%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET860-2 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.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 05:08:50 PM UTC 2026
% Result : Unsatisfiable 156.13s 119.43s
% Output : CNFRefutation 160.86s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 77)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_OUnE_0,axiom,
( c_in(X1,X3,X4)
| c_in(X1,X2,X4)
| ~ c_in(X1,c_union(X2,X3,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).
cnf(cls_Set_OIntI_0,axiom,
( c_in(X1,c_inter(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).
cnf(cls_Set_OsubsetI_1,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
cnf(cls_Set_OinsertE_0,axiom,
( c_in(X1,X3,X4)
| X1 = X2
| ~ c_in(X1,c_insert(X2,X3,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
cnf(cls_Set_OIntE_1,axiom,
( c_in(X1,X2,X4)
| ~ c_in(X1,c_inter(X2,X3,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).
cnf(cls_Set_OIntE_0,axiom,
( c_in(X1,X3,X4)
| ~ c_in(X1,c_inter(X2,X3,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).
cnf(cls_Set_OUnionE_0,axiom,
( c_in(c_Main_OUnionE__1(X1,X2,X3),X2,tc_set(X3))
| ~ c_in(X1,c_Union(X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
cnf(cls_Set_OUnionE_1,axiom,
( c_in(X1,c_Main_OUnionE__1(X1,X2,X3),X3)
| ~ c_in(X1,c_Union(X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
cnf(cls_Set_OCompl__subset__Compl__iff__iff1_0,axiom,
( c_lessequals(X3,X1,tc_set(X2))
| ~ c_lessequals(c_uminus(X1,tc_set(X2)),c_uminus(X3,tc_set(X2)),tc_set(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff1_0) ).
cnf(cls_Set_OUnionI_0,axiom,
( c_in(X1,c_Union(X4,X3),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X2,X4,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
cnf(cls_Set_OinsertCI_0,axiom,
( c_in(X1,c_insert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
cnf(cls_Set_OUnCI_0,axiom,
( c_in(X1,c_union(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).
cnf(cls_Set_OsubsetD_0,axiom,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
cnf(cls_Set_OCompl__subset__Compl__iff__iff2_0,axiom,
( c_lessequals(c_uminus(X2,tc_set(X3)),c_uminus(X1,tc_set(X3)),tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff2_0) ).
cnf(cls_Set_OComplD__dest_0,axiom,
( ~ c_in(X1,X2,X3)
| ~ c_in(X1,c_uminus(X2,tc_set(X3)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplD__dest_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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
cnf(cls_conjecture_2,negated_conjecture,
( c_lessequals(v_B,X1,tc_set(t_a))
| c_lessequals(X1,v_A,tc_set(t_a))
| ~ c_in(X1,v_C,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
cnf(cls_Set_OinsertCI_1,axiom,
c_in(X1,c_insert(X1,X2,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
cnf(cls_Set_OComplI_0,axiom,
( c_in(X1,X2,X3)
| c_in(X1,c_uminus(X2,tc_set(X3)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_lessequals(c_Union(v_C,t_a),v_A,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
~ c_lessequals(v_B,c_Union(v_C,t_a),tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_Set_OemptyE_0,axiom,
~ c_in(X1,c_emptyset,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
cnf(cls_Set_OUNIV__I_0,axiom,
c_in(X1,c_UNIV,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
cnf(i_0_24,axiom,
( c_in(X1,X3,X4)
| c_in(X1,X2,X4)
| ~ c_in(X1,c_union(X2,X3,X4),X4) ),
cls_Set_OUnE_0,
[final] ).
cnf(i_0_25,axiom,
( c_in(X1,c_inter(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
cls_Set_OIntI_0,
[final] ).
cnf(i_0_26,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
cls_Set_OsubsetI_1,
[final] ).
cnf(i_0_27,axiom,
( c_in(X1,X3,X4)
| X1 = X2
| ~ c_in(X1,c_insert(X2,X3,X4),X4) ),
cls_Set_OinsertE_0,
[final] ).
cnf(i_0_28,axiom,
( c_in(X1,X2,X4)
| ~ c_in(X1,c_inter(X2,X3,X4),X4) ),
cls_Set_OIntE_1,
[final] ).
cnf(i_0_29,axiom,
( c_in(X1,X3,X4)
| ~ c_in(X1,c_inter(X2,X3,X4),X4) ),
cls_Set_OIntE_0,
[final] ).
cnf(i_0_30,axiom,
( c_in(c_Main_OUnionE__1(X1,X2,X3),X2,tc_set(X3))
| ~ c_in(X1,c_Union(X2,X3),X3) ),
cls_Set_OUnionE_0,
[final] ).
cnf(i_0_31,axiom,
( c_in(X1,c_Main_OUnionE__1(X1,X2,X3),X3)
| ~ c_in(X1,c_Union(X2,X3),X3) ),
cls_Set_OUnionE_1,
[final] ).
cnf(i_0_32,axiom,
( c_lessequals(X3,X1,tc_set(X2))
| ~ c_lessequals(c_uminus(X1,tc_set(X2)),c_uminus(X3,tc_set(X2)),tc_set(X2)) ),
cls_Set_OCompl__subset__Compl__iff__iff1_0,
[final] ).
cnf(i_0_33,axiom,
( c_in(X1,c_Union(X4,X3),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X2,X4,tc_set(X3)) ),
cls_Set_OUnionI_0,
[final] ).
cnf(i_0_34,axiom,
( c_in(X1,c_insert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
cls_Set_OinsertCI_0,
[final] ).
cnf(i_0_35,axiom,
( c_in(X1,c_union(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
cls_Set_OUnCI_0,
[final] ).
cnf(i_0_36,axiom,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_set(X3)) ),
cls_Set_OsubsetD_0,
[final] ).
cnf(i_0_37,axiom,
( c_lessequals(c_uminus(X2,tc_set(X3)),c_uminus(X1,tc_set(X3)),tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3)) ),
cls_Set_OCompl__subset__Compl__iff__iff2_0,
[final] ).
cnf(i_0_38,axiom,
( ~ c_in(X1,X2,X3)
| ~ c_in(X1,c_uminus(X2,tc_set(X3)),X3) ),
cls_Set_OComplD__dest_0,
[final] ).
cnf(i_0_39,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_40,negated_conjecture,
( c_lessequals(v_B,X1,tc_set(t_a))
| c_lessequals(X1,v_A,tc_set(t_a))
| ~ c_in(X1,v_C,tc_set(t_a)) ),
cls_conjecture_2,
[final] ).
cnf(i_0_41,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_42,axiom,
c_in(X1,c_insert(X1,X2,X3),X3),
cls_Set_OinsertCI_1,
[final] ).
cnf(i_0_43,axiom,
( c_in(X1,X2,X3)
| c_in(X1,c_uminus(X2,tc_set(X3)),X3) ),
cls_Set_OComplI_0,
[final] ).
cnf(i_0_44,negated_conjecture,
~ c_lessequals(c_Union(v_C,t_a),v_A,tc_set(t_a)),
cls_conjecture_0,
[final] ).
cnf(i_0_45,negated_conjecture,
~ c_lessequals(v_B,c_Union(v_C,t_a),tc_set(t_a)),
cls_conjecture_1,
[final] ).
cnf(i_0_46,axiom,
~ c_in(X1,c_emptyset,X2),
cls_Set_OemptyE_0,
[final] ).
cnf(i_0_47,axiom,
c_in(X1,c_UNIV,X2),
cls_Set_OUNIV__I_0,
[final] ).
cnf(i_0_48,axiom,
X1 = X1 ).
cnf(i_0_49,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_50,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_51,axiom,
( X1 != X2
| ~ c_in(X1,X3,X4)
| c_in(X2,X3,X4) ) ).
cnf(i_0_52,axiom,
( X1 != X2
| ~ c_in(X3,X1,X4)
| c_in(X3,X2,X4) ) ).
cnf(i_0_53,axiom,
( X1 != X2
| ~ c_in(X3,X4,X1)
| c_in(X3,X4,X2) ) ).
cnf(i_0_54,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_55,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_56,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_57,plain,
c_lessequals(X1,c_UNIV,tc_set(X2)),
inference(scs_inference,[],[i_0_47,i_0_26]) ).
cnf(i_0_58,plain,
c_in(X1,c_UNIV,X2),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_60,plain,
c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),c_Union(v_C,t_a),t_a),
inference(scs_inference,[],[i_0_44,i_0_47,i_0_26,i_0_39]) ).
cnf(i_0_62,plain,
~ c_in(c_Union(v_C,t_a),v_C,tc_set(t_a)),
inference(scs_inference,[],[i_0_44,i_0_45,i_0_47,i_0_26,i_0_39,i_0_40]) ).
cnf(i_0_65,plain,
c_in(X1,c_UNIV,X2),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_68,plain,
~ c_in(X1,c_emptyset,X2),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_83,plain,
c_in(c_Main_OsubsetI__1(v_B,c_Union(v_C,t_a),t_a),v_B,t_a),
inference(scs_inference,[],[i_0_45,i_0_39]) ).
cnf(i_0_109,plain,
~ c_in(X1,c_emptyset,X2),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_130,plain,
c_in(X1,c_UNIV,X2),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_134,plain,
c_in(X1,c_insert(X1,X2,X3),X3),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_137,plain,
~ c_in(X1,c_emptyset,X2),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_151,plain,
~ c_in(X1,c_emptyset,X2),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_156,plain,
c_in(X1,c_insert(X1,X2,X3),X3),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_160,plain,
~ c_in(X1,c_emptyset,X2),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_174,plain,
c_in(X1,c_Union(c_insert(c_UNIV,X2,tc_set(X3)),X3),X3),
inference(scs_inference,[],[i_0_47,i_0_42,i_0_33]) ).
cnf(i_0_175,plain,
c_in(X1,c_insert(X1,X2,X3),X3),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_205,plain,
c_in(X1,c_insert(X1,X2,X3),X3),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_208,plain,
~ c_in(X1,c_emptyset,X2),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_212,plain,
~ c_in(X1,c_emptyset,X2),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_214,plain,
~ c_in(X1,c_emptyset,X2),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_216,plain,
~ c_in(X1,c_emptyset,X2),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_222,plain,
~ c_in(X1,c_emptyset,X2),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_228,plain,
~ c_in(X1,c_emptyset,X2),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_236,plain,
~ c_in(X1,c_emptyset,X2),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_268,plain,
~ c_in(X1,c_emptyset,X2),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_273,plain,
~ c_in(X1,c_emptyset,X2),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_281,plain,
~ c_in(X1,c_emptyset,X2),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_2393,plain,
c_in(X1,c_UNIV,X2),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_64,plain,
c_in(X1,c_Union(c_UNIV,X2),X2),
inference(scs_inference,[],[i_0_44,i_0_45,i_0_47,i_0_58,i_0_42,i_0_26,i_0_39,i_0_40,i_0_33]) ).
cnf(i_0_67,plain,
c_UNIV != c_emptyset,
inference(scs_inference,[],[i_0_44,i_0_45,i_0_46,i_0_47,i_0_58,i_0_65,i_0_42,i_0_26,i_0_39,i_0_40,i_0_33,i_0_52]) ).
cnf(i_0_69,plain,
c_UNIV != v_A,
inference(scs_inference,[],[i_0_44,i_0_45,i_0_46,i_0_47,i_0_58,i_0_65,i_0_42,i_0_26,i_0_39,i_0_40,i_0_33,i_0_52,i_0_55]) ).
cnf(i_0_70,plain,
c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),v_C,tc_set(t_a)),
inference(scs_inference,[],[i_0_44,i_0_45,i_0_46,i_0_47,i_0_58,i_0_65,i_0_42,i_0_26,i_0_39,i_0_40,i_0_33,i_0_52,i_0_55,i_0_30]) ).
cnf(i_0_72,plain,
c_in(X1,c_Main_OUnionE__1(X1,c_UNIV,X2),X2),
inference(scs_inference,[],[i_0_44,i_0_45,i_0_46,i_0_47,i_0_58,i_0_65,i_0_42,i_0_26,i_0_39,i_0_40,i_0_33,i_0_52,i_0_55,i_0_30,i_0_31]) ).
cnf(i_0_76,plain,
c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a) != c_Union(v_C,t_a),
inference(scs_inference,[],[i_0_44,i_0_45,i_0_46,i_0_47,i_0_58,i_0_65,i_0_42,i_0_26,i_0_39,i_0_40,i_0_33,i_0_52,i_0_55,i_0_30,i_0_31,i_0_41,i_0_51]) ).
cnf(i_0_89,plain,
c_lessequals(X1,c_UNIV,tc_set(X2)),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_97,plain,
c_lessequals(X1,c_UNIV,tc_set(X2)),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_129,plain,
c_UNIV != v_C,
inference(scs_inference,[],[i_0_62,i_0_47,i_0_52]) ).
cnf(i_0_143,plain,
c_lessequals(X1,c_UNIV,tc_set(X2)),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_169,plain,
c_lessequals(X1,c_UNIV,tc_set(X2)),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_184,plain,
c_lessequals(X1,c_UNIV,tc_set(X2)),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_197,plain,
c_lessequals(X1,c_UNIV,tc_set(X2)),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_211,plain,
v_B != c_emptyset,
inference(scs_inference,[],[i_0_83,i_0_46,i_0_52]) ).
cnf(i_0_251,plain,
~ c_in(c_Union(v_C,t_a),c_inter(v_C,X1,tc_set(t_a)),tc_set(t_a)),
inference(scs_inference,[],[i_0_62,i_0_28]) ).
cnf(i_0_253,plain,
~ c_in(c_Union(v_C,t_a),c_inter(X1,v_C,tc_set(t_a)),tc_set(t_a)),
inference(scs_inference,[],[i_0_62,i_0_28,i_0_29]) ).
cnf(i_0_286,plain,
c_lessequals(X1,c_UNIV,tc_set(X2)),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_340,plain,
c_lessequals(X1,c_UNIV,tc_set(X2)),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_620,plain,
c_lessequals(X1,c_UNIV,tc_set(X2)),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_80,plain,
~ c_lessequals(c_Union(v_C,t_a),v_A,tc_set(t_a)),
inference(equality_inference,[],[77]) ).
cnf(i_0_81,plain,
~ c_in(c_Union(v_C,t_a),v_C,tc_set(t_a)),
inference(equality_inference,[],[78]) ).
cnf(i_0_82,plain,
~ c_lessequals(c_Union(v_C,t_a),v_A,tc_set(t_a)),
inference(equality_inference,[],[79]) ).
cnf(i_0_85,plain,
c_lessequals(X1,c_Union(c_UNIV,X2),tc_set(X2)),
inference(scs_inference,[],[i_0_45,i_0_64,i_0_39,i_0_26]) ).
cnf(i_0_86,plain,
c_in(X1,c_Union(c_UNIV,X2),X2),
inference(rename_variables,[],[i_0_64]) ).
cnf(i_0_88,plain,
c_Union(c_UNIV,X1) = c_UNIV,
inference(scs_inference,[],[i_0_45,i_0_64,i_0_57,i_0_39,i_0_26,i_0_41]) ).
cnf(i_0_92,plain,
c_in(X1,c_Union(c_UNIV,X2),X2),
inference(rename_variables,[],[i_0_64]) ).
cnf(i_0_95,plain,
c_in(X1,c_Main_OUnionE__1(X1,c_UNIV,X2),X2),
inference(rename_variables,[],[i_0_72]) ).
cnf(i_0_119,plain,
c_Union(c_UNIV,tc_set(t_a)) != v_C,
inference(scs_inference,[],[i_0_62,i_0_64,i_0_52]) ).
cnf(i_0_120,plain,
c_in(X1,c_Union(c_UNIV,X2),X2),
inference(rename_variables,[],[i_0_64]) ).
cnf(i_0_133,plain,
c_in(X1,c_Union(c_insert(c_Union(c_UNIV,X2),X3,tc_set(X2)),X2),X2),
inference(scs_inference,[],[i_0_64,i_0_42,i_0_33]) ).
cnf(i_0_136,plain,
c_Union(c_UNIV,X1) != c_emptyset,
inference(scs_inference,[],[i_0_46,i_0_64,i_0_42,i_0_33,i_0_52]) ).
cnf(i_0_138,plain,
c_in(X1,c_Main_OUnionE__1(X1,c_insert(c_Union(c_UNIV,X2),X3,tc_set(X2)),X2),X2),
inference(scs_inference,[],[i_0_46,i_0_64,i_0_42,i_0_33,i_0_52,i_0_31]) ).
cnf(i_0_140,plain,
c_lessequals(X1,c_Union(c_insert(c_Union(c_UNIV,X2),X3,tc_set(X2)),X2),tc_set(X2)),
inference(scs_inference,[],[i_0_46,i_0_64,i_0_42,i_0_33,i_0_52,i_0_31,i_0_26]) ).
cnf(i_0_142,plain,
c_Union(c_insert(c_Union(c_UNIV,X1),X2,tc_set(X1)),X1) = c_UNIV,
inference(scs_inference,[],[i_0_46,i_0_64,i_0_57,i_0_42,i_0_33,i_0_52,i_0_31,i_0_26,i_0_41]) ).
cnf(i_0_146,plain,
c_UNIV = c_Union(c_insert(c_Union(c_UNIV,X1),X2,tc_set(X1)),X1),
inference(scs_inference,[],[i_0_46,i_0_64,i_0_57,i_0_42,i_0_33,i_0_52,i_0_31,i_0_26,i_0_41,i_0_50,i_0_49]) ).
cnf(i_0_150,plain,
v_C != c_emptyset,
inference(scs_inference,[],[i_0_46,i_0_70,i_0_52]) ).
cnf(i_0_152,plain,
c_in(X1,c_Union(c_Main_OUnionE__1(c_insert(X1,X2,X3),c_UNIV,tc_set(X3)),X3),X3),
inference(scs_inference,[],[i_0_42,i_0_72,i_0_33]) ).
cnf(i_0_153,plain,
c_in(X1,c_Main_OUnionE__1(X1,c_UNIV,X2),X2),
inference(rename_variables,[],[i_0_72]) ).
cnf(i_0_155,plain,
c_insert(c_Union(v_C,t_a),X1,tc_set(t_a)) != v_C,
inference(scs_inference,[],[i_0_42,i_0_62,i_0_72,i_0_33,i_0_52]) ).
cnf(i_0_161,plain,
c_in(X1,c_Union(c_Main_OUnionE__1(c_UNIV,c_UNIV,tc_set(X2)),X2),X2),
inference(scs_inference,[],[i_0_47,i_0_72,i_0_33]) ).
cnf(i_0_162,plain,
c_in(X1,c_Main_OUnionE__1(X1,c_UNIV,X2),X2),
inference(rename_variables,[],[i_0_72]) ).
cnf(i_0_164,plain,
c_in(X1,c_Main_OUnionE__1(X1,c_Main_OUnionE__1(c_UNIV,c_UNIV,tc_set(X2)),X2),X2),
inference(scs_inference,[],[i_0_47,i_0_72,i_0_33,i_0_31]) ).
cnf(i_0_166,plain,
c_lessequals(X1,c_Union(c_Main_OUnionE__1(c_UNIV,c_UNIV,tc_set(X2)),X2),tc_set(X2)),
inference(scs_inference,[],[i_0_47,i_0_72,i_0_33,i_0_31,i_0_26]) ).
cnf(i_0_168,plain,
c_Union(c_Main_OUnionE__1(c_UNIV,c_UNIV,tc_set(X1)),X1) = c_UNIV,
inference(scs_inference,[],[i_0_47,i_0_57,i_0_72,i_0_33,i_0_31,i_0_26,i_0_41]) ).
cnf(i_0_172,plain,
c_UNIV = c_Union(c_Main_OUnionE__1(c_UNIV,c_UNIV,tc_set(X1)),X1),
inference(scs_inference,[],[i_0_47,i_0_57,i_0_72,i_0_33,i_0_31,i_0_26,i_0_41,i_0_50,i_0_49]) ).
cnf(i_0_189,plain,
c_in(X1,c_Union(c_Main_OUnionE__1(c_Union(c_UNIV,X2),c_UNIV,tc_set(X2)),X2),X2),
inference(scs_inference,[],[i_0_64,i_0_72,i_0_33]) ).
cnf(i_0_190,plain,
c_in(X1,c_Main_OUnionE__1(X1,c_UNIV,X2),X2),
inference(rename_variables,[],[i_0_72]) ).
cnf(i_0_192,plain,
c_in(X1,c_Main_OUnionE__1(X1,c_Main_OUnionE__1(c_Union(c_UNIV,X2),c_UNIV,tc_set(X2)),X2),X2),
inference(scs_inference,[],[i_0_64,i_0_72,i_0_33,i_0_31]) ).
cnf(i_0_194,plain,
c_lessequals(X1,c_Union(c_Main_OUnionE__1(c_Union(c_UNIV,X2),c_UNIV,tc_set(X2)),X2),tc_set(X2)),
inference(scs_inference,[],[i_0_64,i_0_72,i_0_33,i_0_31,i_0_26]) ).
cnf(i_0_196,plain,
c_Union(c_Main_OUnionE__1(c_Union(c_UNIV,X1),c_UNIV,tc_set(X1)),X1) = c_UNIV,
inference(scs_inference,[],[i_0_64,i_0_57,i_0_72,i_0_33,i_0_31,i_0_26,i_0_41]) ).
cnf(i_0_200,plain,
c_UNIV = c_Union(c_Main_OUnionE__1(c_Union(c_UNIV,X1),c_UNIV,tc_set(X1)),X1),
inference(scs_inference,[],[i_0_64,i_0_57,i_0_72,i_0_33,i_0_31,i_0_26,i_0_41,i_0_50,i_0_49]) ).
cnf(i_0_204,plain,
c_in(X1,c_Union(c_insert(c_Main_OUnionE__1(X1,c_UNIV,X2),X3,tc_set(X2)),X2),X2),
inference(scs_inference,[],[i_0_72,i_0_42,i_0_33]) ).
cnf(i_0_207,plain,
c_Main_OUnionE__1(X1,c_UNIV,X2) != c_emptyset,
inference(scs_inference,[],[i_0_72,i_0_46,i_0_42,i_0_33,i_0_52]) ).
cnf(i_0_209,plain,
c_in(X1,c_Main_OUnionE__1(X1,c_insert(c_Main_OUnionE__1(X1,c_UNIV,X2),X3,tc_set(X2)),X2),X2),
inference(scs_inference,[],[i_0_72,i_0_46,i_0_42,i_0_33,i_0_52,i_0_31]) ).
cnf(i_0_354,plain,
~ c_in(c_Union(v_C,t_a),c_inter(c_inter(v_C,X1,tc_set(t_a)),X2,tc_set(t_a)),tc_set(t_a)),
inference(scs_inference,[],[i_0_251,i_0_28]) ).
cnf(i_0_356,plain,
~ c_in(c_Union(v_C,t_a),c_inter(X1,c_inter(v_C,X2,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(scs_inference,[],[i_0_251,i_0_28,i_0_29]) ).
cnf(i_0_91,plain,
c_in(X1,c_Union(c_Union(c_UNIV,tc_set(X2)),X2),X2),
inference(scs_inference,[],[i_0_45,i_0_72,i_0_64,i_0_86,i_0_57,i_0_39,i_0_26,i_0_41,i_0_33]) ).
cnf(i_0_94,plain,
c_Main_OUnionE__1(c_Union(v_C,t_a),c_UNIV,tc_set(t_a)) != v_C,
inference(scs_inference,[],[i_0_62,i_0_45,i_0_72,i_0_64,i_0_86,i_0_57,i_0_39,i_0_26,i_0_41,i_0_33,i_0_52]) ).
cnf(i_0_96,plain,
c_UNIV != c_Union(v_C,t_a),
inference(scs_inference,[],[i_0_62,i_0_45,i_0_72,i_0_64,i_0_86,i_0_57,i_0_89,i_0_39,i_0_26,i_0_41,i_0_33,i_0_52,i_0_55]) ).
cnf(i_0_98,plain,
~ c_lessequals(c_UNIV,c_Union(v_C,t_a),tc_set(t_a)),
inference(scs_inference,[],[i_0_62,i_0_45,i_0_72,i_0_64,i_0_86,i_0_57,i_0_89,i_0_39,i_0_26,i_0_41,i_0_33,i_0_52,i_0_55,i_0_74]) ).
cnf(i_0_99,plain,
c_UNIV = c_Union(c_UNIV,X1),
inference(scs_inference,[],[i_0_62,i_0_45,i_0_72,i_0_64,i_0_86,i_0_57,i_0_89,i_0_39,i_0_26,i_0_41,i_0_33,i_0_52,i_0_55,i_0_74,i_0_49]) ).
cnf(i_0_111,plain,
c_lessequals(X1,c_Union(c_UNIV,X2),tc_set(X2)),
inference(rename_variables,[],[i_0_85]) ).
cnf(i_0_121,plain,
c_Union(c_UNIV,t_a) != c_Union(v_C,t_a),
inference(scs_inference,[],[i_0_62,i_0_45,i_0_64,i_0_85,i_0_52,i_0_55]) ).
cnf(i_0_122,plain,
c_lessequals(X1,c_Union(c_UNIV,X2),tc_set(X2)),
inference(rename_variables,[],[i_0_85]) ).
cnf(i_0_147,plain,
c_Union(c_insert(c_Union(c_UNIV,X1),X2,tc_set(X1)),X1) = c_UNIV,
inference(equality_inference,[],[145]) ).
cnf(i_0_148,plain,
c_Union(c_UNIV,X1) = c_Union(c_insert(c_Union(c_UNIV,X2),X3,tc_set(X2)),X2),
inference(scs_inference,[],[i_0_88,i_0_146,i_0_50]) ).
cnf(i_0_149,plain,
c_Union(c_insert(c_Union(c_UNIV,X1),X2,tc_set(X1)),X1) = c_Union(c_UNIV,X3),
inference(scs_inference,[],[i_0_88,i_0_146,i_0_50,i_0_49]) ).
cnf(i_0_157,plain,
c_in(X1,c_Main_OUnionE__1(X1,c_Main_OUnionE__1(c_insert(X1,X2,X3),c_UNIV,tc_set(X3)),X3),X3),
inference(scs_inference,[],[i_0_152,i_0_31]) ).
cnf(i_0_159,plain,
c_insert(X1,X2,X3) != c_emptyset,
inference(scs_inference,[],[i_0_42,i_0_46,i_0_152,i_0_31,i_0_52]) ).
cnf(i_0_173,plain,
c_Union(c_Main_OUnionE__1(c_UNIV,c_UNIV,tc_set(X1)),X1) = c_UNIV,
inference(equality_inference,[],[171]) ).
cnf(i_0_177,plain,
c_Union(c_UNIV,X1) = c_Union(c_Main_OUnionE__1(c_UNIV,c_UNIV,tc_set(X2)),X2),
inference(scs_inference,[],[i_0_47,i_0_88,i_0_172,i_0_42,i_0_33,i_0_50]) ).
cnf(i_0_178,plain,
c_in(X1,c_Main_OUnionE__1(X1,c_insert(c_UNIV,X2,tc_set(X3)),X3),X3),
inference(scs_inference,[],[i_0_47,i_0_88,i_0_172,i_0_42,i_0_33,i_0_50,i_0_31]) ).
cnf(i_0_180,plain,
c_lessequals(X1,c_Union(c_insert(c_UNIV,X2,tc_set(X3)),X3),tc_set(X3)),
inference(scs_inference,[],[i_0_47,i_0_88,i_0_172,i_0_42,i_0_33,i_0_50,i_0_31,i_0_26]) ).
cnf(i_0_182,plain,
c_Union(c_Main_OUnionE__1(c_UNIV,c_UNIV,tc_set(X1)),X1) = c_Union(c_UNIV,X2),
inference(scs_inference,[],[i_0_47,i_0_88,i_0_172,i_0_42,i_0_33,i_0_50,i_0_31,i_0_26,i_0_49]) ).
cnf(i_0_183,plain,
c_Union(c_insert(c_UNIV,X1,tc_set(X2)),X2) = c_UNIV,
inference(scs_inference,[],[i_0_47,i_0_88,i_0_57,i_0_172,i_0_42,i_0_33,i_0_50,i_0_31,i_0_26,i_0_49,i_0_41]) ).
cnf(i_0_201,plain,
c_Union(c_Main_OUnionE__1(c_Union(c_UNIV,X1),c_UNIV,tc_set(X1)),X1) = c_UNIV,
inference(equality_inference,[],[199]) ).
cnf(i_0_202,plain,
c_Union(c_UNIV,X1) = c_Union(c_Main_OUnionE__1(c_Union(c_UNIV,X2),c_UNIV,tc_set(X2)),X2),
inference(scs_inference,[],[i_0_88,i_0_200,i_0_50]) ).
cnf(i_0_203,plain,
c_Union(c_Main_OUnionE__1(c_Union(c_UNIV,X1),c_UNIV,tc_set(X1)),X1) = c_Union(c_UNIV,X2),
inference(scs_inference,[],[i_0_88,i_0_200,i_0_50,i_0_49]) ).
cnf(i_0_227,plain,
c_Main_OUnionE__1(X1,c_insert(c_Union(c_UNIV,X2),c_emptyset,tc_set(X2)),X2) = c_Union(c_UNIV,X2),
inference(scs_inference,[],[i_0_46,i_0_133,i_0_30,i_0_27]) ).
cnf(i_0_230,plain,
c_Union(c_UNIV,X1) = c_Main_OUnionE__1(X2,c_insert(c_Union(c_UNIV,X1),c_emptyset,tc_set(X1)),X1),
inference(scs_inference,[],[i_0_46,i_0_133,i_0_30,i_0_27,i_0_49]) ).
cnf(i_0_289,plain,
c_in(X1,c_Main_OUnionE__1(X1,c_insert(c_Main_OUnionE__1(X1,c_UNIV,X2),X3,tc_set(X2)),X2),X2),
inference(rename_variables,[],[i_0_209]) ).
cnf(i_0_291,plain,
c_in(X1,c_Main_OUnionE__1(X1,c_insert(c_Main_OUnionE__1(X1,c_UNIV,X2),X3,tc_set(X2)),X2),X2),
inference(rename_variables,[],[i_0_209]) ).
cnf(i_0_297,plain,
c_in(X1,c_Main_OUnionE__1(X1,c_insert(c_Union(c_UNIV,X2),X3,tc_set(X2)),X2),X2),
inference(rename_variables,[],[i_0_138]) ).
cnf(i_0_1240,plain,
c_lessequals(X1,c_Union(c_insert(c_Union(c_UNIV,X2),X3,tc_set(X2)),X2),tc_set(X2)),
inference(rename_variables,[],[i_0_140]) ).
cnf(i_0_1291,plain,
c_Union(c_UNIV,X1) != c_emptyset,
inference(rename_variables,[],[i_0_136]) ).
cnf(i_0_1329,plain,
c_lessequals(X1,c_Union(c_Main_OUnionE__1(c_UNIV,c_UNIV,tc_set(X2)),X2),tc_set(X2)),
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2125,plain,
c_lessequals(X1,c_Union(c_insert(c_Union(c_UNIV,X2),X3,tc_set(X2)),X2),tc_set(X2)),
inference(rename_variables,[],[i_0_140]) ).
cnf(c_0_94,negated_conjecture,
( c_lessequals(v_B,X1,tc_set(t_a))
| c_lessequals(X1,v_A,tc_set(t_a))
| ~ c_in(X1,v_C,tc_set(t_a)) ),
i_0_40 ).
cnf(c_0_95,plain,
c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),v_C,tc_set(t_a)),
i_0_70 ).
cnf(c_0_96,axiom,
( c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3)
| ~ c_lessequals(X4,X2,tc_set(X3)) ),
i_0_36 ).
cnf(c_0_97,plain,
( c_lessequals(v_B,c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),tc_set(t_a))
| c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),v_A,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_98,plain,
( c_lessequals(v_B,c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),tc_set(t_a))
| c_in(X1,v_A,t_a)
| ~ c_in(X1,c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),t_a) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_99,axiom,
( c_in(X1,c_Main_OUnionE__1(X1,X2,X3),X3)
| ~ c_in(X1,c_Union(X2,X3),X3) ),
i_0_31 ).
cnf(c_0_100,plain,
c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),c_Union(v_C,t_a),t_a),
i_0_60 ).
cnf(c_0_101,plain,
( c_lessequals(v_B,c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_A,t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100])]) ).
cnf(c_0_102,axiom,
( c_in(X1,c_Union(X2,X3),X3)
| ~ c_in(X1,X4,X3)
| ~ c_in(X4,X2,tc_set(X3)) ),
i_0_33 ).
cnf(c_0_103,plain,
( c_in(X1,c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),t_a)
| c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_A,t_a)
| ~ c_in(X1,v_B,t_a) ),
inference(spm,[status(thm)],[c_0_96,c_0_101]) ).
cnf(c_0_104,plain,
c_in(c_Main_OsubsetI__1(v_B,c_Union(v_C,t_a),t_a),v_B,t_a),
i_0_83 ).
cnf(c_0_105,plain,
( c_in(X1,c_Union(v_C,t_a),t_a)
| ~ c_in(X1,c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),t_a) ),
inference(spm,[status(thm)],[c_0_102,c_0_95]) ).
cnf(c_0_106,plain,
( c_in(c_Main_OsubsetI__1(v_B,c_Union(v_C,t_a),t_a),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),t_a)
| c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_A,t_a) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_107,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
i_0_26 ).
cnf(c_0_108,plain,
( c_in(c_Main_OsubsetI__1(v_B,c_Union(v_C,t_a),t_a),c_Union(v_C,t_a),t_a)
| c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_A,t_a) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_109,negated_conjecture,
~ c_lessequals(v_B,c_Union(v_C,t_a),tc_set(t_a)),
i_0_45 ).
cnf(c_0_110,plain,
c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_A,t_a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]) ).
cnf(c_0_111,negated_conjecture,
~ c_lessequals(c_Union(v_C,t_a),v_A,tc_set(t_a)),
i_0_44 ).
cnf(c_0_112,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_110]),c_0_111]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET860-2 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n005.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:38:15 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 156.13/119.43 % Version : CSE_E---1.7
% 156.13/119.43 % Problem : theBenchmark.p
% 156.13/119.43 % SZS status Unsatisfiable for theBenchmark.p
% 156.13/119.43 % SZS output start CNFRefutation
% See solution above
% 160.86/124.17 % Total time : 119.081s
%------------------------------------------------------------------------------