%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ064-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:23:16 AM UTC 2026
% Result : Unsatisfiable 28.90s 9.35s
% Output : CNFRefutation 28.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 25
% Syntax : Number of formulae : 193 ( 146 unt; 0 def)
% Number of atoms : 273 ( 168 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 168 ( 88 ~; 80 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-4 aty)
% Number of variables : 369 ( 53 sgn 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
c_in(v_a,v_A,tc_set(t_a)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
c_in(v_a,v_A,tc_set(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_2,axiom,
c_inter(v_a,v_t,t_a) = c_emptyset,
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_2,plain,
c_inter(v_a,v_t,t_a) = c_emptyset,
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_3,plain,
c_emptyset = c_inter(v_a,v_t,t_a),
inference(copy,[status(thm)],[c_2]) ).
fof(cls_conjecture_3,axiom,
c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_4,plain,
c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_4,axiom,
c_inter(c_union(v_a,v_t,t_a),v_u,t_a) = c_emptyset,
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_5,plain,
c_inter(c_union(v_a,v_t,t_a),v_u,t_a) = c_emptyset,
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
cnf(c_6,plain,
c_inter(c_union(v_a,v_t,t_a),v_u,t_a) = c_inter(v_a,v_t,t_a),
inference(paramod,[status(thm)],[c_3,c_5]) ).
fof(cls_conjecture_5,axiom,
~ c_in(c_union(c_union(v_a,v_t,t_a),v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_7,plain,
~ c_in(c_union(c_union(v_a,v_t,t_a),v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
fof(cls_conjecture_6,axiom,
( ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| c_inter(v_t,v_u,t_a) != c_emptyset
| c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
file('theBenchmark.p',cls_conjecture_6) ).
cnf(c_8,plain,
( ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| c_inter(v_t,v_u,t_a) != c_emptyset
| c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_6]) ).
cnf(c_3893,plain,
( ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| c_inter(v_t,v_u,t_a) != c_inter(v_a,v_t,t_a)
| c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(paramod,[status(thm)],[c_3,c_8]) ).
cnf(c_3894,plain,
( ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| c_inter(v_a,v_t,t_a) != c_inter(v_t,v_u,t_a)
| c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(copy,[status(thm)],[c_3893]) ).
cnf(c_9,plain,
( c_inter(v_a,v_t,t_a) != c_inter(v_t,v_u,t_a)
| c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_4,c_3894]) ).
fof(cls_Mutil_Otiling_OUn_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(c_union(VAR_0,VAR_3,VAR_2),c_Mutil_Otiling(VAR_1,VAR_2),tc_set(VAR_2))
| c_inter(VAR_0,VAR_3,VAR_2) != c_emptyset
| ~ c_in(VAR_3,c_Mutil_Otiling(VAR_1,VAR_2),tc_set(VAR_2))
| ~ c_in(VAR_0,VAR_1,tc_set(VAR_2)) ),
file('theBenchmark.p',cls_Mutil_Otiling_OUn_0) ).
cnf(c_10,plain,
( c_in(c_union(A,D,C),c_Mutil_Otiling(B,C),tc_set(C))
| c_inter(A,D,C) != c_emptyset
| ~ c_in(D,c_Mutil_Otiling(B,C),tc_set(C))
| ~ c_in(A,B,tc_set(C)) ),
inference(clausify,[status(thm)],[cls_Mutil_Otiling_OUn_0]) ).
cnf(c_3895,plain,
( c_in(c_union(A,D,C),c_Mutil_Otiling(B,C),tc_set(C))
| c_inter(A,D,C) != c_inter(v_a,v_t,t_a)
| ~ c_in(D,c_Mutil_Otiling(B,C),tc_set(C))
| ~ c_in(A,B,tc_set(C)) ),
inference(paramod,[status(thm)],[c_3,c_10]) ).
cnf(c_11,plain,
( c_in(c_union(A,D,C),c_Mutil_Otiling(B,C),tc_set(C))
| c_inter(v_a,v_t,t_a) != c_inter(A,D,C)
| ~ c_in(D,c_Mutil_Otiling(B,C),tc_set(C))
| ~ c_in(A,B,tc_set(C)) ),
inference(copy,[status(thm)],[c_3895]) ).
fof(cls_Relation_OImage__diag_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_Relation_OImage(c_Relation_Odiag(VAR_0,VAR_1),VAR_2,VAR_1,VAR_1) = c_inter(VAR_0,VAR_2,VAR_1),
file('theBenchmark.p',cls_Relation_OImage__diag_0) ).
cnf(c_12,plain,
c_Relation_OImage(c_Relation_Odiag(A,B),C,B,B) = c_inter(A,C,B),
inference(clausify,[status(thm)],[cls_Relation_OImage__diag_0]) ).
cnf(c_13,plain,
c_inter(A,B,C) = c_Relation_OImage(c_Relation_Odiag(A,C),B,C,C),
inference(copy,[status(thm)],[c_12]) ).
fof(cls_Set_OCompl__Diff__eq_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_uminus(c_minus(VAR_0,VAR_1,tc_set(VAR_2)),tc_set(VAR_2)) = c_union(c_uminus(VAR_0,tc_set(VAR_2)),VAR_1,VAR_2),
file('theBenchmark.p',cls_Set_OCompl__Diff__eq_0) ).
cnf(c_14,plain,
c_uminus(c_minus(A,B,tc_set(C)),tc_set(C)) = c_union(c_uminus(A,tc_set(C)),B,C),
inference(clausify,[status(thm)],[cls_Set_OCompl__Diff__eq_0]) ).
fof(cls_Set_OCompl__UNIV__eq_0,axiom,
! [VAR_0] : c_uminus(c_UNIV,tc_set(VAR_0)) = c_emptyset,
file('theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
cnf(c_15,plain,
c_uminus(c_UNIV,tc_set(A)) = c_emptyset,
inference(clausify,[status(thm)],[cls_Set_OCompl__UNIV__eq_0]) ).
cnf(c_3896,plain,
c_uminus(c_UNIV,tc_set(A)) = c_inter(v_a,v_t,t_a),
inference(paramod,[status(thm)],[c_3,c_15]) ).
cnf(c_16,plain,
c_uminus(c_UNIV,tc_set(A)) = c_Relation_OImage(c_Relation_Odiag(v_a,t_a),v_t,t_a,t_a),
inference(paramod,[status(thm)],[c_13,c_3896]) ).
fof(cls_Set_ODiff__Compl_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_minus(VAR_0,c_uminus(VAR_1,tc_set(VAR_2)),tc_set(VAR_2)) = c_inter(VAR_0,VAR_1,VAR_2),
file('theBenchmark.p',cls_Set_ODiff__Compl_0) ).
cnf(c_17,plain,
c_minus(A,c_uminus(B,tc_set(C)),tc_set(C)) = c_inter(A,B,C),
inference(clausify,[status(thm)],[cls_Set_ODiff__Compl_0]) ).
cnf(c_3897,plain,
c_minus(A,c_uminus(B,tc_set(C)),tc_set(C)) = c_Relation_OImage(c_Relation_Odiag(A,C),B,C,C),
inference(paramod,[status(thm)],[c_13,c_17]) ).
cnf(c_18,plain,
c_Relation_OImage(c_Relation_Odiag(A,B),C,B,B) = c_minus(A,c_uminus(C,tc_set(B)),tc_set(B)),
inference(copy,[status(thm)],[c_3897]) ).
fof(cls_Set_OInt__UNIV__left_0,axiom,
! [VAR_0,VAR_1] : c_inter(c_UNIV,VAR_0,VAR_1) = VAR_0,
file('theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).
cnf(c_19,plain,
c_inter(c_UNIV,A,B) = A,
inference(clausify,[status(thm)],[cls_Set_OInt__UNIV__left_0]) ).
cnf(c_3898,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,B),A,B,B) = A,
inference(paramod,[status(thm)],[c_13,c_19]) ).
cnf(c_20,plain,
c_minus(c_UNIV,c_uminus(A,tc_set(B)),tc_set(B)) = A,
inference(paramod,[status(thm)],[c_18,c_3898]) ).
fof(cls_Set_OUn__Diff__cancel2_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_union(c_minus(VAR_0,VAR_1,tc_set(VAR_2)),VAR_1,VAR_2) = c_union(VAR_0,VAR_1,VAR_2),
file('theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
cnf(c_23,plain,
c_union(c_minus(A,B,tc_set(C)),B,C) = c_union(A,B,C),
inference(clausify,[status(thm)],[cls_Set_OUn__Diff__cancel2_0]) ).
fof(cls_Set_OUn__Diff__cancel_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_union(VAR_0,c_minus(VAR_1,VAR_0,tc_set(VAR_2)),VAR_2) = c_union(VAR_0,VAR_1,VAR_2),
file('theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
cnf(c_24,plain,
c_union(A,c_minus(B,A,tc_set(C)),C) = c_union(A,B,C),
inference(clausify,[status(thm)],[cls_Set_OUn__Diff__cancel_0]) ).
fof(cls_Set_OUn__UNIV__left_0,axiom,
! [VAR_0,VAR_1] : c_union(c_UNIV,VAR_0,VAR_1) = c_UNIV,
file('theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).
cnf(c_25,plain,
c_union(c_UNIV,A,B) = c_UNIV,
inference(clausify,[status(thm)],[cls_Set_OUn__UNIV__left_0]) ).
fof(cls_Set_OUn__absorb_0,axiom,
! [VAR_0,VAR_1] : c_union(VAR_0,VAR_0,VAR_1) = VAR_0,
file('theBenchmark.p',cls_Set_OUn__absorb_0) ).
cnf(c_26,plain,
c_union(A,A,B) = A,
inference(clausify,[status(thm)],[cls_Set_OUn__absorb_0]) ).
fof(cls_Set_OUn__assoc_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : c_union(c_union(VAR_0,VAR_1,VAR_2),VAR_3,VAR_2) = c_union(VAR_0,c_union(VAR_1,VAR_3,VAR_2),VAR_2),
file('theBenchmark.p',cls_Set_OUn__assoc_0) ).
cnf(c_27,plain,
c_union(c_union(A,B,C),D,C) = c_union(A,c_union(B,D,C),C),
inference(clausify,[status(thm)],[cls_Set_OUn__assoc_0]) ).
fof(cls_Set_OUn__empty__left_0,axiom,
! [VAR_0,VAR_1] : c_union(c_emptyset,VAR_0,VAR_1) = VAR_0,
file('theBenchmark.p',cls_Set_OUn__empty__left_0) ).
cnf(c_28,plain,
c_union(c_emptyset,A,B) = A,
inference(clausify,[status(thm)],[cls_Set_OUn__empty__left_0]) ).
cnf(c_3899,plain,
c_union(c_inter(v_a,v_t,t_a),A,B) = A,
inference(paramod,[status(thm)],[c_3,c_28]) ).
cnf(c_3900,plain,
c_union(c_Relation_OImage(c_Relation_Odiag(v_a,t_a),v_t,t_a,t_a),A,B) = A,
inference(paramod,[status(thm)],[c_13,c_3899]) ).
cnf(c_29,plain,
c_union(c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),A,B) = A,
inference(paramod,[status(thm)],[c_18,c_3900]) ).
fof(cls_Set_OUn__empty__right_0,axiom,
! [VAR_0,VAR_1] : c_union(VAR_0,c_emptyset,VAR_1) = VAR_0,
file('theBenchmark.p',cls_Set_OUn__empty__right_0) ).
cnf(c_30,plain,
c_union(A,c_emptyset,B) = A,
inference(clausify,[status(thm)],[cls_Set_OUn__empty__right_0]) ).
cnf(c_3901,plain,
c_union(A,c_inter(v_a,v_t,t_a),B) = A,
inference(paramod,[status(thm)],[c_3,c_30]) ).
cnf(c_3902,plain,
c_union(A,c_Relation_OImage(c_Relation_Odiag(v_a,t_a),v_t,t_a,t_a),B) = A,
inference(paramod,[status(thm)],[c_13,c_3901]) ).
cnf(c_31,plain,
c_union(A,c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),B) = A,
inference(paramod,[status(thm)],[c_18,c_3902]) ).
fof(cls_Set_OUn__subset__iff_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(VAR_0,VAR_3,tc_set(VAR_2))
| ~ c_lessequals(c_union(VAR_0,VAR_1,VAR_2),VAR_3,tc_set(VAR_2)) ),
file('theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
cnf(c_32,plain,
( c_lessequals(A,D,tc_set(C))
| ~ c_lessequals(c_union(A,B,C),D,tc_set(C)) ),
inference(clausify,[status(thm)],[cls_Set_OUn__subset__iff_0]) ).
fof(cls_Set_OUn__subset__iff_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(VAR_1,VAR_3,tc_set(VAR_2))
| ~ c_lessequals(c_union(VAR_0,VAR_1,VAR_2),VAR_3,tc_set(VAR_2)) ),
file('theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
cnf(c_33,plain,
( c_lessequals(B,D,tc_set(C))
| ~ c_lessequals(c_union(A,B,C),D,tc_set(C)) ),
inference(clausify,[status(thm)],[cls_Set_OUn__subset__iff_1]) ).
fof(cls_Set_OUn__subset__iff_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_union(VAR_3,VAR_0,VAR_2),VAR_1,tc_set(VAR_2))
| ~ c_lessequals(VAR_3,VAR_1,tc_set(VAR_2))
| ~ c_lessequals(VAR_0,VAR_1,tc_set(VAR_2)) ),
file('theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
cnf(c_34,plain,
( c_lessequals(c_union(D,A,C),B,tc_set(C))
| ~ c_lessequals(D,B,tc_set(C))
| ~ c_lessequals(A,B,tc_set(C)) ),
inference(clausify,[status(thm)],[cls_Set_OUn__subset__iff_2]) ).
fof(cls_Set_Odouble__complement_0,axiom,
! [VAR_0,VAR_1] : c_uminus(c_uminus(VAR_0,tc_set(VAR_1)),tc_set(VAR_1)) = VAR_0,
file('theBenchmark.p',cls_Set_Odouble__complement_0) ).
cnf(c_35,plain,
c_uminus(c_uminus(A,tc_set(B)),tc_set(B)) = A,
inference(clausify,[status(thm)],[cls_Set_Odouble__complement_0]) ).
fof(cls_Set_Osubset__antisym_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_1 = VAR_0
| ~ c_lessequals(VAR_1,VAR_0,tc_set(VAR_2))
| ~ c_lessequals(VAR_0,VAR_1,tc_set(VAR_2)) ),
file('theBenchmark.p',cls_Set_Osubset__antisym_0) ).
cnf(c_41,plain,
( B = A
| ~ c_lessequals(B,A,tc_set(C))
| ~ c_lessequals(A,B,tc_set(C)) ),
inference(clausify,[status(thm)],[cls_Set_Osubset__antisym_0]) ).
fof(cls_Set_Osubset__refl_0,axiom,
! [VAR_0,VAR_1] : c_lessequals(VAR_0,VAR_0,tc_set(VAR_1)),
file('theBenchmark.p',cls_Set_Osubset__refl_0) ).
cnf(c_42,plain,
c_lessequals(A,A,tc_set(B)),
inference(clausify,[status(thm)],[cls_Set_Osubset__refl_0]) ).
cnf(c_3903,plain,
( c_in(c_union(A,D,C),c_Mutil_Otiling(B,C),tc_set(C))
| c_Relation_OImage(c_Relation_Odiag(v_a,t_a),v_t,t_a,t_a) != c_inter(A,D,C)
| ~ c_in(D,c_Mutil_Otiling(B,C),tc_set(C))
| ~ c_in(A,B,tc_set(C)) ),
inference(paramod,[status(thm)],[c_13,c_11]) ).
cnf(c_3904,plain,
( c_in(c_union(A,D,C),c_Mutil_Otiling(B,C),tc_set(C))
| c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) != c_inter(A,D,C)
| ~ c_in(D,c_Mutil_Otiling(B,C),tc_set(C))
| ~ c_in(A,B,tc_set(C)) ),
inference(paramod,[status(thm)],[c_18,c_3903]) ).
cnf(c_3905,plain,
( c_in(c_union(A,D,C),c_Mutil_Otiling(B,C),tc_set(C))
| c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) != c_Relation_OImage(c_Relation_Odiag(A,C),D,C,C)
| ~ c_in(D,c_Mutil_Otiling(B,C),tc_set(C))
| ~ c_in(A,B,tc_set(C)) ),
inference(paramod,[status(thm)],[c_13,c_3904]) ).
cnf(c_43,plain,
( c_in(c_union(A,D,C),c_Mutil_Otiling(B,C),tc_set(C))
| c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) != c_minus(A,c_uminus(D,tc_set(C)),tc_set(C))
| ~ c_in(D,c_Mutil_Otiling(B,C),tc_set(C))
| ~ c_in(A,B,tc_set(C)) ),
inference(paramod,[status(thm)],[c_18,c_3905]) ).
cnf(c_3906,plain,
( c_Relation_OImage(c_Relation_Odiag(v_a,t_a),v_t,t_a,t_a) != c_inter(v_t,v_u,t_a)
| c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(paramod,[status(thm)],[c_13,c_9]) ).
cnf(c_3907,plain,
( c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) != c_inter(v_t,v_u,t_a)
| c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(paramod,[status(thm)],[c_18,c_3906]) ).
cnf(c_3908,plain,
( c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) != c_Relation_OImage(c_Relation_Odiag(v_t,t_a),v_u,t_a,t_a)
| c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(paramod,[status(thm)],[c_13,c_3907]) ).
cnf(c_44,plain,
( c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) != c_minus(v_t,c_uminus(v_u,tc_set(t_a)),tc_set(t_a))
| c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(paramod,[status(thm)],[c_18,c_3908]) ).
cnf(c_3909,plain,
c_Relation_OImage(c_Relation_Odiag(c_union(v_a,v_t,t_a),t_a),v_u,t_a,t_a) = c_inter(v_a,v_t,t_a),
inference(paramod,[status(thm)],[c_13,c_6]) ).
cnf(c_3910,plain,
c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) = c_inter(v_a,v_t,t_a),
inference(paramod,[status(thm)],[c_18,c_3909]) ).
cnf(c_3911,plain,
c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) = c_Relation_OImage(c_Relation_Odiag(v_a,t_a),v_t,t_a,t_a),
inference(paramod,[status(thm)],[c_13,c_3910]) ).
cnf(c_45,plain,
c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) = c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),
inference(paramod,[status(thm)],[c_18,c_3911]) ).
cnf(c_47,plain,
c_uminus(c_UNIV,tc_set(A)) = c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),
inference(paramod,[status(thm)],[c_18,c_16]) ).
cnf(c_49,plain,
~ c_in(c_union(v_a,c_union(v_t,v_u,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(paramod,[status(thm)],[c_27,c_7]) ).
cnf(c_3912,plain,
c_union(A,c_uminus(A,tc_set(B)),B) = c_union(c_UNIV,c_uminus(A,tc_set(B)),B),
inference(paramod,[status(thm)],[c_20,c_23]) ).
cnf(c_53,plain,
c_union(A,c_uminus(A,tc_set(B)),B) = c_UNIV,
inference(paramod,[status(thm)],[c_25,c_3912]) ).
cnf(c_3913,plain,
c_union(c_uminus(A,tc_set(B)),A,B) = c_union(c_uminus(A,tc_set(B)),c_UNIV,B),
inference(paramod,[status(thm)],[c_20,c_24]) ).
cnf(c_54,plain,
c_union(c_uminus(A,tc_set(B)),c_UNIV,B) = c_union(c_uminus(A,tc_set(B)),A,B),
inference(copy,[status(thm)],[c_3913]) ).
cnf(c_3914,plain,
c_union(c_union(A,B,C),D,C) = c_union(c_minus(A,B,tc_set(C)),c_union(B,D,C),C),
inference(paramod,[status(thm)],[c_23,c_27]) ).
cnf(c_3915,plain,
c_union(A,c_union(B,D,C),C) = c_union(c_minus(A,B,tc_set(C)),c_union(B,D,C),C),
inference(paramod,[status(thm)],[c_27,c_3914]) ).
cnf(c_55,plain,
c_union(c_minus(A,B,tc_set(C)),c_union(B,D,C),C) = c_union(A,c_union(B,D,C),C),
inference(copy,[status(thm)],[c_3915]) ).
cnf(c_3916,plain,
c_union(c_union(A,B,C),D,C) = c_union(A,c_union(c_minus(B,A,tc_set(C)),D,C),C),
inference(paramod,[status(thm)],[c_24,c_27]) ).
cnf(c_3917,plain,
c_union(A,c_union(B,D,C),C) = c_union(A,c_union(c_minus(B,A,tc_set(C)),D,C),C),
inference(paramod,[status(thm)],[c_27,c_3916]) ).
cnf(c_57,plain,
c_union(A,c_union(c_minus(B,A,tc_set(C)),D,C),C) = c_union(A,c_union(B,D,C),C),
inference(copy,[status(thm)],[c_3917]) ).
cnf(c_58,plain,
c_union(A,c_union(B,c_union(A,B,C),C),C) = c_union(A,B,C),
inference(paramod,[status(thm)],[c_27,c_26]) ).
cnf(c_3918,plain,
c_union(A,B,C) = c_union(A,c_union(A,B,C),C),
inference(paramod,[status(thm)],[c_26,c_27]) ).
cnf(c_59,plain,
c_union(A,c_union(A,B,C),C) = c_union(A,B,C),
inference(copy,[status(thm)],[c_3918]) ).
cnf(c_3919,plain,
c_uminus(v_t,tc_set(t_a)) = c_union(v_a,c_uminus(v_t,tc_set(t_a)),t_a),
inference(paramod,[status(thm)],[c_29,c_23]) ).
cnf(c_60,plain,
c_union(v_a,c_uminus(v_t,tc_set(t_a)),t_a) = c_uminus(v_t,tc_set(t_a)),
inference(copy,[status(thm)],[c_3919]) ).
cnf(c_3920,plain,
c_uminus(c_union(c_uminus(A,tc_set(B)),C,B),tc_set(B)) = c_minus(A,C,tc_set(B)),
inference(paramod,[status(thm)],[c_14,c_35]) ).
cnf(c_68,plain,
c_minus(A,B,tc_set(C)) = c_uminus(c_union(c_uminus(A,tc_set(C)),B,C),tc_set(C)),
inference(copy,[status(thm)],[c_3920]) ).
cnf(c_74,plain,
c_union(A,c_union(c_uminus(c_union(c_uminus(B,tc_set(C)),A,C),tc_set(C)),D,C),C) = c_union(A,c_union(B,D,C),C),
inference(paramod,[status(thm)],[c_68,c_57]) ).
cnf(c_76,plain,
c_union(c_uminus(c_union(c_uminus(A,tc_set(B)),C,B),tc_set(B)),c_union(C,D,B),B) = c_union(A,c_union(C,D,B),B),
inference(paramod,[status(thm)],[c_68,c_55]) ).
cnf(c_3921,plain,
c_uminus(c_UNIV,tc_set(A)) = c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)),
inference(paramod,[status(thm)],[c_68,c_47]) ).
cnf(c_78,plain,
c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)) = c_uminus(c_UNIV,tc_set(A)),
inference(copy,[status(thm)],[c_3921]) ).
cnf(c_3922,plain,
c_uminus(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a),tc_set(t_a)) = c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),
inference(paramod,[status(thm)],[c_68,c_45]) ).
cnf(c_80,plain,
c_uminus(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a),tc_set(t_a)) = c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)),
inference(paramod,[status(thm)],[c_68,c_3922]) ).
cnf(c_3923,plain,
( c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)) != c_minus(v_t,c_uminus(v_u,tc_set(t_a)),tc_set(t_a))
| c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(paramod,[status(thm)],[c_68,c_44]) ).
cnf(c_81,plain,
( c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)) != c_uminus(c_union(c_uminus(v_t,tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a),tc_set(t_a))
| c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(paramod,[status(thm)],[c_68,c_3923]) ).
cnf(c_3924,plain,
( c_in(c_union(A,D,C),c_Mutil_Otiling(B,C),tc_set(C))
| c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)) != c_minus(A,c_uminus(D,tc_set(C)),tc_set(C))
| ~ c_in(D,c_Mutil_Otiling(B,C),tc_set(C))
| ~ c_in(A,B,tc_set(C)) ),
inference(paramod,[status(thm)],[c_68,c_43]) ).
cnf(c_82,plain,
( c_in(c_union(A,D,C),c_Mutil_Otiling(B,C),tc_set(C))
| c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)) != c_uminus(c_union(c_uminus(A,tc_set(C)),c_uminus(D,tc_set(C)),C),tc_set(C))
| ~ c_in(D,c_Mutil_Otiling(B,C),tc_set(C))
| ~ c_in(A,B,tc_set(C)) ),
inference(paramod,[status(thm)],[c_68,c_3924]) ).
cnf(c_85,plain,
c_union(A,c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)),B) = A,
inference(paramod,[status(thm)],[c_68,c_31]) ).
cnf(c_86,plain,
c_union(c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)),A,B) = A,
inference(paramod,[status(thm)],[c_68,c_29]) ).
cnf(c_87,plain,
c_union(A,c_uminus(c_union(c_uminus(B,tc_set(C)),A,C),tc_set(C)),C) = c_union(A,B,C),
inference(paramod,[status(thm)],[c_68,c_24]) ).
cnf(c_91,plain,
( c_lessequals(c_union(B,A,C),B,tc_set(C))
| ~ c_lessequals(A,B,tc_set(C)) ),
inference(resolve,[status(thm)],[c_42,c_34]) ).
cnf(c_93,plain,
c_lessequals(A,c_union(B,A,C),tc_set(C)),
inference(resolve,[status(thm)],[c_42,c_33]) ).
cnf(c_94,plain,
c_lessequals(A,c_union(A,B,C),tc_set(C)),
inference(resolve,[status(thm)],[c_42,c_32]) ).
cnf(c_3925,plain,
( B = c_union(A,B,C)
| ~ c_lessequals(c_union(A,B,C),B,tc_set(C)) ),
inference(resolve,[status(thm)],[c_93,c_41]) ).
cnf(c_98,plain,
( c_union(A,B,C) = B
| ~ c_lessequals(c_union(A,B,C),B,tc_set(C)) ),
inference(copy,[status(thm)],[c_3925]) ).
cnf(c_103,plain,
c_lessequals(A,c_UNIV,tc_set(B)),
inference(paramod,[status(thm)],[c_25,c_93]) ).
cnf(c_3926,plain,
( A = c_UNIV
| ~ c_lessequals(c_UNIV,A,tc_set(B)) ),
inference(resolve,[status(thm)],[c_103,c_41]) ).
cnf(c_104,plain,
( c_UNIV = A
| ~ c_lessequals(c_UNIV,A,tc_set(B)) ),
inference(copy,[status(thm)],[c_3926]) ).
cnf(c_3927,plain,
c_UNIV = c_union(A,c_UNIV,B),
inference(resolve,[status(thm)],[c_104,c_93]) ).
cnf(c_109,plain,
c_union(A,c_UNIV,B) = c_UNIV,
inference(copy,[status(thm)],[c_3927]) ).
cnf(c_3928,plain,
c_UNIV = c_union(c_uminus(A,tc_set(B)),A,B),
inference(paramod,[status(thm)],[c_109,c_54]) ).
cnf(c_110,plain,
c_union(c_uminus(A,tc_set(B)),A,B) = c_UNIV,
inference(copy,[status(thm)],[c_3928]) ).
cnf(c_3929,plain,
c_union(c_UNIV,A,B) = c_union(C,c_union(c_uminus(C,tc_set(B)),A,B),B),
inference(paramod,[status(thm)],[c_53,c_27]) ).
cnf(c_3930,plain,
c_UNIV = c_union(C,c_union(c_uminus(C,tc_set(B)),A,B),B),
inference(paramod,[status(thm)],[c_25,c_3929]) ).
cnf(c_111,plain,
c_union(A,c_union(c_uminus(A,tc_set(B)),C,B),B) = c_UNIV,
inference(copy,[status(thm)],[c_3930]) ).
cnf(c_3931,plain,
c_union(c_UNIV,A,B) = c_union(c_uminus(C,tc_set(B)),c_union(C,A,B),B),
inference(paramod,[status(thm)],[c_110,c_27]) ).
cnf(c_3932,plain,
c_UNIV = c_union(c_uminus(C,tc_set(B)),c_union(C,A,B),B),
inference(paramod,[status(thm)],[c_25,c_3931]) ).
cnf(c_117,plain,
c_union(c_uminus(A,tc_set(B)),c_union(A,C,B),B) = c_UNIV,
inference(copy,[status(thm)],[c_3932]) ).
cnf(c_151,plain,
c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a) = c_UNIV,
inference(paramod,[status(thm)],[c_60,c_117]) ).
cnf(c_152,plain,
c_union(c_uminus(c_UNIV,tc_set(t_a)),A,B) = A,
inference(paramod,[status(thm)],[c_151,c_86]) ).
cnf(c_153,plain,
c_union(A,c_uminus(c_UNIV,tc_set(t_a)),B) = A,
inference(paramod,[status(thm)],[c_151,c_85]) ).
cnf(c_3933,plain,
( c_in(c_union(A,D,C),c_Mutil_Otiling(B,C),tc_set(C))
| c_uminus(c_UNIV,tc_set(t_a)) != c_uminus(c_union(c_uminus(A,tc_set(C)),c_uminus(D,tc_set(C)),C),tc_set(C))
| ~ c_in(D,c_Mutil_Otiling(B,C),tc_set(C))
| ~ c_in(A,B,tc_set(C)) ),
inference(paramod,[status(thm)],[c_151,c_82]) ).
cnf(c_156,plain,
( c_in(c_union(A,D,C),c_Mutil_Otiling(B,C),tc_set(C))
| c_uminus(c_union(c_uminus(A,tc_set(C)),c_uminus(D,tc_set(C)),C),tc_set(C)) != c_uminus(c_UNIV,tc_set(t_a))
| ~ c_in(D,c_Mutil_Otiling(B,C),tc_set(C))
| ~ c_in(A,B,tc_set(C)) ),
inference(copy,[status(thm)],[c_3933]) ).
cnf(c_3934,plain,
( c_uminus(c_UNIV,tc_set(t_a)) != c_uminus(c_union(c_uminus(v_t,tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a),tc_set(t_a))
| c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(paramod,[status(thm)],[c_151,c_81]) ).
cnf(c_157,plain,
( c_uminus(c_union(c_uminus(v_t,tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a),tc_set(t_a)) != c_uminus(c_UNIV,tc_set(t_a))
| c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(copy,[status(thm)],[c_3934]) ).
cnf(c_158,plain,
c_uminus(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a),tc_set(t_a)) = c_uminus(c_UNIV,tc_set(t_a)),
inference(paramod,[status(thm)],[c_151,c_80]) ).
cnf(c_160,plain,
c_uminus(c_UNIV,tc_set(t_a)) = c_uminus(c_UNIV,tc_set(A)),
inference(paramod,[status(thm)],[c_151,c_78]) ).
cnf(c_172,plain,
c_union(c_uminus(c_UNIV,tc_set(A)),B,C) = B,
inference(paramod,[status(thm)],[c_160,c_152]) ).
cnf(c_174,plain,
c_union(A,c_uminus(c_UNIV,tc_set(B)),C) = A,
inference(paramod,[status(thm)],[c_160,c_153]) ).
cnf(c_3935,plain,
c_lessequals(c_union(c_union(A,B,C),A,C),c_union(A,B,C),tc_set(C)),
inference(resolve,[status(thm)],[c_91,c_94]) ).
cnf(c_198,plain,
c_lessequals(c_union(A,c_union(B,A,C),C),c_union(A,B,C),tc_set(C)),
inference(paramod,[status(thm)],[c_27,c_3935]) ).
cnf(c_3936,plain,
( c_union(A,c_union(B,c_union(A,B,C),C),C) = c_union(B,c_union(A,B,C),C)
| ~ c_lessequals(c_union(A,B,C),c_union(B,c_union(A,B,C),C),tc_set(C)) ),
inference(paramod,[status(thm)],[c_58,c_98]) ).
cnf(c_3937,plain,
( c_union(A,B,C) = c_union(B,c_union(A,B,C),C)
| ~ c_lessequals(c_union(A,B,C),c_union(B,c_union(A,B,C),C),tc_set(C)) ),
inference(paramod,[status(thm)],[c_58,c_3936]) ).
cnf(c_3938,plain,
( c_union(B,c_union(A,B,C),C) = c_union(A,B,C)
| ~ c_lessequals(c_union(A,B,C),c_union(B,c_union(A,B,C),C),tc_set(C)) ),
inference(copy,[status(thm)],[c_3937]) ).
cnf(c_216,plain,
c_union(A,c_union(B,A,C),C) = c_union(B,A,C),
inference(resolve,[status(thm)],[c_93,c_3938]) ).
cnf(c_219,plain,
c_lessequals(c_union(A,B,C),c_union(B,A,C),tc_set(C)),
inference(paramod,[status(thm)],[c_216,c_198]) ).
cnf(c_3939,plain,
c_union(c_union(c_uminus(A,tc_set(B)),C,B),c_union(c_uminus(c_union(c_uminus(A,tc_set(B)),C,B),tc_set(B)),D,B),B) = c_union(c_union(c_uminus(A,tc_set(B)),C,B),c_union(A,D,B),B),
inference(paramod,[status(thm)],[c_59,c_74]) ).
cnf(c_3940,plain,
c_UNIV = c_union(c_union(c_uminus(A,tc_set(B)),C,B),c_union(A,D,B),B),
inference(paramod,[status(thm)],[c_111,c_3939]) ).
cnf(c_3941,plain,
c_UNIV = c_union(c_uminus(A,tc_set(B)),c_union(C,c_union(A,D,B),B),B),
inference(paramod,[status(thm)],[c_27,c_3940]) ).
cnf(c_228,plain,
c_union(c_uminus(A,tc_set(B)),c_union(C,c_union(A,D,B),B),B) = c_UNIV,
inference(copy,[status(thm)],[c_3941]) ).
cnf(c_3942,plain,
( c_union(B,A,C) = c_union(A,B,C)
| ~ c_lessequals(c_union(A,B,C),c_union(B,A,C),tc_set(C)) ),
inference(resolve,[status(thm)],[c_219,c_41]) ).
cnf(c_240,plain,
c_union(A,B,C) = c_union(B,A,C),
inference(resolve,[status(thm)],[c_219,c_3942]) ).
cnf(c_3943,plain,
c_uminus(c_union(c_uminus(c_union(v_t,v_a,t_a),tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a),tc_set(t_a)) = c_uminus(c_UNIV,tc_set(t_a)),
inference(paramod,[status(thm)],[c_240,c_158]) ).
cnf(c_248,plain,
c_uminus(c_union(c_uminus(v_u,tc_set(t_a)),c_uminus(c_union(v_t,v_a,t_a),tc_set(t_a)),t_a),tc_set(t_a)) = c_uminus(c_UNIV,tc_set(t_a)),
inference(paramod,[status(thm)],[c_240,c_3943]) ).
cnf(c_3944,plain,
( c_uminus(c_union(c_uminus(v_t,tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a),tc_set(t_a)) != c_uminus(c_UNIV,tc_set(t_a))
| c_in(c_union(v_u,v_t,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(paramod,[status(thm)],[c_240,c_157]) ).
cnf(c_249,plain,
( c_uminus(c_union(c_uminus(v_u,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)) != c_uminus(c_UNIV,tc_set(t_a))
| c_in(c_union(v_u,v_t,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(paramod,[status(thm)],[c_240,c_3944]) ).
cnf(c_250,plain,
c_union(c_uminus(v_t,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a) = c_UNIV,
inference(paramod,[status(thm)],[c_240,c_151]) ).
cnf(c_251,plain,
~ c_in(c_union(v_a,c_union(v_u,v_t,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(paramod,[status(thm)],[c_240,c_49]) ).
cnf(c_3945,plain,
c_union(c_union(A,B,C),D,C) = c_union(B,c_union(A,D,C),C),
inference(paramod,[status(thm)],[c_240,c_27]) ).
cnf(c_252,plain,
c_union(A,c_union(B,C,D),D) = c_union(B,c_union(A,C,D),D),
inference(paramod,[status(thm)],[c_27,c_3945]) ).
cnf(c_258,plain,
c_union(c_uminus(A,tc_set(B)),c_union(C,A,B),B) = c_UNIV,
inference(paramod,[status(thm)],[c_240,c_117]) ).
cnf(c_283,plain,
c_union(c_uminus(A,tc_set(B)),c_union(C,c_union(D,A,B),B),B) = c_UNIV,
inference(paramod,[status(thm)],[c_27,c_258]) ).
cnf(c_3946,plain,
c_union(c_uminus(c_UNIV,tc_set(t_a)),c_union(c_uminus(v_a,tc_set(t_a)),A,t_a),t_a) = c_union(v_t,c_union(c_uminus(v_a,tc_set(t_a)),A,t_a),t_a),
inference(paramod,[status(thm)],[c_250,c_76]) ).
cnf(c_3947,plain,
c_union(c_uminus(v_a,tc_set(t_a)),A,t_a) = c_union(v_t,c_union(c_uminus(v_a,tc_set(t_a)),A,t_a),t_a),
inference(paramod,[status(thm)],[c_172,c_3946]) ).
cnf(c_306,plain,
c_union(v_t,c_union(c_uminus(v_a,tc_set(t_a)),A,t_a),t_a) = c_union(c_uminus(v_a,tc_set(t_a)),A,t_a),
inference(copy,[status(thm)],[c_3947]) ).
cnf(c_338,plain,
c_union(A,c_uminus(c_union(B,A,C),tc_set(C)),C) = c_union(A,c_uminus(B,tc_set(C)),C),
inference(paramod,[status(thm)],[c_35,c_87]) ).
cnf(c_3948,plain,
c_union(c_uminus(v_a,tc_set(t_a)),A,t_a) = c_union(c_uminus(v_a,tc_set(t_a)),c_union(v_t,A,t_a),t_a),
inference(paramod,[status(thm)],[c_306,c_252]) ).
cnf(c_1588,plain,
c_union(c_uminus(v_a,tc_set(t_a)),c_union(v_t,A,t_a),t_a) = c_union(c_uminus(v_a,tc_set(t_a)),A,t_a),
inference(copy,[status(thm)],[c_3948]) ).
cnf(c_1646,plain,
c_union(A,c_uminus(c_union(A,B,C),tc_set(C)),C) = c_union(A,c_uminus(B,tc_set(C)),C),
inference(paramod,[status(thm)],[c_240,c_338]) ).
cnf(c_3949,plain,
c_union(c_uminus(v_a,tc_set(t_a)),c_union(v_t,c_uminus(A,tc_set(t_a)),t_a),t_a) = c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(c_union(A,v_t,t_a),tc_set(t_a)),t_a),
inference(paramod,[status(thm)],[c_338,c_1588]) ).
cnf(c_3950,plain,
c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(A,tc_set(t_a)),t_a) = c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(c_union(A,v_t,t_a),tc_set(t_a)),t_a),
inference(paramod,[status(thm)],[c_1588,c_3949]) ).
cnf(c_2051,plain,
c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(c_union(A,v_t,t_a),tc_set(t_a)),t_a) = c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(A,tc_set(t_a)),t_a),
inference(copy,[status(thm)],[c_3950]) ).
cnf(c_3951,plain,
c_union(c_uminus(v_u,tc_set(t_a)),c_uminus(c_UNIV,tc_set(t_a)),t_a) = c_union(c_uminus(v_u,tc_set(t_a)),c_uminus(c_uminus(c_union(v_t,v_a,t_a),tc_set(t_a)),tc_set(t_a)),t_a),
inference(paramod,[status(thm)],[c_248,c_1646]) ).
cnf(c_3952,plain,
c_uminus(v_u,tc_set(t_a)) = c_union(c_uminus(v_u,tc_set(t_a)),c_uminus(c_uminus(c_union(v_t,v_a,t_a),tc_set(t_a)),tc_set(t_a)),t_a),
inference(paramod,[status(thm)],[c_174,c_3951]) ).
cnf(c_3953,plain,
c_uminus(v_u,tc_set(t_a)) = c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_t,v_a,t_a),t_a),
inference(paramod,[status(thm)],[c_35,c_3952]) ).
cnf(c_3743,plain,
c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_t,v_a,t_a),t_a) = c_uminus(v_u,tc_set(t_a)),
inference(copy,[status(thm)],[c_3953]) ).
cnf(c_3954,plain,
c_union(c_uminus(v_t,tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a) = c_UNIV,
inference(paramod,[status(thm)],[c_3743,c_228]) ).
cnf(c_3773,plain,
c_union(c_uminus(v_u,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a) = c_UNIV,
inference(paramod,[status(thm)],[c_240,c_3954]) ).
cnf(c_3955,plain,
c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a) = c_UNIV,
inference(paramod,[status(thm)],[c_3743,c_283]) ).
cnf(c_3781,plain,
c_union(c_uminus(v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a) = c_UNIV,
inference(paramod,[status(thm)],[c_240,c_3955]) ).
cnf(c_3956,plain,
( c_uminus(c_UNIV,tc_set(t_a)) != c_uminus(c_UNIV,tc_set(t_a))
| c_in(c_union(v_u,v_t,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(paramod,[status(thm)],[c_3773,c_249]) ).
cnf(c_3833,plain,
c_in(c_union(v_u,v_t,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(copy,[status(thm)],[c_3956]) ).
cnf(c_3957,plain,
( c_in(c_union(v_a,A,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(A,tc_set(t_a)),t_a),tc_set(t_a)) != c_uminus(c_UNIV,tc_set(t_a))
| ~ c_in(A,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_156,c_1]) ).
cnf(c_3958,plain,
( c_in(c_union(v_a,c_union(v_u,v_t,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(c_union(v_u,v_t,t_a),tc_set(t_a)),t_a),tc_set(t_a)) != c_uminus(c_UNIV,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_3957,c_3833]) ).
cnf(c_3959,plain,
c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(c_union(v_u,v_t,t_a),tc_set(t_a)),t_a),tc_set(t_a)) != c_uminus(c_UNIV,tc_set(t_a)),
inference(resolve,[status(thm)],[c_3958,c_251]) ).
cnf(c_3960,plain,
c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a),tc_set(t_a)) != c_uminus(c_UNIV,tc_set(t_a)),
inference(paramod,[status(thm)],[c_2051,c_3959]) ).
cnf(c_3961,plain,
c_uminus(c_union(c_uminus(v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a),tc_set(t_a)) != c_uminus(c_UNIV,tc_set(t_a)),
inference(paramod,[status(thm)],[c_240,c_3960]) ).
cnf(c_3962,plain,
c_uminus(c_UNIV,tc_set(t_a)) != c_uminus(c_UNIV,tc_set(t_a)),
inference(paramod,[status(thm)],[c_3781,c_3961]) ).
cnf(c_3892,plain,
$false,
inference(copy,[status(thm)],[c_3962]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ064-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 05:12:33 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 687284 was started by sandbox on n020,
% 0.10/0.36 % Sat Sep 26 05:12:33 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 28.90/9.35
% 28.90/9.35 % SZS status Unsatisfiable for theBenchmark
% 28.90/9.35
% 28.90/9.35 % Proof 1 at 3.27 (+ 0.82) seconds.
% 28.90/9.35 % Length of proof is 98.
% 28.90/9.35 % Level of proof is 13.
% 28.90/9.35 % Maximum clause weight is 49.000.
% 28.90/9.35 % Given clauses 471.
% 28.90/9.35
% 28.90/9.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------