%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : PUZ064-2 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n010.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 : Tue May 5 05:02:50 PM UTC 2026
% Result : Unsatisfiable 268.86s 126.01s
% Output : CNFRefutation 271.55s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_30)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_OInt__iff_1,axiom,
( c_in(X1,X3,X4)
| ~ c_in(X1,c_inter(X2,X3,X4),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
cnf(cls_Relation_OImage__diag_0,axiom,
c_Relation_OImage(c_Relation_Odiag(X1,X2),X3,X2,X2) = c_inter(X1,X3,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__diag_0) ).
cnf(cls_Mutil_Otiling_OUn_0,axiom,
( c_in(c_union(X1,X4,X3),c_Mutil_Otiling(X2,X3),tc_set(X3))
| ~ c_in(X1,X2,tc_set(X3))
| ~ c_in(X4,c_Mutil_Otiling(X2,X3),tc_set(X3))
| c_inter(X1,X4,X3) != c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Mutil_Otiling_OUn_0) ).
cnf(cls_conjecture_6,negated_conjecture,
( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| c_inter(v_t,v_u,t_a) != c_emptyset
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
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/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
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/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__Compl_0) ).
cnf(cls_Set_OInt__UNIV__left_0,axiom,
c_inter(c_UNIV,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).
cnf(cls_conjecture_2,negated_conjecture,
c_inter(v_a,v_t,t_a) = c_emptyset,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_Set_OUn__subset__iff_2,axiom,
( c_lessequals(c_union(X4,X1,X3),X2,tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X4,X2,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
cnf(cls_Set_OUn__subset__iff_0,axiom,
( c_lessequals(X1,X4,tc_set(X3))
| ~ c_lessequals(c_union(X1,X2,X3),X4,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
cnf(cls_Set_OUn__subset__iff_1,axiom,
( c_lessequals(X2,X4,tc_set(X3))
| ~ c_lessequals(c_union(X1,X2,X3),X4,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__assoc_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/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__Diff__eq_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_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/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
cnf(cls_Set_OsubsetI_0,axiom,
( c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
cnf(cls_Set_Osubset__antisym_0,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X2,X1,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
cnf(cls_Set_Oempty__iff_0,axiom,
~ c_in(X1,c_emptyset,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__iff_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/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_Set_Osubset__refl_0,axiom,
c_lessequals(X1,X1,tc_set(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
cnf(cls_Set_Odouble__complement_0,axiom,
c_uminus(c_uminus(X1,tc_set(X2)),tc_set(X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
cnf(cls_Set_Oempty__subsetI_0,axiom,
c_lessequals(c_emptyset,X1,tc_set(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
cnf(cls_Set_OUn__absorb_0,axiom,
c_union(X1,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_a,v_A,tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_Set_OUn__empty__left_0,axiom,
c_union(c_emptyset,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
cnf(cls_Set_OUn__empty__right_0,axiom,
c_union(X1,c_emptyset,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
cnf(cls_Set_OUn__UNIV__left_0,axiom,
c_union(c_UNIV,X1,X2) = c_UNIV,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).
cnf(cls_Set_OCompl__UNIV__eq_0,axiom,
c_uminus(c_UNIV,tc_set(X1)) = c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
cnf(i_0_29,axiom,
( c_in(X1,X3,X4)
| ~ c_in(X1,c_inter(X2,X3,X4),X4) ),
cls_Set_OInt__iff_1 ).
cnf(i_0_30,axiom,
c_Relation_OImage(c_Relation_Odiag(X1,X2),X3,X2,X2) = c_inter(X1,X3,X2),
cls_Relation_OImage__diag_0 ).
cnf(i_0_31,axiom,
( c_in(c_union(X1,X4,X3),c_Mutil_Otiling(X2,X3),tc_set(X3))
| ~ c_in(X1,X2,tc_set(X3))
| ~ c_in(X4,c_Mutil_Otiling(X2,X3),tc_set(X3))
| c_inter(X1,X4,X3) != c_emptyset ),
cls_Mutil_Otiling_OUn_0 ).
cnf(i_0_32,negated_conjecture,
( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| c_inter(v_t,v_u,t_a) != c_emptyset
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
cls_conjecture_6 ).
cnf(i_0_33,negated_conjecture,
c_inter(c_union(v_a,v_t,t_a),v_u,t_a) = c_emptyset,
cls_conjecture_4 ).
cnf(i_0_34,axiom,
c_minus(X1,c_uminus(X2,tc_set(X3)),tc_set(X3)) = c_inter(X1,X2,X3),
cls_Set_ODiff__Compl_0 ).
cnf(i_0_35,axiom,
c_inter(c_UNIV,X1,X2) = X1,
cls_Set_OInt__UNIV__left_0 ).
cnf(i_0_36,negated_conjecture,
c_inter(v_a,v_t,t_a) = c_emptyset,
cls_conjecture_2 ).
cnf(i_0_37,plain,
( c_in(X1,X3,X4)
| ~ c_in(X1,c_Relation_OImage(c_Relation_Odiag(X2,X4),X3,X4,X4),X4) ),
inference(rw,[status(thm)],[i_0_29,c_0_30]),
[final] ).
cnf(i_0_38,plain,
( c_in(c_union(X1,X4,X3),c_Mutil_Otiling(X2,X3),tc_set(X3))
| c_Relation_OImage(c_Relation_Odiag(X1,X3),X4,X3,X3) != c_emptyset
| ~ c_in(X1,X2,tc_set(X3))
| ~ c_in(X4,c_Mutil_Otiling(X2,X3),tc_set(X3)) ),
inference(rw,[status(thm)],[i_0_31,c_0_30]),
[final] ).
cnf(i_0_39,negated_conjecture,
( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| c_Relation_OImage(c_Relation_Odiag(v_t,t_a),v_u,t_a,t_a) != c_emptyset
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(rw,[status(thm)],[i_0_32,c_0_30]),
[final] ).
cnf(i_0_40,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)),
cls_conjecture_5,
[final] ).
cnf(i_0_41,negated_conjecture,
c_Relation_OImage(c_Relation_Odiag(c_union(v_a,v_t,t_a),t_a),v_u,t_a,t_a) = c_emptyset,
inference(rw,[status(thm)],[i_0_33,c_0_30]),
[final] ).
cnf(i_0_42,plain,
c_minus(X1,c_uminus(X2,tc_set(X3)),tc_set(X3)) = c_Relation_OImage(c_Relation_Odiag(X1,X3),X2,X3,X3),
inference(rw,[status(thm)],[i_0_34,c_0_30]),
[final] ).
cnf(i_0_43,axiom,
( c_lessequals(c_union(X4,X1,X3),X2,tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X4,X2,tc_set(X3)) ),
cls_Set_OUn__subset__iff_2,
[final] ).
cnf(i_0_44,axiom,
( c_lessequals(X1,X4,tc_set(X3))
| ~ c_lessequals(c_union(X1,X2,X3),X4,tc_set(X3)) ),
cls_Set_OUn__subset__iff_0,
[final] ).
cnf(i_0_45,axiom,
( c_lessequals(X2,X4,tc_set(X3))
| ~ c_lessequals(c_union(X1,X2,X3),X4,tc_set(X3)) ),
cls_Set_OUn__subset__iff_1,
[final] ).
cnf(i_0_46,axiom,
c_union(c_union(X1,X2,X3),X4,X3) = c_union(X1,c_union(X2,X4,X3),X3),
cls_Set_OUn__assoc_0,
[final] ).
cnf(i_0_47,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X2),X1,X2,X2) = X1,
inference(rw,[status(thm)],[i_0_35,c_0_30]),
[final] ).
cnf(i_0_48,negated_conjecture,
c_Relation_OImage(c_Relation_Odiag(v_a,t_a),v_t,t_a,t_a) = c_emptyset,
inference(rw,[status(thm)],[i_0_36,c_0_30]),
[final] ).
cnf(i_0_49,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,
[final] ).
cnf(i_0_50,axiom,
c_union(c_minus(X1,X2,tc_set(X3)),X2,X3) = c_union(X1,X2,X3),
cls_Set_OUn__Diff__cancel2_0,
[final] ).
cnf(i_0_51,axiom,
c_union(X1,c_minus(X2,X1,tc_set(X3)),X3) = c_union(X1,X2,X3),
cls_Set_OUn__Diff__cancel_0,
[final] ).
cnf(i_0_52,axiom,
( c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
cls_Set_OsubsetI_0,
[final] ).
cnf(i_0_53,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X2,X1,tc_set(X3)) ),
cls_Set_Osubset__antisym_0,
[final] ).
cnf(i_0_54,axiom,
~ c_in(X1,c_emptyset,X2),
cls_Set_Oempty__iff_0,
[final] ).
cnf(i_0_55,negated_conjecture,
c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
cls_conjecture_3,
[final] ).
cnf(i_0_56,axiom,
c_lessequals(X1,X1,tc_set(X2)),
cls_Set_Osubset__refl_0,
[final] ).
cnf(i_0_57,axiom,
c_uminus(c_uminus(X1,tc_set(X2)),tc_set(X2)) = X1,
cls_Set_Odouble__complement_0,
[final] ).
cnf(i_0_58,axiom,
c_lessequals(c_emptyset,X1,tc_set(X2)),
cls_Set_Oempty__subsetI_0,
[final] ).
cnf(i_0_59,axiom,
c_union(X1,X1,X2) = X1,
cls_Set_OUn__absorb_0,
[final] ).
cnf(i_0_60,negated_conjecture,
c_in(v_a,v_A,tc_set(t_a)),
cls_conjecture_0,
[final] ).
cnf(i_0_61,axiom,
c_union(c_emptyset,X1,X2) = X1,
cls_Set_OUn__empty__left_0,
[final] ).
cnf(i_0_62,axiom,
c_union(X1,c_emptyset,X2) = X1,
cls_Set_OUn__empty__right_0,
[final] ).
cnf(i_0_63,axiom,
c_union(c_UNIV,X1,X2) = c_UNIV,
cls_Set_OUn__UNIV__left_0,
[final] ).
cnf(i_0_64,axiom,
c_uminus(c_UNIV,tc_set(X1)) = c_emptyset,
cls_Set_OCompl__UNIV__eq_0,
[final] ).
cnf(i_0_65,axiom,
X1 = X1 ).
cnf(i_0_66,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_67,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_68,axiom,
( X1 != X2
| c_Relation_OImage(X1,X3,X4,X5) = c_Relation_OImage(X2,X3,X4,X5) ) ).
cnf(i_0_69,axiom,
( X1 != X2
| c_Relation_OImage(X3,X1,X4,X5) = c_Relation_OImage(X3,X2,X4,X5) ) ).
cnf(i_0_70,axiom,
( X1 != X2
| c_Relation_OImage(X3,X4,X1,X5) = c_Relation_OImage(X3,X4,X2,X5) ) ).
cnf(i_0_71,axiom,
( X1 != X2
| c_Relation_OImage(X3,X4,X5,X1) = c_Relation_OImage(X3,X4,X5,X2) ) ).
cnf(i_0_72,axiom,
( X1 != X2
| c_union(X1,X3,X4) = c_union(X2,X3,X4) ) ).
cnf(i_0_73,axiom,
( X1 != X2
| c_union(X3,X1,X4) = c_union(X3,X2,X4) ) ).
cnf(i_0_74,axiom,
( X1 != X2
| c_union(X3,X4,X1) = c_union(X3,X4,X2) ) ).
cnf(i_0_75,axiom,
( X1 != X2
| c_minus(X1,X3,X4) = c_minus(X2,X3,X4) ) ).
cnf(i_0_76,axiom,
( X1 != X2
| c_minus(X3,X1,X4) = c_minus(X3,X2,X4) ) ).
cnf(i_0_77,axiom,
( X1 != X2
| c_minus(X3,X4,X1) = c_minus(X3,X4,X2) ) ).
cnf(i_0_78,axiom,
( X1 != X2
| c_uminus(X1,X3) = c_uminus(X2,X3) ) ).
cnf(i_0_79,axiom,
( X1 != X2
| c_uminus(X3,X1) = c_uminus(X3,X2) ) ).
cnf(i_0_80,axiom,
( X1 != X2
| ~ c_in(X1,X3,X4)
| c_in(X2,X3,X4) ) ).
cnf(i_0_81,axiom,
( X1 != X2
| ~ c_in(X3,X1,X4)
| c_in(X3,X2,X4) ) ).
cnf(i_0_82,axiom,
( X1 != X2
| ~ c_in(X3,X4,X1)
| c_in(X3,X4,X2) ) ).
cnf(i_0_83,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_84,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_85,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_87,plain,
c_lessequals(X1,c_union(X1,X2,X3),tc_set(X3)),
inference(scs_inference,[],[i_0_56,i_0_44]) ).
cnf(i_0_88,plain,
c_lessequals(X1,X1,tc_set(X2)),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_91,plain,
c_lessequals(X1,X1,tc_set(X2)),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_95,plain,
c_union(X1,X1,X2) = X1,
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_97,plain,
c_union(X1,X1,X2) = X1,
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_99,plain,
c_union(X1,X1,X2) = X1,
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_103,plain,
c_union(X1,X1,X2) = X1,
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_107,plain,
c_lessequals(c_emptyset,X1,tc_set(X2)),
inference(rename_variables,[],[i_0_58]) ).
cnf(i_0_123,plain,
c_union(c_emptyset,X1,X2) = X1,
inference(rename_variables,[],[i_0_61]) ).
cnf(i_0_125,plain,
c_union(c_emptyset,X1,X2) = X1,
inference(rename_variables,[],[i_0_61]) ).
cnf(i_0_127,plain,
c_union(c_emptyset,X1,X2) = X1,
inference(rename_variables,[],[i_0_61]) ).
cnf(i_0_129,plain,
c_union(c_emptyset,X1,X2) = X1,
inference(rename_variables,[],[i_0_61]) ).
cnf(i_0_146,plain,
c_union(X1,c_emptyset,X2) = X1,
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_148,plain,
c_union(X1,c_emptyset,X2) = X1,
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_150,plain,
c_union(X1,c_emptyset,X2) = X1,
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_152,plain,
c_union(X1,c_emptyset,X2) = X1,
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_153,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_171,plain,
c_uminus(c_uminus(X1,tc_set(X2)),tc_set(X2)) = X1,
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_173,plain,
c_uminus(c_uminus(X1,tc_set(X2)),tc_set(X2)) = X1,
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_175,plain,
c_uminus(c_uminus(X1,tc_set(X2)),tc_set(X2)) = X1,
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_178,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_203,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_215,plain,
c_lessequals(c_emptyset,X1,tc_set(X2)),
inference(rename_variables,[],[i_0_58]) ).
cnf(i_0_224,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_245,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_264,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_279,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_291,plain,
c_union(c_minus(X1,X2,tc_set(X3)),X2,X3) = c_union(X1,X2,X3),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_293,plain,
c_union(c_minus(X1,X2,tc_set(X3)),X2,X3) = c_union(X1,X2,X3),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_295,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_296,plain,
c_minus(X1,c_uminus(X2,tc_set(X3)),tc_set(X3)) = c_Relation_OImage(c_Relation_Odiag(X1,X3),X2,X3,X3),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_299,plain,
c_union(c_minus(X1,X2,tc_set(X3)),X2,X3) = c_union(X1,X2,X3),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_300,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_320,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_331,plain,
c_union(X1,c_minus(X2,X1,tc_set(X3)),X3) = c_union(X1,X2,X3),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_333,plain,
c_union(X1,c_minus(X2,X1,tc_set(X3)),X3) = c_union(X1,X2,X3),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_338,plain,
c_union(X1,c_minus(X2,X1,tc_set(X3)),X3) = c_union(X1,X2,X3),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_341,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_354,plain,
c_union(c_union(X1,X2,X3),X4,X3) = c_union(X1,c_union(X2,X4,X3),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_361,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_375,plain,
c_minus(X1,c_uminus(X2,tc_set(X3)),tc_set(X3)) = c_Relation_OImage(c_Relation_Odiag(X1,X3),X2,X3,X3),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_378,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_394,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_405,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_412,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_419,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_426,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_434,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_444,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_454,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_464,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_469,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_478,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_483,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_489,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_496,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_501,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_504,plain,
c_UNIV = c_union(c_UNIV,X1,X2),
inference(scs_inference,[],[i_0_63,i_0_66]) ).
cnf(i_0_506,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_512,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_517,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_523,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_535,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_546,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_551,plain,
c_union(X1,X1,X2) = X1,
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_553,plain,
c_union(X1,X1,X2) = X1,
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_555,plain,
c_union(X1,X1,X2) = X1,
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_558,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_561,plain,
c_union(c_uminus(X1,tc_set(X2)),X3,X2) = c_uminus(c_minus(X1,X3,tc_set(X2)),tc_set(X2)),
inference(scs_inference,[],[i_0_49,i_0_66]) ).
cnf(i_0_563,plain,
c_union(c_emptyset,X1,X2) = X1,
inference(rename_variables,[],[i_0_61]) ).
cnf(i_0_565,plain,
c_union(c_emptyset,X1,X2) = X1,
inference(rename_variables,[],[i_0_61]) ).
cnf(i_0_567,plain,
c_union(c_emptyset,X1,X2) = X1,
inference(rename_variables,[],[i_0_61]) ).
cnf(i_0_571,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_576,plain,
c_union(X1,c_emptyset,X2) = X1,
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_578,plain,
c_union(X1,c_emptyset,X2) = X1,
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_580,plain,
c_union(X1,c_emptyset,X2) = X1,
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_583,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_588,plain,
c_uminus(c_uminus(X1,tc_set(X2)),tc_set(X2)) = X1,
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_590,plain,
c_uminus(c_uminus(X1,tc_set(X2)),tc_set(X2)) = X1,
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_595,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_601,plain,
c_union(c_minus(X1,X2,tc_set(X3)),X2,X3) = c_union(X1,X2,X3),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_603,plain,
c_union(c_minus(X1,X2,tc_set(X3)),X2,X3) = c_union(X1,X2,X3),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_606,plain,
c_union(c_minus(X1,X2,tc_set(X3)),X2,X3) = c_union(X1,X2,X3),
inference(rename_variables,[],[i_0_50]) ).
cnf(c_0_589,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(c_union(X4,X1,X3),X2,tc_set(X3)) ),
i_0_45 ).
cnf(c_0_590,plain,
c_UNIV = c_union(c_UNIV,X1,X2),
i_0_504 ).
cnf(c_0_591,axiom,
c_lessequals(X1,X1,tc_set(X2)),
i_0_56 ).
cnf(c_0_592,axiom,
( X1 = X2
| ~ c_lessequals(X2,X1,tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3)) ),
i_0_53 ).
cnf(c_0_593,plain,
c_lessequals(X1,c_union(X1,X2,X3),tc_set(X3)),
i_0_87 ).
cnf(c_0_594,plain,
( c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(c_UNIV,X2,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_589,c_0_590]) ).
cnf(c_0_595,plain,
( c_in(X1,X2,X3)
| ~ c_in(X1,c_Relation_OImage(c_Relation_Odiag(X4,X3),X2,X3,X3),X3) ),
i_0_37 ).
cnf(c_0_596,axiom,
( c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
i_0_52 ).
cnf(c_0_597,plain,
c_lessequals(X1,c_union(X2,X1,X3),tc_set(X3)),
inference(spm,[status(thm)],[c_0_589,c_0_591]) ).
cnf(c_0_598,plain,
( c_union(X1,X2,X3) = X1
| ~ c_lessequals(c_union(X1,X2,X3),X1,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_592,c_0_593]) ).
cnf(c_0_599,axiom,
( c_lessequals(c_union(X1,X2,X3),X4,tc_set(X3))
| ~ c_lessequals(X2,X4,tc_set(X3))
| ~ c_lessequals(X1,X4,tc_set(X3)) ),
i_0_43 ).
cnf(c_0_600,plain,
c_lessequals(X1,c_UNIV,tc_set(X2)),
inference(spm,[status(thm)],[c_0_594,c_0_591]) ).
cnf(c_0_601,axiom,
c_lessequals(c_emptyset,X1,tc_set(X2)),
i_0_58 ).
cnf(c_0_602,axiom,
~ c_in(X1,c_emptyset,X2),
i_0_54 ).
cnf(c_0_603,plain,
( c_lessequals(c_Relation_OImage(c_Relation_Odiag(X1,X2),X3,X2,X2),X4,tc_set(X2))
| c_in(c_Main_OsubsetI__1(c_Relation_OImage(c_Relation_Odiag(X1,X2),X3,X2,X2),X4,X2),X3,X2) ),
inference(spm,[status(thm)],[c_0_595,c_0_596]) ).
cnf(c_0_604,plain,
( c_union(X1,X2,X3) = X2
| ~ c_lessequals(c_union(X1,X2,X3),X2,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_592,c_0_597]) ).
cnf(c_0_605,plain,
( c_union(X1,X2,X3) = X1
| ~ c_lessequals(X2,X1,tc_set(X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_598,c_0_599]),c_0_591])]) ).
cnf(c_0_606,axiom,
c_union(c_union(X1,X2,X3),X4,X3) = c_union(X1,c_union(X2,X4,X3),X3),
i_0_46 ).
cnf(c_0_607,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X2,X1,X1) = X2,
i_0_47 ).
cnf(c_0_608,plain,
c_minus(X1,c_uminus(X2,tc_set(X3)),tc_set(X3)) = c_Relation_OImage(c_Relation_Odiag(X1,X3),X2,X3,X3),
i_0_42 ).
cnf(c_0_609,plain,
( c_UNIV = X1
| ~ c_lessequals(c_UNIV,X1,tc_set(X2)) ),
inference(spm,[status(thm)],[c_0_592,c_0_600]) ).
cnf(c_0_610,plain,
( X1 = c_emptyset
| ~ c_lessequals(X1,c_emptyset,tc_set(X2)) ),
inference(spm,[status(thm)],[c_0_592,c_0_601]) ).
cnf(c_0_611,plain,
c_lessequals(c_Relation_OImage(c_Relation_Odiag(X1,X2),c_emptyset,X2,X2),X3,tc_set(X2)),
inference(spm,[status(thm)],[c_0_602,c_0_603]) ).
cnf(c_0_612,axiom,
c_uminus(c_uminus(X1,tc_set(X2)),tc_set(X2)) = X1,
i_0_57 ).
cnf(c_0_613,axiom,
c_uminus(c_UNIV,tc_set(X1)) = c_emptyset,
i_0_64 ).
cnf(c_0_614,plain,
( c_union(X1,X2,X3) = X2
| ~ c_lessequals(X1,X2,tc_set(X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_604,c_0_599]),c_0_591])]) ).
cnf(c_0_615,plain,
c_union(X1,c_union(X2,X1,X3),X3) = c_union(X1,X2,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_605,c_0_593]),c_0_606]) ).
cnf(c_0_616,axiom,
c_union(X1,c_minus(X2,X1,tc_set(X3)),X3) = c_union(X1,X2,X3),
i_0_51 ).
cnf(c_0_617,plain,
c_minus(c_UNIV,c_uminus(X1,tc_set(X2)),tc_set(X2)) = X1,
inference(spm,[status(thm)],[c_0_607,c_0_608]) ).
cnf(c_0_618,plain,
c_union(X1,c_UNIV,X2) = c_UNIV,
inference(spm,[status(thm)],[c_0_609,c_0_597]) ).
cnf(c_0_619,plain,
c_Relation_OImage(c_Relation_Odiag(X1,X2),c_emptyset,X2,X2) = c_emptyset,
inference(spm,[status(thm)],[c_0_610,c_0_611]) ).
cnf(c_0_620,plain,
c_uminus(c_emptyset,tc_set(X1)) = c_UNIV,
inference(spm,[status(thm)],[c_0_612,c_0_613]) ).
cnf(c_0_621,negated_conjecture,
c_Relation_OImage(c_Relation_Odiag(c_union(v_a,v_t,t_a),t_a),v_u,t_a,t_a) = c_emptyset,
i_0_41 ).
cnf(c_0_622,plain,
c_union(X1,X2,X3) = c_union(X2,X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_614,c_0_597]),c_0_615]) ).
cnf(c_0_623,plain,
c_union(X1,c_union(X2,c_minus(X3,c_union(X1,X2,X4),tc_set(X4)),X4),X4) = c_union(X1,c_union(X2,X3,X4),X4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_616,c_0_606]),c_0_606]) ).
cnf(c_0_624,plain,
c_union(c_uminus(X1,tc_set(X2)),X1,X2) = c_UNIV,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_616,c_0_617]),c_0_618]) ).
cnf(c_0_625,plain,
c_minus(X1,c_UNIV,tc_set(X2)) = c_emptyset,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_608,c_0_619]),c_0_620]) ).
cnf(c_0_626,axiom,
c_union(X1,c_emptyset,X2) = X1,
i_0_62 ).
cnf(c_0_627,plain,
c_union(c_uminus(X1,tc_set(X2)),c_Relation_OImage(c_Relation_Odiag(X3,X2),X1,X2,X2),X2) = c_union(c_uminus(X1,tc_set(X2)),X3,X2),
inference(spm,[status(thm)],[c_0_616,c_0_608]) ).
cnf(c_0_628,negated_conjecture,
c_Relation_OImage(c_Relation_Odiag(c_union(v_t,v_a,t_a),t_a),v_u,t_a,t_a) = c_emptyset,
inference(rw,[status(thm)],[c_0_621,c_0_622]) ).
cnf(c_0_629,plain,
c_union(c_uminus(X1,tc_set(X2)),c_union(X1,X3,X2),X2) = c_UNIV,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_623,c_0_624]),c_0_625]),c_0_626]),c_0_624]) ).
cnf(c_0_630,plain,
c_union(c_uminus(X1,tc_set(X2)),X3,X2) = c_uminus(c_minus(X1,X3,tc_set(X2)),tc_set(X2)),
i_0_561 ).
cnf(c_0_631,plain,
c_union(X1,c_union(c_minus(X2,X1,tc_set(X3)),X4,X3),X3) = c_union(X1,c_union(X2,X4,X3),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_606,c_0_616]),c_0_606]) ).
cnf(c_0_632,negated_conjecture,
c_union(v_t,c_union(v_a,c_uminus(v_u,tc_set(t_a)),t_a),t_a) = c_uminus(v_u,tc_set(t_a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_627,c_0_628]),c_0_626]),c_0_622]),c_0_606]) ).
cnf(c_0_633,plain,
c_union(c_uminus(X1,tc_set(X2)),c_union(X3,c_union(X1,X4,X2),X2),X2) = c_UNIV,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_629,c_0_630]),c_0_606]),c_0_631]) ).
cnf(c_0_634,negated_conjecture,
c_union(v_a,c_uminus(v_u,tc_set(t_a)),t_a) = c_uminus(v_u,tc_set(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_604,c_0_632]),c_0_597])]) ).
cnf(c_0_635,plain,
c_union(X1,c_union(X2,X3,X4),X4) = c_union(X2,c_union(X3,X1,X4),X4),
inference(spm,[status(thm)],[c_0_606,c_0_622]) ).
cnf(c_0_636,negated_conjecture,
c_union(c_uminus(v_u,tc_set(t_a)),c_union(c_uminus(v_a,tc_set(t_a)),X1,t_a),t_a) = c_UNIV,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_633,c_0_634]),c_0_635]) ).
cnf(c_0_637,plain,
c_uminus(c_Relation_OImage(c_Relation_Odiag(X1,X2),X3,X2,X2),tc_set(X2)) = c_union(c_uminus(X1,tc_set(X2)),c_uminus(X3,tc_set(X2)),X2),
inference(spm,[status(thm)],[c_0_630,c_0_608]) ).
cnf(c_0_638,negated_conjecture,
c_Relation_OImage(c_Relation_Odiag(v_a,t_a),v_t,t_a,t_a) = c_emptyset,
i_0_48 ).
cnf(c_0_639,plain,
c_uminus(c_Relation_OImage(c_Relation_Odiag(v_u,t_a),v_a,t_a,t_a),tc_set(t_a)) = c_UNIV,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_615,c_0_636]),c_0_637]) ).
cnf(c_0_640,negated_conjecture,
c_union(v_a,c_uminus(v_t,tc_set(t_a)),t_a) = c_uminus(v_t,tc_set(t_a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_627,c_0_638]),c_0_626]),c_0_622]) ).
cnf(c_0_641,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_612,c_0_630]) ).
cnf(c_0_642,plain,
c_Relation_OImage(c_Relation_Odiag(v_u,t_a),v_a,t_a,t_a) = c_emptyset,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_612,c_0_639]),c_0_613]) ).
cnf(c_0_643,axiom,
c_union(X1,X1,X2) = X1,
i_0_59 ).
cnf(c_0_644,negated_conjecture,
c_union(c_uminus(v_t,tc_set(t_a)),c_union(c_uminus(v_a,tc_set(t_a)),X1,t_a),t_a) = c_UNIV,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_633,c_0_640]),c_0_635]) ).
cnf(c_0_645,plain,
c_union(X1,c_union(X2,c_uminus(X1,tc_set(X3)),X3),X3) = c_UNIV,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_615,c_0_629]),c_0_606]),c_0_618]),c_0_618]),c_0_606]) ).
cnf(c_0_646,plain,
c_minus(X1,c_union(X2,c_uminus(X1,tc_set(X3)),X3),tc_set(X3)) = c_minus(X1,X2,tc_set(X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_641,c_0_615]),c_0_641]) ).
cnf(c_0_647,plain,
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_627,c_0_642]),c_0_626]),c_0_622]) ).
cnf(c_0_648,plain,
c_minus(X1,c_uminus(X1,tc_set(X2)),tc_set(X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_641,c_0_643]),c_0_612]) ).
cnf(c_0_649,plain,
c_uminus(c_Relation_OImage(c_Relation_Odiag(v_t,t_a),v_a,t_a,t_a),tc_set(t_a)) = c_UNIV,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_615,c_0_644]),c_0_637]) ).
cnf(c_0_650,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)),
i_0_40 ).
cnf(c_0_651,axiom,
c_union(c_minus(X1,X2,tc_set(X3)),X2,X3) = c_union(X1,X2,X3),
i_0_50 ).
cnf(c_0_652,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_641,c_0_645]),c_0_613]),c_0_612]) ).
cnf(c_0_653,plain,
c_minus(X1,c_union(c_uminus(X2,tc_set(X3)),X4,X3),tc_set(X3)) = c_Relation_OImage(c_Relation_Odiag(X1,X3),c_minus(X2,X4,tc_set(X3)),X3,X3),
inference(spm,[status(thm)],[c_0_608,c_0_630]) ).
cnf(c_0_654,plain,
c_minus(c_minus(X1,X2,tc_set(X3)),X4,tc_set(X3)) = c_minus(X1,c_union(X2,X4,X3),tc_set(X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_641,c_0_630]),c_0_606]),c_0_641]) ).
cnf(c_0_655,plain,
c_minus(v_a,v_u,tc_set(t_a)) = v_a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_646,c_0_647]),c_0_648]) ).
cnf(c_0_656,plain,
c_Relation_OImage(c_Relation_Odiag(v_t,t_a),v_a,t_a,t_a) = c_emptyset,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_612,c_0_649]),c_0_613]) ).
cnf(c_0_657,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_650,c_0_606]) ).
cnf(c_0_658,plain,
( c_in(c_union(X1,X2,X3),c_Mutil_Otiling(X4,X3),tc_set(X3))
| c_Relation_OImage(c_Relation_Odiag(X1,X3),X2,X3,X3) != c_emptyset
| ~ c_in(X1,X4,tc_set(X3))
| ~ c_in(X2,c_Mutil_Otiling(X4,X3),tc_set(X3)) ),
i_0_38 ).
cnf(c_0_659,negated_conjecture,
c_in(v_a,v_A,tc_set(t_a)),
i_0_60 ).
cnf(c_0_660,negated_conjecture,
( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| c_Relation_OImage(c_Relation_Odiag(v_t,t_a),v_u,t_a,t_a) != c_emptyset
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
i_0_39 ).
cnf(c_0_661,negated_conjecture,
c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
i_0_55 ).
cnf(c_0_662,plain,
c_union(X1,c_uminus(X1,tc_set(X2)),X2) = c_UNIV,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_651,c_0_617]),c_0_590]) ).
cnf(c_0_663,plain,
c_Relation_OImage(c_Relation_Odiag(X1,X2),c_minus(X3,X1,tc_set(X2)),X2,X2) = c_emptyset,
inference(spm,[status(thm)],[c_0_652,c_0_653]) ).
cnf(c_0_664,plain,
c_minus(v_a,c_union(v_u,X1,t_a),tc_set(t_a)) = c_minus(v_a,X1,tc_set(t_a)),
inference(spm,[status(thm)],[c_0_654,c_0_655]) ).
cnf(c_0_665,plain,
c_union(v_t,c_uminus(v_a,tc_set(t_a)),t_a) = c_uminus(v_a,tc_set(t_a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_627,c_0_656]),c_0_626]),c_0_622]) ).
cnf(c_0_666,negated_conjecture,
( c_Relation_OImage(c_Relation_Odiag(v_a,t_a),c_union(v_t,v_u,t_a),t_a,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)],[inference(spm,[status(thm)],[c_0_657,c_0_658]),c_0_659])]) ).
cnf(c_0_667,negated_conjecture,
( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| c_Relation_OImage(c_Relation_Odiag(v_t,t_a),v_u,t_a,t_a) != c_emptyset ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_660,c_0_661])]) ).
cnf(c_0_668,plain,
c_union(X1,c_union(c_uminus(X1,tc_set(X2)),X3,X2),X2) = c_UNIV,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_623,c_0_662]),c_0_625]),c_0_626]),c_0_662]) ).
cnf(c_0_669,plain,
c_Relation_OImage(c_Relation_Odiag(c_union(v_u,X1,t_a),t_a),c_minus(v_a,X1,tc_set(t_a)),t_a,t_a) = c_emptyset,
inference(spm,[status(thm)],[c_0_663,c_0_664]) ).
cnf(c_0_670,plain,
c_minus(v_a,v_t,tc_set(t_a)) = v_a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_646,c_0_665]),c_0_648]) ).
cnf(c_0_671,negated_conjecture,
( c_Relation_OImage(c_Relation_Odiag(v_a,t_a),c_union(v_t,v_u,t_a),t_a,t_a) != c_emptyset
| c_Relation_OImage(c_Relation_Odiag(v_t,t_a),v_u,t_a,t_a) != c_emptyset ),
inference(spm,[status(thm)],[c_0_666,c_0_667]) ).
cnf(c_0_672,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_641,c_0_668]),c_0_613]),c_0_612]) ).
cnf(c_0_673,plain,
c_union(c_uminus(X1,tc_set(X2)),c_uminus(c_Relation_OImage(c_Relation_Odiag(X3,X2),X1,X2,X2),tc_set(X2)),X2) = c_union(c_uminus(X1,tc_set(X2)),c_uminus(X3,tc_set(X2)),X2),
inference(spm,[status(thm)],[c_0_615,c_0_637]) ).
cnf(c_0_674,plain,
c_Relation_OImage(c_Relation_Odiag(c_union(v_u,v_t,t_a),t_a),v_a,t_a,t_a) = c_emptyset,
inference(spm,[status(thm)],[c_0_669,c_0_670]) ).
cnf(c_0_675,negated_conjecture,
( c_Relation_OImage(c_Relation_Odiag(v_a,t_a),c_union(v_u,v_t,t_a),t_a,t_a) != c_emptyset
| c_Relation_OImage(c_Relation_Odiag(v_t,t_a),v_u,t_a,t_a) != c_emptyset ),
inference(rw,[status(thm)],[c_0_671,c_0_622]) ).
cnf(c_0_676,plain,
c_Relation_OImage(c_Relation_Odiag(v_t,t_a),v_u,t_a,t_a) = c_emptyset,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_672,c_0_632]),c_0_608]) ).
cnf(c_0_677,plain,
c_uminus(c_Relation_OImage(c_Relation_Odiag(v_a,t_a),c_union(v_u,v_t,t_a),t_a,t_a),tc_set(t_a)) = c_UNIV,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_673,c_0_674]),c_0_620]),c_0_618]),c_0_637]) ).
cnf(c_0_678,negated_conjecture,
c_Relation_OImage(c_Relation_Odiag(v_a,t_a),c_union(v_u,v_t,t_a),t_a,t_a) != c_emptyset,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_675,c_0_676])]) ).
cnf(c_0_679,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_612,c_0_677]),c_0_613]),c_0_678]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : PUZ064-2 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.31 % Computer : n010.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.31 % WCLimit : 300
% 0.14/0.31 % DateTime : Tue May 5 01:35:06 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 268.86/126.01 % Version : CSE_E---1.7
% 268.86/126.01 % Problem : theBenchmark.p
% 268.86/126.01 % SZS status Unsatisfiable for theBenchmark.p
% 268.86/126.01 % SZS output start CNFRefutation
% See solution above
% 271.55/128.69 % Total time : 123.532s
%------------------------------------------------------------------------------