%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : PUZ064-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 : Thu Sep 24 02:01:46 PM UTC 2026
% Result : Unsatisfiable 6.05s 6.22s
% Output : CNFRefutation 6.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 24
% Syntax : Number of clauses : 133 ( 108 unt; 0 nHn; 52 RR)
% Number of literals : 173 ( 108 equ; 46 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 278 ( 61 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_ODiff__Compl_0,axiom,
c_minus(X1,c_uminus(X2,tc_set(X3)),tc_set(X3)) = c_inter(X1,X2,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__Compl_0) ).
cnf(cls_Set_Odouble__complement_0,axiom,
c_uminus(c_uminus(X1,tc_set(X2)),tc_set(X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
cnf(cls_Set_OInt__UNIV__left_0,axiom,
c_inter(c_UNIV,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).
cnf(cls_Set_OUn__subset__iff_1,axiom,
( ~ c_lessequals(c_union(X1,X2,X3),X4,tc_set(X3))
| c_lessequals(X2,X4,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
cnf(cls_Set_OUn__Diff__cancel2_0,axiom,
c_union(c_minus(X1,X2,tc_set(X3)),X2,X3) = c_union(X1,X2,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
cnf(cls_Set_OUn__UNIV__left_0,axiom,
c_union(c_UNIV,X1,X2) = c_UNIV,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).
cnf(cls_Set_OUn__subset__iff_0,axiom,
( ~ c_lessequals(c_union(X1,X2,X3),X4,tc_set(X3))
| c_lessequals(X1,X4,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
cnf(cls_Set_Osubset__antisym_0,axiom,
( ~ c_lessequals(X2,X1,tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3))
| X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
cnf(cls_Set_Osubset__refl_0,axiom,
c_lessequals(X1,X1,tc_set(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
cnf(cls_Set_OCompl__Diff__eq_0,axiom,
c_uminus(c_minus(X1,X2,tc_set(X3)),tc_set(X3)) = c_union(c_uminus(X1,tc_set(X3)),X2,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Diff__eq_0) ).
cnf(cls_Set_OUn__assoc_0,axiom,
c_union(c_union(X1,X2,X3),X4,X3) = c_union(X1,c_union(X2,X4,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__assoc_0) ).
cnf(cls_Set_OUn__Diff__cancel_0,axiom,
c_union(X1,c_minus(X2,X1,tc_set(X3)),X3) = c_union(X1,X2,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
cnf(cls_Set_OUn__subset__iff_2,axiom,
( ~ c_lessequals(X4,X2,tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3))
| c_lessequals(c_union(X4,X1,X3),X2,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
cnf(cls_Set_OCompl__UNIV__eq_0,axiom,
c_uminus(c_UNIV,tc_set(X1)) = c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
cnf(cls_Set_OUn__absorb_0,axiom,
c_union(X1,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
cnf(cls_Set_OUn__empty__left_0,axiom,
c_union(c_emptyset,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
cnf(cls_conjecture_4,negated_conjecture,
c_inter(c_union(v_a,v_t,t_a),v_u,t_a) = c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_Set_OUn__empty__right_0,axiom,
c_union(X1,c_emptyset,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
cnf(cls_conjecture_2,negated_conjecture,
c_inter(v_a,v_t,t_a) = c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_5,negated_conjecture,
~ 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('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_conjecture_6,negated_conjecture,
( ~ 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('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
cnf(cls_Mutil_Otiling_OUn_0,axiom,
( c_inter(X1,X4,X3) != c_emptyset
| ~ c_in(X4,c_Mutil_Otiling(X2,X3),tc_set(X3))
| ~ c_in(X1,X2,tc_set(X3))
| c_in(c_union(X1,X4,X3),c_Mutil_Otiling(X2,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Mutil_Otiling_OUn_0) ).
cnf(cls_conjecture_3,negated_conjecture,
c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_a,v_A,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(c_0_24,axiom,
c_minus(X1,c_uminus(X2,tc_set(X3)),tc_set(X3)) = c_inter(X1,X2,X3),
cls_Set_ODiff__Compl_0 ).
cnf(c_0_25,axiom,
c_uminus(c_uminus(X1,tc_set(X2)),tc_set(X2)) = X1,
cls_Set_Odouble__complement_0 ).
cnf(c_0_26,axiom,
c_inter(c_UNIV,X1,X2) = X1,
cls_Set_OInt__UNIV__left_0 ).
cnf(c_0_27,plain,
c_inter(X1,c_uminus(X2,tc_set(X3)),X3) = c_minus(X1,X2,tc_set(X3)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
( ~ c_lessequals(c_union(X1,X2,X3),X4,tc_set(X3))
| c_lessequals(X2,X4,tc_set(X3)) ),
inference(fof_simplification,[status(thm)],[cls_Set_OUn__subset__iff_1]) ).
cnf(c_0_29,axiom,
c_union(c_minus(X1,X2,tc_set(X3)),X2,X3) = c_union(X1,X2,X3),
cls_Set_OUn__Diff__cancel2_0 ).
cnf(c_0_30,plain,
c_minus(c_UNIV,X1,tc_set(X2)) = c_uminus(X1,tc_set(X2)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,axiom,
c_union(c_UNIV,X1,X2) = c_UNIV,
cls_Set_OUn__UNIV__left_0 ).
cnf(c_0_32,plain,
( ~ c_lessequals(c_union(X1,X2,X3),X4,tc_set(X3))
| c_lessequals(X1,X4,tc_set(X3)) ),
inference(fof_simplification,[status(thm)],[cls_Set_OUn__subset__iff_0]) ).
cnf(c_0_33,plain,
( ~ c_lessequals(X2,X1,tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3))
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[cls_Set_Osubset__antisym_0]) ).
cnf(c_0_34,plain,
( ~ c_lessequals(c_union(X1,X2,X3),X4,tc_set(X3))
| c_lessequals(X2,X4,tc_set(X3)) ),
c_0_28 ).
cnf(c_0_35,axiom,
c_lessequals(X1,X1,tc_set(X2)),
cls_Set_Osubset__refl_0 ).
cnf(c_0_36,plain,
c_union(c_uminus(X1,tc_set(X2)),X1,X2) = c_UNIV,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_37,axiom,
c_uminus(c_minus(X1,X2,tc_set(X3)),tc_set(X3)) = c_union(c_uminus(X1,tc_set(X3)),X2,X3),
cls_Set_OCompl__Diff__eq_0 ).
cnf(c_0_38,axiom,
c_union(c_union(X1,X2,X3),X4,X3) = c_union(X1,c_union(X2,X4,X3),X3),
cls_Set_OUn__assoc_0 ).
cnf(c_0_39,axiom,
c_union(X1,c_minus(X2,X1,tc_set(X3)),X3) = c_union(X1,X2,X3),
cls_Set_OUn__Diff__cancel_0 ).
cnf(c_0_40,plain,
( ~ c_lessequals(c_union(X1,X2,X3),X4,tc_set(X3))
| c_lessequals(X1,X4,tc_set(X3)) ),
c_0_32 ).
cnf(c_0_41,plain,
( ~ c_lessequals(X2,X1,tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3))
| X2 = X1 ),
c_0_33 ).
cnf(c_0_42,plain,
c_lessequals(X1,c_union(X2,X1,X3),tc_set(X3)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_43,plain,
( ~ c_lessequals(X4,X2,tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3))
| c_lessequals(c_union(X4,X1,X3),X2,tc_set(X3)) ),
inference(fof_simplification,[status(thm)],[cls_Set_OUn__subset__iff_2]) ).
cnf(c_0_44,plain,
c_union(c_uminus(X1,tc_set(X2)),c_union(X3,X1,X2),X2) = c_UNIV,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39]) ).
cnf(c_0_45,plain,
c_lessequals(X1,c_union(X1,X2,X3),tc_set(X3)),
inference(spm,[status(thm)],[c_0_40,c_0_35]) ).
cnf(c_0_46,plain,
( ~ c_lessequals(c_union(X1,X2,X3),X2,tc_set(X3))
| c_union(X1,X2,X3) = X2 ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,plain,
( ~ c_lessequals(X4,X2,tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3))
| c_lessequals(c_union(X4,X1,X3),X2,tc_set(X3)) ),
c_0_43 ).
cnf(c_0_48,plain,
c_uminus(c_union(c_uminus(X1,tc_set(X2)),X3,X2),tc_set(X2)) = c_minus(X1,X3,tc_set(X2)),
inference(spm,[status(thm)],[c_0_25,c_0_37]) ).
cnf(c_0_49,plain,
c_union(X1,c_union(X2,c_uminus(X1,tc_set(X3)),X3),X3) = c_UNIV,
inference(spm,[status(thm)],[c_0_44,c_0_25]) ).
cnf(c_0_50,axiom,
c_uminus(c_UNIV,tc_set(X1)) = c_emptyset,
cls_Set_OCompl__UNIV__eq_0 ).
cnf(c_0_51,axiom,
c_union(X1,X1,X2) = X1,
cls_Set_OUn__absorb_0 ).
cnf(c_0_52,plain,
( ~ c_lessequals(c_union(X1,X2,X3),X1,tc_set(X3))
| c_union(X1,X2,X3) = X1 ),
inference(spm,[status(thm)],[c_0_41,c_0_45]) ).
cnf(c_0_53,plain,
( ~ c_lessequals(X1,X2,tc_set(X3))
| c_union(X1,X2,X3) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_35])]) ).
cnf(c_0_54,plain,
c_minus(X1,c_union(X2,X1,X3),tc_set(X3)) = c_emptyset,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_25]) ).
cnf(c_0_55,plain,
c_union(c_uminus(X1,tc_set(X2)),c_inter(X3,X1,X2),X2) = c_union(c_uminus(X1,tc_set(X2)),X3,X2),
inference(spm,[status(thm)],[c_0_39,c_0_24]) ).
cnf(c_0_56,plain,
c_minus(X1,c_union(c_uminus(X2,tc_set(X3)),X4,X3),tc_set(X3)) = c_inter(X1,c_minus(X2,X4,tc_set(X3)),X3),
inference(spm,[status(thm)],[c_0_24,c_0_37]) ).
cnf(c_0_57,plain,
c_union(X1,c_union(X1,X2,X3),X3) = c_union(X1,X2,X3),
inference(spm,[status(thm)],[c_0_38,c_0_51]) ).
cnf(c_0_58,plain,
( ~ c_lessequals(X2,X1,tc_set(X3))
| c_union(X1,X2,X3) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_47]),c_0_35])]) ).
cnf(c_0_59,plain,
c_lessequals(c_minus(X1,X2,tc_set(X3)),c_union(X1,X2,X3),tc_set(X3)),
inference(spm,[status(thm)],[c_0_45,c_0_29]) ).
cnf(c_0_60,plain,
c_union(X1,c_union(X2,X1,X3),X3) = c_union(X2,X1,X3),
inference(spm,[status(thm)],[c_0_53,c_0_42]) ).
cnf(c_0_61,axiom,
c_union(c_emptyset,X1,X2) = X1,
cls_Set_OUn__empty__left_0 ).
cnf(c_0_62,plain,
c_minus(X1,c_emptyset,tc_set(X2)) = c_inter(X1,c_UNIV,X2),
inference(spm,[status(thm)],[c_0_24,c_0_50]) ).
cnf(c_0_63,plain,
c_inter(c_inter(X1,X2,X3),c_minus(X2,X1,tc_set(X3)),X3) = c_emptyset,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
cnf(c_0_64,plain,
c_inter(X1,c_minus(X1,X2,tc_set(X3)),X3) = c_minus(X1,X2,tc_set(X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_57]),c_0_48]),c_0_56]) ).
cnf(c_0_65,negated_conjecture,
c_inter(c_union(v_a,v_t,t_a),v_u,t_a) = c_emptyset,
cls_conjecture_4 ).
cnf(c_0_66,plain,
c_union(X1,X2,X3) = c_union(X2,X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_38]),c_0_39]),c_0_60]) ).
cnf(c_0_67,plain,
c_inter(X1,c_UNIV,X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_39]),c_0_61]),c_0_62]) ).
cnf(c_0_68,plain,
c_minus(c_minus(X1,X2,tc_set(X3)),X1,tc_set(X3)) = c_emptyset,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_64]) ).
cnf(c_0_69,axiom,
c_union(X1,c_emptyset,X2) = X1,
cls_Set_OUn__empty__right_0 ).
cnf(c_0_70,plain,
c_minus(X1,c_union(X2,c_union(X3,X1,X4),X4),tc_set(X4)) = c_emptyset,
inference(spm,[status(thm)],[c_0_54,c_0_38]) ).
cnf(c_0_71,plain,
c_minus(X1,c_inter(X2,X1,X3),tc_set(X3)) = c_minus(X1,X2,tc_set(X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_39]),c_0_48]),c_0_24]) ).
cnf(c_0_72,negated_conjecture,
c_inter(c_union(v_t,v_a,t_a),v_u,t_a) = c_emptyset,
inference(rw,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_73,plain,
c_minus(X1,c_emptyset,tc_set(X2)) = X1,
inference(rw,[status(thm)],[c_0_62,c_0_67]) ).
cnf(c_0_74,plain,
c_union(X1,c_minus(X1,X2,tc_set(X3)),X3) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_68]),c_0_69]) ).
cnf(c_0_75,plain,
c_inter(X1,c_minus(X2,c_union(X3,X1,X4),tc_set(X4)),X4) = c_emptyset,
inference(spm,[status(thm)],[c_0_56,c_0_70]) ).
cnf(c_0_76,negated_conjecture,
c_minus(v_u,c_union(v_t,v_a,t_a),tc_set(t_a)) = v_u,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_77,plain,
c_lessequals(X1,c_UNIV,tc_set(X2)),
inference(spm,[status(thm)],[c_0_42,c_0_31]) ).
cnf(c_0_78,plain,
c_union(X1,c_inter(X1,X2,X3),X3) = X1,
inference(spm,[status(thm)],[c_0_74,c_0_24]) ).
cnf(c_0_79,negated_conjecture,
c_inter(v_a,v_u,t_a) = c_emptyset,
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,plain,
( ~ c_lessequals(c_UNIV,X1,tc_set(X2))
| c_UNIV = X1 ),
inference(spm,[status(thm)],[c_0_41,c_0_77]) ).
cnf(c_0_81,plain,
c_inter(c_inter(X1,X2,X3),c_minus(X4,X1,tc_set(X3)),X3) = c_emptyset,
inference(spm,[status(thm)],[c_0_75,c_0_78]) ).
cnf(c_0_82,negated_conjecture,
c_minus(v_u,v_a,tc_set(t_a)) = v_u,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_79]),c_0_73]) ).
cnf(c_0_83,plain,
c_union(X1,c_UNIV,X2) = c_UNIV,
inference(spm,[status(thm)],[c_0_80,c_0_42]) ).
cnf(c_0_84,negated_conjecture,
c_inter(c_inter(v_a,X1,t_a),v_u,t_a) = c_emptyset,
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_85,plain,
c_union(X1,c_uminus(X1,tc_set(X2)),X2) = c_UNIV,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_30]),c_0_83]) ).
cnf(c_0_86,negated_conjecture,
c_minus(v_u,c_inter(v_a,X1,t_a),tc_set(t_a)) = v_u,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_84]),c_0_73]) ).
cnf(c_0_87,plain,
c_inter(X1,c_union(c_uminus(X2,tc_set(X3)),X4,X3),X3) = c_minus(X1,c_minus(X2,X4,tc_set(X3)),tc_set(X3)),
inference(spm,[status(thm)],[c_0_27,c_0_37]) ).
cnf(c_0_88,plain,
c_union(X1,c_union(c_uminus(X1,tc_set(X2)),X3,X2),X2) = c_UNIV,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_85]),c_0_31]) ).
cnf(c_0_89,negated_conjecture,
c_inter(v_u,c_union(c_uminus(v_a,tc_set(t_a)),X1,t_a),t_a) = v_u,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_27]),c_0_87]) ).
cnf(c_0_90,negated_conjecture,
c_inter(v_a,v_t,t_a) = c_emptyset,
cls_conjecture_2 ).
cnf(c_0_91,plain,
c_uminus(c_emptyset,tc_set(X1)) = c_UNIV,
inference(spm,[status(thm)],[c_0_25,c_0_50]) ).
cnf(c_0_92,plain,
c_minus(X1,c_union(X1,X2,X3),tc_set(X3)) = c_emptyset,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_88]),c_0_50]),c_0_25]) ).
cnf(c_0_93,plain,
c_union(c_uminus(X1,tc_set(X2)),c_uminus(X3,tc_set(X2)),X2) = c_uminus(c_inter(X1,X3,X2),tc_set(X2)),
inference(spm,[status(thm)],[c_0_37,c_0_24]) ).
cnf(c_0_94,negated_conjecture,
c_inter(v_u,c_union(X1,c_uminus(v_a,tc_set(t_a)),t_a),t_a) = v_u,
inference(spm,[status(thm)],[c_0_89,c_0_60]) ).
cnf(c_0_95,negated_conjecture,
c_union(c_uminus(v_t,tc_set(t_a)),v_a,t_a) = c_uminus(v_t,tc_set(t_a)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_90]),c_0_69]) ).
cnf(c_0_96,plain,
c_minus(X1,c_UNIV,tc_set(X2)) = c_inter(X1,c_emptyset,X2),
inference(spm,[status(thm)],[c_0_24,c_0_91]) ).
cnf(c_0_97,plain,
c_inter(c_uminus(X1,tc_set(X2)),c_inter(X1,X3,X2),X2) = c_emptyset,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_24]) ).
cnf(c_0_98,plain,
c_inter(X1,c_minus(X2,X1,tc_set(X3)),X3) = c_emptyset,
inference(spm,[status(thm)],[c_0_56,c_0_54]) ).
cnf(c_0_99,negated_conjecture,
c_minus(v_u,c_inter(X1,v_a,t_a),tc_set(t_a)) = v_u,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_93]),c_0_27]) ).
cnf(c_0_100,negated_conjecture,
c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a) = c_UNIV,
inference(spm,[status(thm)],[c_0_44,c_0_95]) ).
cnf(c_0_101,plain,
c_inter(X1,c_inter(X2,c_emptyset,X3),X3) = c_inter(X1,c_emptyset,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_83]),c_0_96]),c_0_96]) ).
cnf(c_0_102,negated_conjecture,
~ 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(fof_simplification,[status(thm)],[cls_conjecture_5]) ).
cnf(c_0_103,negated_conjecture,
( ~ 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(fof_simplification,[status(thm)],[cls_conjecture_6]) ).
cnf(c_0_104,plain,
c_inter(c_inter(X1,X2,X3),X1,X3) = c_inter(X1,X2,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_97]),c_0_73]),c_0_24]) ).
cnf(c_0_105,negated_conjecture,
c_inter(c_inter(X1,v_a,t_a),v_u,t_a) = c_emptyset,
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_106,negated_conjecture,
c_union(c_uminus(v_t,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a) = c_UNIV,
inference(rw,[status(thm)],[c_0_100,c_0_66]) ).
cnf(c_0_107,plain,
c_inter(X1,c_emptyset,X2) = c_emptyset,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_101]),c_0_26]) ).
cnf(c_0_108,negated_conjecture,
~ 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)),
c_0_102 ).
cnf(c_0_109,plain,
( c_inter(X1,X4,X3) != c_emptyset
| ~ c_in(X4,c_Mutil_Otiling(X2,X3),tc_set(X3))
| ~ c_in(X1,X2,tc_set(X3))
| c_in(c_union(X1,X4,X3),c_Mutil_Otiling(X2,X3),tc_set(X3)) ),
inference(fof_simplification,[status(thm)],[cls_Mutil_Otiling_OUn_0]) ).
cnf(c_0_110,negated_conjecture,
( ~ 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)) ),
c_0_103 ).
cnf(c_0_111,negated_conjecture,
c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
cls_conjecture_3 ).
cnf(c_0_112,plain,
c_inter(X1,c_minus(X2,c_union(X1,X3,X4),tc_set(X4)),X4) = c_emptyset,
inference(spm,[status(thm)],[c_0_75,c_0_66]) ).
cnf(c_0_113,plain,
c_union(c_inter(X1,X2,X3),c_uminus(X2,tc_set(X3)),X3) = c_union(X1,c_uminus(X2,tc_set(X3)),X3),
inference(spm,[status(thm)],[c_0_29,c_0_24]) ).
cnf(c_0_114,negated_conjecture,
c_inter(v_u,v_a,t_a) = c_emptyset,
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_115,negated_conjecture,
c_inter(X1,c_inter(v_t,v_a,t_a),t_a) = c_emptyset,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_106]),c_0_96]),c_0_24]),c_0_107]) ).
cnf(c_0_116,plain,
c_minus(X1,c_union(X2,c_uminus(X3,tc_set(X4)),X4),tc_set(X4)) = c_inter(X1,c_minus(X3,X2,tc_set(X4)),X4),
inference(spm,[status(thm)],[c_0_56,c_0_66]) ).
cnf(c_0_117,negated_conjecture,
~ 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(rw,[status(thm)],[c_0_108,c_0_38]) ).
cnf(c_0_118,plain,
( c_inter(X1,X4,X3) != c_emptyset
| ~ c_in(X4,c_Mutil_Otiling(X2,X3),tc_set(X3))
| ~ c_in(X1,X2,tc_set(X3))
| c_in(c_union(X1,X4,X3),c_Mutil_Otiling(X2,X3),tc_set(X3)) ),
c_0_109 ).
cnf(c_0_119,negated_conjecture,
c_in(v_a,v_A,tc_set(t_a)),
cls_conjecture_0 ).
cnf(c_0_120,negated_conjecture,
( 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(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_111])]) ).
cnf(c_0_121,negated_conjecture,
c_inter(v_t,v_u,t_a) = c_emptyset,
inference(spm,[status(thm)],[c_0_112,c_0_76]) ).
cnf(c_0_122,plain,
c_minus(c_union(X1,X2,X3),c_union(X1,c_union(X2,X4,X3),X3),tc_set(X3)) = c_emptyset,
inference(spm,[status(thm)],[c_0_92,c_0_38]) ).
cnf(c_0_123,negated_conjecture,
c_union(v_u,c_uminus(v_a,tc_set(t_a)),t_a) = c_uminus(v_a,tc_set(t_a)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_61]) ).
cnf(c_0_124,negated_conjecture,
c_inter(v_t,v_a,t_a) = c_emptyset,
inference(spm,[status(thm)],[c_0_26,c_0_115]) ).
cnf(c_0_125,plain,
c_uminus(c_union(X1,c_uminus(X2,tc_set(X3)),X3),tc_set(X3)) = c_minus(X2,X1,tc_set(X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_60]),c_0_116]),c_0_64]) ).
cnf(c_0_126,negated_conjecture,
( ~ c_in(c_union(v_u,v_t,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| c_inter(v_a,c_union(v_u,v_t,t_a),t_a) != c_emptyset ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_119])]),c_0_66]),c_0_66]) ).
cnf(c_0_127,negated_conjecture,
c_in(c_union(v_u,v_t,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_66]),c_0_121])]) ).
cnf(c_0_128,negated_conjecture,
c_inter(c_union(X1,v_u,t_a),c_minus(v_a,X1,tc_set(t_a)),t_a) = c_emptyset,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_116]) ).
cnf(c_0_129,negated_conjecture,
c_minus(v_a,v_t,tc_set(t_a)) = v_a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_124]),c_0_73]) ).
cnf(c_0_130,plain,
c_inter(X1,X2,X3) = c_inter(X2,X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_125]),c_0_24]),c_0_24]) ).
cnf(c_0_131,negated_conjecture,
c_inter(v_a,c_union(v_u,v_t,t_a),t_a) != c_emptyset,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_127])]) ).
cnf(c_0_132,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_66]),c_0_130]),c_0_131]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ064-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/5.38 % Computer : n010.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Mon Sep 21 03:50:00 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.05/6.22 % Version: 3.5.1
% 6.05/6.22 % Preprocessing class: FSMSSMSSSSSNFFN.
% 6.05/6.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.05/6.22 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.05/6.22 % Starting new_bool_3 with 300s (1) cores
% 6.05/6.22 % Starting new_bool_1 with 300s (1) cores
% 6.05/6.22 % Starting sh5l with 300s (1) cores
% 6.05/6.22 % sh5l with pid 4159246 completed with status 0
% 6.05/6.22 % Result found by sh5l
% 6.05/6.22 % Preprocessing class: FSMSSMSSSSSNFFN.
% 6.05/6.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.05/6.22 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.05/6.22 % Starting new_bool_3 with 300s (1) cores
% 6.05/6.22 % Starting new_bool_1 with 300s (1) cores
% 6.05/6.22 % Starting sh5l with 300s (1) cores
% 6.05/6.22 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 6.05/6.22 % SinE strategy is gf500_gu_R04_F100_L20000
% 6.05/6.22 % Search class: FHUSM-FFMS32-MFFFFFNN
% 6.05/6.22 % partial match(2): FGUSF-FFMS32-MFFFFFNN
% 6.05/6.22 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 6.05/6.22 % Starting SubtermCWHack with 31s (1) cores
% 6.05/6.22 % SubtermCWHack with pid 4159258 completed with status 0
% 6.05/6.22 % Result found by SubtermCWHack
% 6.05/6.22 % Preprocessing class: FSMSSMSSSSSNFFN.
% 6.05/6.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.05/6.22 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.05/6.22 % Starting new_bool_3 with 300s (1) cores
% 6.05/6.22 % Starting new_bool_1 with 300s (1) cores
% 6.05/6.22 % Starting sh5l with 300s (1) cores
% 6.05/6.22 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 6.05/6.22 % SinE strategy is gf500_gu_R04_F100_L20000
% 6.05/6.22 % Search class: FHUSM-FFMS32-MFFFFFNN
% 6.05/6.22 % partial match(2): FGUSF-FFMS32-MFFFFFNN
% 6.05/6.22 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 6.05/6.22 % Starting SubtermCWHack with 31s (1) cores
% 6.05/6.22 % Preprocessing time : 0.001 s
% 6.05/6.22
% 6.05/6.22 % Proof found!
% 6.05/6.22 % SZS status Unsatisfiable
% 6.05/6.22 % SZS output start CNFRefutation
% See solution above
% 6.05/6.23 % Parsed axioms : 29
% 6.05/6.23 % Removed by relevancy pruning/SinE : 2
% 6.05/6.23 % Initial clauses : 27
% 6.05/6.23 % Removed in clause preprocessing : 0
% 6.05/6.23 % Initial clauses in saturation : 27
% 6.05/6.23 % Processed clauses : 2509
% 6.05/6.23 % ...of these trivial : 410
% 6.05/6.23 % ...subsumed : 1403
% 6.05/6.23 % ...remaining for further processing : 695
% 6.05/6.23 % Other redundant clauses eliminated : 12
% 6.05/6.23 % Clauses deleted for lack of memory : 0
% 6.05/6.23 % Backward-subsumed : 1
% 6.05/6.23 % Backward-rewritten : 122
% 6.05/6.23 % Generated clauses : 62077
% 6.05/6.23 % ...of the previous two non-redundant : 18793
% 6.05/6.23 % ...aggressively subsumed : 0
% 6.05/6.23 % Contextual simplify-reflections : 0
% 6.05/6.23 % Paramodulations : 62065
% 6.05/6.23 % Factorizations : 0
% 6.05/6.23 % NegExts : 0
% 6.05/6.23 % Equation resolutions : 12
% 6.05/6.23 % Disequality decompositions : 0
% 6.05/6.23 % Total rewrite steps : 74790
% 6.05/6.23 % ...of those cached : 64218
% 6.05/6.23 % Propositional unsat checks : 0
% 6.05/6.23 % Propositional check models : 0
% 6.05/6.23 % Propositional check unsatisfiable : 0
% 6.05/6.23 % Propositional clauses : 0
% 6.05/6.23 % Propositional clauses after purity: 0
% 6.05/6.23 % Propositional unsat core size : 0
% 6.05/6.23 % Propositional preprocessing time : 0.000
% 6.05/6.23 % Propositional encoding time : 0.000
% 6.05/6.23 % Propositional solver time : 0.000
% 6.05/6.23 % Success case prop preproc time : 0.000
% 6.05/6.23 % Success case prop encoding time : 0.000
% 6.05/6.23 % Success case prop solver time : 0.000
% 6.05/6.23 % Current number of processed clauses : 572
% 6.05/6.23 % Positive orientable unit clauses : 430
% 6.05/6.23 % Positive unorientable unit clauses: 7
% 6.05/6.23 % Negative unit clauses : 7
% 6.05/6.23 % Non-unit-clauses : 128
% 6.05/6.23 % Current number of unprocessed clauses: 16169
% 6.05/6.23 % ...number of literals in the above : 27991
% 6.05/6.23 % Current number of archived formulas : 0
% 6.05/6.23 % Current number of archived clauses : 123
% 6.05/6.23 % Clause-clause subsumption calls (NU) : 5540
% 6.05/6.23 % Rec. Clause-clause subsumption calls : 4570
% 6.05/6.23 % Non-unit clause-clause subsumptions : 969
% 6.05/6.23 % Unit Clause-clause subsumption calls : 1565
% 6.05/6.23 % Rewrite failures with RHS unbound : 0
% 6.05/6.23 % BW rewrite match attempts : 1785
% 6.05/6.23 % BW rewrite match successes : 949
% 6.05/6.23 % Condensation attempts : 0
% 6.05/6.23 % Condensation successes : 0
% 6.05/6.23 % Termbank termtop insertions : 697670
% 6.05/6.23 % Search garbage collected termcells : 43
% 6.05/6.23
% 6.05/6.23 % -------------------------------------------------
% 6.05/6.23 % User time : 0.705 s
% 6.05/6.23 % System time : 0.042 s
% 6.05/6.23 % Total time : 0.746 s
% 6.05/6.23 % Maximum resident set size: 3908 pages
% 6.05/6.23
% 6.05/6.23 % -------------------------------------------------
% 6.05/6.23 % User time : 0.708 s
% 6.05/6.23 % System time : 0.045 s
% 6.05/6.23 % Total time : 0.753 s
% 6.05/6.23 % Maximum resident set size: 4864 pages
% 6.05/6.23 % E exiting
%------------------------------------------------------------------------------