (step t30.t2.t3.t2 (cl (= (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0))) (forall ((X $$unsorted)) true))) :rule bind)
% 0.23/0.57 (step t30.t2.t3.t3 (cl (= (forall ((X $$unsorted)) true) true)) :rule all_simplify)
% 0.23/0.57 (step t30.t2.t3.t4 (cl (= (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0))) true)) :rule trans :premises (t30.t2.t3.t2 t30.t2.t3.t3))
% 0.23/0.57 (step t30.t2.t3 (cl (= (lambda ((__flatten_var_0 tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0)))) (lambda ((__flatten_var_0 tptp.mworld)) true))) :rule bind)
% 0.23/0.57 (step t30.t2.t4 (cl (= (lambda ((__flatten_var_0 tptp.mworld)) true) (lambda ((BOUND_VARIABLE_1011 tptp.mworld)) true))) :rule all_simplify)
% 0.23/0.57 (step t30.t2.t5 (cl (= (lambda ((__flatten_var_0 tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0)))) (lambda ((BOUND_VARIABLE_1011 tptp.mworld)) true))) :rule trans :premises (t30.t2.t3 t30.t2.t4))
% 0.23/0.57 (step t30.t2.t6 (cl (= (@ (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0)))) X) (lambda ((BOUND_VARIABLE_1011 tptp.mworld)) true))) :rule trans :premises (t30.t2.t2 t30.t2.t5))
% 0.23/0.57 (step t30.t2.t7 (cl (= W W)) :rule refl)
% 0.23/0.57 (step t30.t2.t8 (cl (= (@ (@ (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0)))) X) W) (@ (lambda ((BOUND_VARIABLE_1011 tptp.mworld)) true) W))) :rule cong :premises (t30.t2.t6 t30.t2.t7))
% 0.23/0.57 (step t30.t2.t9 (cl (= (@ (lambda ((BOUND_VARIABLE_1011 tptp.mworld)) true) W) true)) :rule all_simplify)
% 0.23/0.57 (step t30.t2.t10 (cl (= (@ (@ (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0)))) X) W) true)) :rule trans :premises (t30.t2.t8 t30.t2.t9))
% 0.23/0.57 (step t30.t2 (cl (= (forall ((X $$unsorted)) (@ (@ (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0)))) X) W)) (forall ((X $$unsorted)) true))) :rule bind)
% 0.23/0.57 (step t30.t3 (cl (= (forall ((X $$unsorted)) true) true)) :rule all_simplify)
% 0.23/0.57 (step t30.t4 (cl (= (forall ((X $$unsorted)) (@ (@ (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0)))) X) W)) true)) :rule trans :premises (t30.t2 t30.t3))
% 0.23/0.57 (step t30 (cl (= (lambda ((W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0)))) X) W))) (lambda ((W tptp.mworld)) true))) :rule bind)
% 0.23/0.57 (step t31 (cl (= (lambda ((W tptp.mworld)) true) (lambda ((BOUND_VARIABLE_1011 tptp.mworld)) true))) :rule all_simplify)
% 0.23/0.57 (step t32 (cl (= (lambda ((W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0)))) X) W))) (lambda ((BOUND_VARIABLE_1011 tptp.mworld)) true))) :rule trans :premises (t30 t31))
% 0.23/0.57 (step t33 (cl (= (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (forall ((X $$unsorted)) (= (@ (@ (@ tptp.set_equal X) X) __flatten_var_0) (@ (@ (@ tptp.set_equal X) X) __flatten_var_0))))) (lambda ((BOUND_VARIABLE_1011 tptp.mworld)) true))) :rule trans :premises (t29 t32))
% 0.23/0.57 (step t34 (cl (= (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0))) (lambda ((BOUND_VARIABLE_1011 tptp.mworld)) true))) :rule trans :premises (t28 t33))
% 0.23/0.57 (step t35 (cl (= (@ (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual)) (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0)))) (@ (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual)) (lambda ((BOUND_VARIABLE_1011 tptp.mworld)) true)))) :rule cong :premises (t25 t34))
% 0.23/0.57 (step t36 (cl (= (@ (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual)) (lambda ((BOUND_VARIABLE_1011 tptp.mworld)) true)) (@ (lambda ((BOUND_VARIABLE_1011 tptp.mworld)) true) tptp.mactual))) :rule all_simplify)
% 0.23/0.57 (step t37 (cl (= (@ (lambda ((BOUND_VARIABLE_1011 tptp.mworld)) true) tptp.mactual) true)) :rule all_simplify)
% 0.23/0.57 (step t38 (cl (= (@ (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual)) (lambda ((BOUND_VARIABLE_1011 tptp.mworld)) true)) true)) :rule trans :premises (t36 t37))
% 0.23/0.57 (step t39 (cl (= (@ (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual)) (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0)))) true)) :rule trans :premises (t35 t38))
% 0.23/0.57 (step t40 (cl (= (not (@ (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual)) (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0))))) (not true))) :rule cong :premises (t39))
% 0.41/0.58 (step t41 (cl (= (not true) false)) :rule all_simplify)
% 0.41/0.58 (step t42 (cl (= (not (@ (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual)) (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W))) (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W))) (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0))))) false)) :rule trans :premises (t40 t41))
% 0.41/0.58 (step t43 (cl (= (not (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0))))) false)) :rule trans :premises (t24 t42))
% 0.41/0.58 (step t44 (cl false) :rule resolution :premises (t1 t43 a11))
% 0.41/0.58 (step t45 (cl (not false)) :rule false)
% 0.41/0.58 (step t46 (cl) :rule resolution :premises (t44 t45))
% 0.41/0.58
% 0.41/0.58 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.3uSzS6FaKb/cvc5---1.0.5_29965.smt2
% 0.41/0.58 % cvc5---1.0.5 exiting
% 0.41/0.58 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------