%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : TOP001-2 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n028.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 18:36:19 EDT 2024

% Result   : Unsatisfiable 0.20s 0.53s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : TOP001-2 : TPTP v8.2.0. Released v1.0.0.
% 0.07/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n028.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Sat May 25 20:28:54 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.50  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.53  % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.6wzLd2vY2p/cvc5---1.0.5_11697.smt2
% 0.20/0.53  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.6wzLd2vY2p/cvc5---1.0.5_11697.smt2
% 0.20/0.54  (assume a0 (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_set U (tptp.f1 Vf U)))))
% 0.20/0.54  (assume a1 (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_collection (tptp.f1 Vf U) Vf))))
% 0.20/0.54  (assume a2 (forall ((U $$unsorted) (Vf $$unsorted) (Uu1 $$unsorted)) (or (tptp.element_of_set U (tptp.union_of_members Vf)) (not (tptp.element_of_set U Uu1)) (not (tptp.element_of_collection Uu1 Vf)))))
% 0.20/0.54  (assume a3 (forall ((X $$unsorted) (Vf $$unsorted)) (or (not (tptp.basis X Vf)) (tptp.equal_sets (tptp.union_of_members Vf) X))))
% 0.20/0.54  (assume a4 (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_set X (tptp.f10 Vf U X)))))
% 0.20/0.54  (assume a5 (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_collection (tptp.f10 Vf U X) Vf))))
% 0.20/0.54  (assume a6 (forall ((X $$unsorted)) (tptp.subset_sets X X)))
% 0.20/0.54  (assume a7 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset_sets X Y)) (not (tptp.element_of_set U X)) (tptp.element_of_set U Y))))
% 0.20/0.54  (assume a8 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.equal_sets X Y)) (tptp.subset_sets X Y))))
% 0.20/0.54  (assume a9 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (tptp.element_of_set (tptp.in_1st_set X Y) X))))
% 0.20/0.54  (assume a10 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (not (tptp.element_of_set (tptp.in_1st_set X Y) Y)))))
% 0.20/0.54  (assume a11 (tptp.basis tptp.cx tptp.f))
% 0.20/0.54  (assume a12 (not (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))
% 0.20/0.54  (step t1 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset_sets X Y)) (not (tptp.element_of_set U X)) (tptp.element_of_set U Y))) (or (not (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset_sets X Y)) (not (tptp.element_of_set U X)) (tptp.element_of_set U Y)))) :rule implies_neg1)
% 0.20/0.54  (anchor :step t2)
% 0.20/0.54  (assume t2.a0 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset_sets X Y)) (not (tptp.element_of_set U X)) (tptp.element_of_set U Y))))
% 0.20/0.54  (step t2.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset_sets X Y)) (not (tptp.element_of_set U X)) (tptp.element_of_set U Y)))) (or (not (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx)))) :rule forall_inst :args ((:= X (tptp.union_of_members tptp.f)) (:= Y tptp.cx) (:= U (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))
% 0.20/0.54  (step t2.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset_sets X Y)) (not (tptp.element_of_set U X)) (tptp.element_of_set U Y)))) (or (not (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx))) :rule or :premises (t2.t1))
% 0.20/0.54  (step t2.t3 (cl (or (not (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx))) :rule resolution :premises (t2.t2 t2.a0))
% 0.20/0.54  (step t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset_sets X Y)) (not (tptp.element_of_set U X)) (tptp.element_of_set U Y)))) (or (not (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx))) :rule subproof :discharge (t2.a0))
% 0.20/0.54  (step t3 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset_sets X Y)) (not (tptp.element_of_set U X)) (tptp.element_of_set U Y))) (or (not (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx))) (or (not (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx))) :rule resolution :premises (t1 t2))
% 0.20/0.54  (step t4 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset_sets X Y)) (not (tptp.element_of_set U X)) (tptp.element_of_set U Y))) (or (not (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx))) (not (or (not (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx)))) :rule implies_neg2)
% 0.20/0.54  (step t5 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset_sets X Y)) (not (tptp.element_of_set U X)) (tptp.element_of_set U Y))) (or (not (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx))) (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset_sets X Y)) (not (tptp.element_of_set U X)) (tptp.element_of_set U Y))) (or (not (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx)))) :rule resolution :premises (t3 t4))
% 0.20/0.54  (step t6 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset_sets X Y)) (not (tptp.element_of_set U X)) (tptp.element_of_set U Y))) (or (not (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx)))) :rule contraction :premises (t5))
% 0.20/0.54  (step t7 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset_sets X Y)) (not (tptp.element_of_set U X)) (tptp.element_of_set U Y)))) (or (not (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx))) :rule implies :premises (t6))
% 0.20/0.54  (step t8 (cl (not (or (not (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx))) (not (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx)) :rule or_pos)
% 0.20/0.54  (step t9 (cl (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx) (not (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f))) (not (or (not (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx)))) :rule reordering :premises (t8))
% 0.20/0.54  (step t10 (cl (not (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx)))) (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx))) :rule or_pos)
% 0.20/0.54  (step t11 (cl (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx)) (not (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx))))) :rule reordering :premises (t10))
% 0.20/0.54  (step t12 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (not (tptp.element_of_set (tptp.in_1st_set X Y) Y)))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (not (tptp.element_of_set (tptp.in_1st_set X Y) Y))))) :rule implies_neg1)
% 0.20/0.54  (anchor :step t13)
% 0.20/0.54  (assume t13.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (not (tptp.element_of_set (tptp.in_1st_set X Y) Y)))))
% 0.20/0.54  (step t13.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (not (tptp.element_of_set (tptp.in_1st_set X Y) Y))))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx))))) :rule forall_inst :args ((:= X (tptp.union_of_members (tptp.top_of_basis tptp.f))) (:= Y tptp.cx)))
% 0.20/0.54  (step t13.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (not (tptp.element_of_set (tptp.in_1st_set X Y) Y))))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx)))) :rule or :premises (t13.t1))
% 0.20/0.54  (step t13.t3 (cl (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx)))) :rule resolution :premises (t13.t2 t13.a0))
% 0.20/0.54  (step t13 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (not (tptp.element_of_set (tptp.in_1st_set X Y) Y))))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx)))) :rule subproof :discharge (t13.a0))
% 0.20/0.54  (step t14 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (not (tptp.element_of_set (tptp.in_1st_set X Y) Y)))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx)))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx)))) :rule resolution :premises (t12 t13))
% 0.20/0.54  (step t15 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (not (tptp.element_of_set (tptp.in_1st_set X Y) Y)))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx)))) (not (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx))))) :rule implies_neg2)
% 0.20/0.54  (step t16 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (not (tptp.element_of_set (tptp.in_1st_set X Y) Y)))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (not (tptp.element_of_set (tptp.in_1st_set X Y) Y)))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx))))) :rule resolution :premises (t14 t15))
% 0.20/0.54  (step t17 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (not (tptp.element_of_set (tptp.in_1st_set X Y) Y)))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx))))) :rule contraction :premises (t16))
% 0.20/0.54  (step t18 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (not (tptp.element_of_set (tptp.in_1st_set X Y) Y))))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx)))) :rule implies :premises (t17))
% 0.20/0.54  (step t19 (cl (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx)))) :rule resolution :premises (t18 a10))
% 0.20/0.54  (step t20 (cl (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx))) :rule resolution :premises (t11 a12 t19))
% 0.20/0.54  (step t21 (cl (not (or (not (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)) (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx))) (not (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)) (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)) :rule or_pos)
% 0.20/0.54  (step t22 (cl (not (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)) (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx) (not (or (not (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)) (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)))) :rule reordering :premises (t21))
% 0.20/0.54  (step t23 (cl (not (or (not (tptp.basis tptp.cx tptp.f)) (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx))) (not (tptp.basis tptp.cx tptp.f)) (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)) :rule or_pos)
% 0.20/0.54  (step t24 (cl (not (tptp.basis tptp.cx tptp.f)) (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx) (not (or (not (tptp.basis tptp.cx tptp.f)) (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)))) :rule reordering :premises (t23))
% 0.20/0.54  (step t25 (cl (=> (forall ((X $$unsorted) (Vf $$unsorted)) (or (not (tptp.basis X Vf)) (tptp.equal_sets (tptp.union_of_members Vf) X))) (or (not (tptp.basis tptp.cx tptp.f)) (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx))) (forall ((X $$unsorted) (Vf $$unsorted)) (or (not (tptp.basis X Vf)) (tptp.equal_sets (tptp.union_of_members Vf) X)))) :rule implies_neg1)
% 0.20/0.54  (anchor :step t26)
% 0.20/0.54  (assume t26.a0 (forall ((X $$unsorted) (Vf $$unsorted)) (or (not (tptp.basis X Vf)) (tptp.equal_sets (tptp.union_of_members Vf) X))))
% 0.20/0.54  (step t26.t1 (cl (or (not (forall ((X $$unsorted) (Vf $$unsorted)) (or (not (tptp.basis X Vf)) (tptp.equal_sets (tptp.union_of_members Vf) X)))) (or (not (tptp.basis tptp.cx tptp.f)) (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)))) :rule forall_inst :args ((:= X tptp.cx) (:= Vf tptp.f)))
% 0.20/0.54  (step t26.t2 (cl (not (forall ((X $$unsorted) (Vf $$unsorted)) (or (not (tptp.basis X Vf)) (tptp.equal_sets (tptp.union_of_members Vf) X)))) (or (not (tptp.basis tptp.cx tptp.f)) (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx))) :rule or :premises (t26.t1))
% 0.20/0.54  (step t26.t3 (cl (or (not (tptp.basis tptp.cx tptp.f)) (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx))) :rule resolution :premises (t26.t2 t26.a0))
% 0.20/0.54  (step t26 (cl (not (forall ((X $$unsorted) (Vf $$unsorted)) (or (not (tptp.basis X Vf)) (tptp.equal_sets (tptp.union_of_members Vf) X)))) (or (not (tptp.basis tptp.cx tptp.f)) (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx))) :rule subproof :discharge (t26.a0))
% 0.20/0.54  (step t27 (cl (=> (forall ((X $$unsorted) (Vf $$unsorted)) (or (not (tptp.basis X Vf)) (tptp.equal_sets (tptp.union_of_members Vf) X))) (or (not (tptp.basis tptp.cx tptp.f)) (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx))) (or (not (tptp.basis tptp.cx tptp.f)) (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx))) :rule resolution :premises (t25 t26))
% 0.20/0.54  (step t28 (cl (=> (forall ((X $$unsorted) (Vf $$unsorted)) (or (not (tptp.basis X Vf)) (tptp.equal_sets (tptp.union_of_members Vf) X))) (or (not (tptp.basis tptp.cx tptp.f)) (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx))) (not (or (not (tptp.basis tptp.cx tptp.f)) (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)))) :rule implies_neg2)
% 0.20/0.54  (step t29 (cl (=> (forall ((X $$unsorted) (Vf $$unsorted)) (or (not (tptp.basis X Vf)) (tptp.equal_sets (tptp.union_of_members Vf) X))) (or (not (tptp.basis tptp.cx tptp.f)) (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx))) (=> (forall ((X $$unsorted) (Vf $$unsorted)) (or (not (tptp.basis X Vf)) (tptp.equal_sets (tptp.union_of_members Vf) X))) (or (not (tptp.basis tptp.cx tptp.f)) (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)))) :rule resolution :premises (t27 t28))
% 0.20/0.54  (step t30 (cl (=> (forall ((X $$unsorted) (Vf $$unsorted)) (or (not (tptp.basis X Vf)) (tptp.equal_sets (tptp.union_of_members Vf) X))) (or (not (tptp.basis tptp.cx tptp.f)) (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)))) :rule contraction :premises (t29))
% 0.20/0.54  (step t31 (cl (not (forall ((X $$unsorted) (Vf $$unsorted)) (or (not (tptp.basis X Vf)) (tptp.equal_sets (tptp.union_of_members Vf) X)))) (or (not (tptp.basis tptp.cx tptp.f)) (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx))) :rule implies :premises (t30))
% 0.20/0.54  (step t32 (cl (or (not (tptp.basis tptp.cx tptp.f)) (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx))) :rule resolution :premises (t31 a3))
% 0.20/0.54  (step t33 (cl (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)) :rule resolution :premises (t24 a11 t32))
% 0.20/0.54  (step t34 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.equal_sets X Y)) (tptp.subset_sets X Y))) (or (not (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)) (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.equal_sets X Y)) (tptp.subset_sets X Y)))) :rule implies_neg1)
% 0.20/0.54  (anchor :step t35)
% 0.20/0.54  (assume t35.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.equal_sets X Y)) (tptp.subset_sets X Y))))
% 0.20/0.54  (step t35.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.equal_sets X Y)) (tptp.subset_sets X Y)))) (or (not (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)) (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)))) :rule forall_inst :args ((:= X (tptp.union_of_members tptp.f)) (:= Y tptp.cx)))
% 0.20/0.54  (step t35.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.equal_sets X Y)) (tptp.subset_sets X Y)))) (or (not (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)) (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx))) :rule or :premises (t35.t1))
% 0.20/0.54  (step t35.t3 (cl (or (not (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)) (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx))) :rule resolution :premises (t35.t2 t35.a0))
% 0.20/0.54  (step t35 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.equal_sets X Y)) (tptp.subset_sets X Y)))) (or (not (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)) (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx))) :rule subproof :discharge (t35.a0))
% 0.20/0.54  (step t36 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.equal_sets X Y)) (tptp.subset_sets X Y))) (or (not (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)) (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx))) (or (not (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)) (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx))) :rule resolution :premises (t34 t35))
% 0.20/0.54  (step t37 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.equal_sets X Y)) (tptp.subset_sets X Y))) (or (not (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)) (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx))) (not (or (not (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)) (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)))) :rule implies_neg2)
% 0.20/0.54  (step t38 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.equal_sets X Y)) (tptp.subset_sets X Y))) (or (not (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)) (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.equal_sets X Y)) (tptp.subset_sets X Y))) (or (not (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)) (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)))) :rule resolution :premises (t36 t37))
% 0.20/0.54  (step t39 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.equal_sets X Y)) (tptp.subset_sets X Y))) (or (not (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)) (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)))) :rule contraction :premises (t38))
% 0.20/0.54  (step t40 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.equal_sets X Y)) (tptp.subset_sets X Y)))) (or (not (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)) (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx))) :rule implies :premises (t39))
% 0.20/0.54  (step t41 (cl (or (not (tptp.equal_sets (tptp.union_of_members tptp.f) tptp.cx)) (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx))) :rule resolution :premises (t40 a8))
% 0.20/0.54  (step t42 (cl (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)) :rule resolution :premises (t22 t33 t41))
% 0.20/0.54  (step t43 (cl (not (or (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (not (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (not (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f))) :rule or_pos)
% 0.20/0.54  (step t44 (cl (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f)) (not (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (not (or (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (not (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f))))) :rule reordering :premises (t43))
% 0.20/0.54  (step t45 (cl (not (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f))) (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f)) :rule or_pos)
% 0.20/0.54  (step t46 (cl (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f) (not (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f)))) :rule reordering :premises (t45))
% 0.20/0.54  (step t47 (cl (not (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) :rule or_pos)
% 0.20/0.54  (step t48 (cl (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))) (not (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))))) :rule reordering :premises (t47))
% 0.20/0.54  (step t49 (cl (not (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f))))) (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) :rule or_pos)
% 0.20/0.54  (step t50 (cl (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f))) (not (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))))) :rule reordering :premises (t49))
% 0.20/0.54  (step t51 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (tptp.element_of_set (tptp.in_1st_set X Y) X))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (tptp.element_of_set (tptp.in_1st_set X Y) X)))) :rule implies_neg1)
% 0.20/0.54  (anchor :step t52)
% 0.20/0.54  (assume t52.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (tptp.element_of_set (tptp.in_1st_set X Y) X))))
% 0.20/0.54  (step t52.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (tptp.element_of_set (tptp.in_1st_set X Y) X)))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))))) :rule forall_inst :args ((:= X (tptp.union_of_members (tptp.top_of_basis tptp.f))) (:= Y tptp.cx)))
% 0.20/0.54  (step t52.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (tptp.element_of_set (tptp.in_1st_set X Y) X)))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f))))) :rule or :premises (t52.t1))
% 0.20/0.54  (step t52.t3 (cl (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f))))) :rule resolution :premises (t52.t2 t52.a0))
% 0.20/0.54  (step t52 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (tptp.element_of_set (tptp.in_1st_set X Y) X)))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f))))) :rule subproof :discharge (t52.a0))
% 0.20/0.54  (step t53 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (tptp.element_of_set (tptp.in_1st_set X Y) X))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f))))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f))))) :rule resolution :premises (t51 t52))
% 0.20/0.54  (step t54 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (tptp.element_of_set (tptp.in_1st_set X Y) X))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f))))) (not (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))))) :rule implies_neg2)
% 0.20/0.54  (step t55 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (tptp.element_of_set (tptp.in_1st_set X Y) X))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (tptp.element_of_set (tptp.in_1st_set X Y) X))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))))) :rule resolution :premises (t53 t54))
% 0.20/0.54  (step t56 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (tptp.element_of_set (tptp.in_1st_set X Y) X))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))))) :rule contraction :premises (t55))
% 0.20/0.54  (step t57 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset_sets X Y) (tptp.element_of_set (tptp.in_1st_set X Y) X)))) (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f))))) :rule implies :premises (t56))
% 0.20/0.54  (step t58 (cl (or (tptp.subset_sets (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f))))) :rule resolution :premises (t57 a9))
% 0.20/0.54  (step t59 (cl (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) :rule resolution :premises (t50 a12 t58))
% 0.20/0.54  (step t60 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_set U (tptp.f1 Vf U)))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_set U (tptp.f1 Vf U))))) :rule implies_neg1)
% 0.20/0.55  (anchor :step t61)
% 0.20/0.55  (assume t61.a0 (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_set U (tptp.f1 Vf U)))))
% 0.20/0.55  (step t61.t1 (cl (or (not (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_set U (tptp.f1 Vf U))))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))))) :rule forall_inst :args ((:= U (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (:= Vf (tptp.top_of_basis tptp.f))))
% 0.20/0.55  (step t61.t2 (cl (not (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_set U (tptp.f1 Vf U))))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) :rule or :premises (t61.t1))
% 0.20/0.55  (step t61.t3 (cl (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) :rule resolution :premises (t61.t2 t61.a0))
% 0.20/0.55  (step t61 (cl (not (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_set U (tptp.f1 Vf U))))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) :rule subproof :discharge (t61.a0))
% 0.20/0.55  (step t62 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_set U (tptp.f1 Vf U)))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) :rule resolution :premises (t60 t61))
% 0.20/0.55  (step t63 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_set U (tptp.f1 Vf U)))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) (not (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))))) :rule implies_neg2)
% 0.20/0.55  (step t64 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_set U (tptp.f1 Vf U)))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) (=> (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_set U (tptp.f1 Vf U)))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))))) :rule resolution :premises (t62 t63))
% 0.20/0.55  (step t65 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_set U (tptp.f1 Vf U)))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))))) :rule contraction :premises (t64))
% 0.20/0.55  (step t66 (cl (not (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_set U (tptp.f1 Vf U))))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) :rule implies :premises (t65))
% 0.20/0.55  (step t67 (cl (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) :rule resolution :premises (t66 a0))
% 0.20/0.55  (step t68 (cl (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) :rule resolution :premises (t48 t59 t67))
% 0.20/0.55  (step t69 (cl (not (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f)))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) :rule or_pos)
% 0.20/0.55  (step t70 (cl (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f)) (not (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))))) :rule reordering :premises (t69))
% 0.20/0.55  (step t71 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_collection (tptp.f1 Vf U) Vf))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f)))) (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_collection (tptp.f1 Vf U) Vf)))) :rule implies_neg1)
% 0.20/0.55  (anchor :step t72)
% 0.20/0.55  (assume t72.a0 (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_collection (tptp.f1 Vf U) Vf))))
% 0.20/0.55  (step t72.t1 (cl (or (not (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_collection (tptp.f1 Vf U) Vf)))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))))) :rule forall_inst :args ((:= U (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (:= Vf (tptp.top_of_basis tptp.f))))
% 0.20/0.55  (step t72.t2 (cl (not (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_collection (tptp.f1 Vf U) Vf)))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f)))) :rule or :premises (t72.t1))
% 0.20/0.55  (step t72.t3 (cl (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f)))) :rule resolution :premises (t72.t2 t72.a0))
% 0.20/0.55  (step t72 (cl (not (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_collection (tptp.f1 Vf U) Vf)))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f)))) :rule subproof :discharge (t72.a0))
% 0.20/0.55  (step t73 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_collection (tptp.f1 Vf U) Vf))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f)))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f)))) :rule resolution :premises (t71 t72))
% 0.20/0.55  (step t74 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_collection (tptp.f1 Vf U) Vf))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f)))) (not (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))))) :rule implies_neg2)
% 0.20/0.55  (step t75 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_collection (tptp.f1 Vf U) Vf))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f)))) (=> (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_collection (tptp.f1 Vf U) Vf))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))))) :rule resolution :premises (t73 t74))
% 0.20/0.55  (step t76 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_collection (tptp.f1 Vf U) Vf))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))))) :rule contraction :premises (t75))
% 0.20/0.55  (step t77 (cl (not (forall ((U $$unsorted) (Vf $$unsorted)) (or (not (tptp.element_of_set U (tptp.union_of_members Vf))) (tptp.element_of_collection (tptp.f1 Vf U) Vf)))) (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f)))) :rule implies :premises (t76))
% 0.20/0.55  (step t78 (cl (or (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members (tptp.top_of_basis tptp.f)))) (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f)))) :rule resolution :premises (t77 a1))
% 0.20/0.55  (step t79 (cl (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) :rule resolution :premises (t70 t59 t78))
% 0.20/0.55  (step t80 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_collection (tptp.f10 Vf U X) Vf))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f))) (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_collection (tptp.f10 Vf U X) Vf)))) :rule implies_neg1)
% 0.20/0.55  (anchor :step t81)
% 0.20/0.55  (assume t81.a0 (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_collection (tptp.f10 Vf U X) Vf))))
% 0.20/0.55  (step t81.t1 (cl (or (not (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_collection (tptp.f10 Vf U X) Vf)))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f)))) :rule forall_inst :args ((:= U (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))) (:= Vf tptp.f) (:= X (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))
% 0.20/0.55  (step t81.t2 (cl (not (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_collection (tptp.f10 Vf U X) Vf)))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f))) :rule or :premises (t81.t1))
% 0.20/0.55  (step t81.t3 (cl (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f))) :rule resolution :premises (t81.t2 t81.a0))
% 0.20/0.55  (step t81 (cl (not (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_collection (tptp.f10 Vf U X) Vf)))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f))) :rule subproof :discharge (t81.a0))
% 0.20/0.55  (step t82 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_collection (tptp.f10 Vf U X) Vf))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f))) :rule resolution :premises (t80 t81))
% 0.20/0.55  (step t83 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_collection (tptp.f10 Vf U X) Vf))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f))) (not (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f)))) :rule implies_neg2)
% 0.20/0.55  (step t84 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_collection (tptp.f10 Vf U X) Vf))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f))) (=> (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_collection (tptp.f10 Vf U X) Vf))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f)))) :rule resolution :premises (t82 t83))
% 0.20/0.55  (step t85 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_collection (tptp.f10 Vf U X) Vf))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f)))) :rule contraction :premises (t84))
% 0.20/0.55  (step t86 (cl (not (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_collection (tptp.f10 Vf U X) Vf)))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f))) :rule implies :premises (t85))
% 0.20/0.55  (step t87 (cl (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f))) :rule resolution :premises (t86 a5))
% 0.20/0.55  (step t88 (cl (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f)) :rule resolution :premises (t46 t68 t79 t87))
% 0.20/0.55  (step t89 (cl (not (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) :rule or_pos)
% 0.20/0.55  (step t90 (cl (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))) (not (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))))) :rule reordering :premises (t89))
% 0.20/0.55  (step t91 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_set X (tptp.f10 Vf U X)))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_set X (tptp.f10 Vf U X))))) :rule implies_neg1)
% 0.20/0.55  (anchor :step t92)
% 0.20/0.55  (assume t92.a0 (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_set X (tptp.f10 Vf U X)))))
% 0.20/0.55  (step t92.t1 (cl (or (not (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_set X (tptp.f10 Vf U X))))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))))) :rule forall_inst :args ((:= U (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))) (:= Vf tptp.f) (:= X (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))
% 0.20/0.55  (step t92.t2 (cl (not (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_set X (tptp.f10 Vf U X))))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) :rule or :premises (t92.t1))
% 0.20/0.55  (step t92.t3 (cl (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) :rule resolution :premises (t92.t2 t92.a0))
% 0.20/0.55  (step t92 (cl (not (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_set X (tptp.f10 Vf U X))))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) :rule subproof :discharge (t92.a0))
% 0.20/0.55  (step t93 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_set X (tptp.f10 Vf U X)))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) :rule resolution :premises (t91 t92))
% 0.20/0.55  (step t94 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_set X (tptp.f10 Vf U X)))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) (not (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))))) :rule implies_neg2)
% 0.20/0.55  (step t95 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_set X (tptp.f10 Vf U X)))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) (=> (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_set X (tptp.f10 Vf U X)))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))))) :rule resolution :premises (t93 t94))
% 0.20/0.55  (step t96 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_set X (tptp.f10 Vf U X)))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))))) :rule contraction :premises (t95))
% 0.20/0.55  (step t97 (cl (not (forall ((U $$unsorted) (Vf $$unsorted) (X $$unsorted)) (or (not (tptp.element_of_collection U (tptp.top_of_basis Vf))) (not (tptp.element_of_set X U)) (tptp.element_of_set X (tptp.f10 Vf U X))))) (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) :rule implies :premises (t96))
% 0.20/0.55  (step t98 (cl (or (not (tptp.element_of_collection (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.top_of_basis tptp.f))) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx))))) :rule resolution :premises (t97 a4))
% 0.20/0.55  (step t99 (cl (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) :rule resolution :premises (t90 t68 t79 t98))
% 0.20/0.55  (step t100 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted) (Uu1 $$unsorted)) (or (tptp.element_of_set U (tptp.union_of_members Vf)) (not (tptp.element_of_set U Uu1)) (not (tptp.element_of_collection Uu1 Vf)))) (or (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (not (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f)))) (forall ((U $$unsorted) (Vf $$unsorted) (Uu1 $$unsorted)) (or (tptp.element_of_set U (tptp.union_of_members Vf)) (not (tptp.element_of_set U Uu1)) (not (tptp.element_of_collection Uu1 Vf))))) :rule implies_neg1)
% 0.20/0.55  (anchor :step t101)
% 0.20/0.55  (assume t101.a0 (forall ((U $$unsorted) (Vf $$unsorted) (Uu1 $$unsorted)) (or (tptp.element_of_set U (tptp.union_of_members Vf)) (not (tptp.element_of_set U Uu1)) (not (tptp.element_of_collection Uu1 Vf)))))
% 0.20/0.55  (step t101.t1 (cl (or (not (forall ((U $$unsorted) (Vf $$unsorted) (Uu1 $$unsorted)) (or (tptp.element_of_set U (tptp.union_of_members Vf)) (not (tptp.element_of_set U Uu1)) (not (tptp.element_of_collection Uu1 Vf))))) (or (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (not (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f))))) :rule forall_inst :args ((:= U (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (:= Vf tptp.f) (:= Uu1 (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))))
% 0.20/0.55  (step t101.t2 (cl (not (forall ((U $$unsorted) (Vf $$unsorted) (Uu1 $$unsorted)) (or (tptp.element_of_set U (tptp.union_of_members Vf)) (not (tptp.element_of_set U Uu1)) (not (tptp.element_of_collection Uu1 Vf))))) (or (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (not (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f)))) :rule or :premises (t101.t1))
% 0.20/0.55  (step t101.t3 (cl (or (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (not (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f)))) :rule resolution :premises (t101.t2 t101.a0))
% 0.20/0.55  (step t101 (cl (not (forall ((U $$unsorted) (Vf $$unsorted) (Uu1 $$unsorted)) (or (tptp.element_of_set U (tptp.union_of_members Vf)) (not (tptp.element_of_set U Uu1)) (not (tptp.element_of_collection Uu1 Vf))))) (or (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (not (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f)))) :rule subproof :discharge (t101.a0))
% 0.20/0.55  (step t102 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted) (Uu1 $$unsorted)) (or (tptp.element_of_set U (tptp.union_of_members Vf)) (not (tptp.element_of_set U Uu1)) (not (tptp.element_of_collection Uu1 Vf)))) (or (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (not (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f)))) (or (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (not (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f)))) :rule resolution :premises (t100 t101))
% 0.20/0.55  (step t103 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted) (Uu1 $$unsorted)) (or (tptp.element_of_set U (tptp.union_of_members Vf)) (not (tptp.element_of_set U Uu1)) (not (tptp.element_of_collection Uu1 Vf)))) (or (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (not (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f)))) (not (or (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (not (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f))))) :rule implies_neg2)
% 0.20/0.55  (step t104 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted) (Uu1 $$unsorted)) (or (tptp.element_of_set U (tptp.union_of_members Vf)) (not (tptp.element_of_set U Uu1)) (not (tptp.element_of_collection Uu1 Vf)))) (or (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (not (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f)))) (=> (forall ((U $$unsorted) (Vf $$unsorted) (Uu1 $$unsorted)) (or (tptp.element_of_set U (tptp.union_of_members Vf)) (not (tptp.element_of_set U Uu1)) (not (tptp.element_of_collection Uu1 Vf)))) (or (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (not (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f))))) :rule resolution :premises (t102 t103))
% 0.20/0.55  (step t105 (cl (=> (forall ((U $$unsorted) (Vf $$unsorted) (Uu1 $$unsorted)) (or (tptp.element_of_set U (tptp.union_of_members Vf)) (not (tptp.element_of_set U Uu1)) (not (tptp.element_of_collection Uu1 Vf)))) (or (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (not (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f))))) :rule contraction :premises (t104))
% 0.20/0.55  (step t106 (cl (not (forall ((U $$unsorted) (Vf $$unsorted) (Uu1 $$unsorted)) (or (tptp.element_of_set U (tptp.union_of_members Vf)) (not (tptp.element_of_set U Uu1)) (not (tptp.element_of_collection Uu1 Vf))))) (or (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (not (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f)))) :rule implies :premises (t105))
% 0.20/0.55  (step t107 (cl (or (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)))) (not (tptp.element_of_collection (tptp.f10 tptp.f (tptp.f1 (tptp.top_of_basis tptp.f) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx)) tptp.f)))) :rule resolution :premises (t106 a2))
% 0.20/0.55  (step t108 (cl (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f))) :rule resolution :premises (t44 t88 t99 t107))
% 0.20/0.55  (step t109 (cl (not (or (not (tptp.subset_sets (tptp.union_of_members tptp.f) tptp.cx)) (not (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) (tptp.union_of_members tptp.f))) (tptp.element_of_set (tptp.in_1st_set (tptp.union_of_members (tptp.top_of_basis tptp.f)) tptp.cx) tptp.cx)))) :rule resolution :premises (t9 t20 t42 t108))
% 0.20/0.55  (step t110 (cl) :rule resolution :premises (t7 t109 a7))
% 0.20/0.55  
% 0.20/0.55  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.6wzLd2vY2p/cvc5---1.0.5_11697.smt2
% 0.20/0.55  % cvc5---1.0.5 exiting
% 0.20/0.55  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------