TSTP Solution File: PUZ064-2 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : PUZ064-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n003.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 : Thu Aug 31 13:12:28 EDT 2023
% Result : Unsatisfiable 8.55s 8.66s
% Output : CNFRefutation 8.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 46
% Syntax : Number of formulae : 143 ( 88 unt; 18 typ; 0 def)
% Number of atoms : 177 ( 88 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 109 ( 57 ~; 52 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 11 >; 18 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-4 aty)
% Number of variables : 253 ( 50 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
v_a: $i ).
tff(decl_23,type,
v_A: $i ).
tff(decl_24,type,
t_a: $i ).
tff(decl_25,type,
tc_set: $i > $i ).
tff(decl_26,type,
c_in: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
v_t: $i ).
tff(decl_28,type,
c_inter: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
c_emptyset: $i ).
tff(decl_30,type,
v_u: $i ).
tff(decl_31,type,
c_Mutil_Otiling: ( $i * $i ) > $i ).
tff(decl_32,type,
c_union: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
c_Relation_Odiag: ( $i * $i ) > $i ).
tff(decl_34,type,
c_Relation_OImage: ( $i * $i * $i * $i ) > $i ).
tff(decl_35,type,
c_minus: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
c_uminus: ( $i * $i ) > $i ).
tff(decl_37,type,
c_UNIV: $i ).
tff(decl_38,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_39,type,
c_Main_OsubsetI__1: ( $i * $i * $i ) > $i ).
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_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_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_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_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_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_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_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_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_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_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_Oempty__iff_0,axiom,
~ c_in(X1,c_emptyset,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__iff_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_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(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_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_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_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_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_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_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_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_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_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(c_0_28,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 ).
cnf(c_0_29,axiom,
c_lessequals(X1,X1,tc_set(X2)),
cls_Set_Osubset__refl_0 ).
cnf(c_0_30,axiom,
c_union(c_UNIV,X1,X2) = c_UNIV,
cls_Set_OUn__UNIV__left_0 ).
cnf(c_0_31,axiom,
( c_in(X1,X3,X4)
| ~ c_in(X1,c_inter(X2,X3,X4),X4) ),
cls_Set_OInt__iff_1 ).
cnf(c_0_32,axiom,
c_Relation_OImage(c_Relation_Odiag(X1,X2),X3,X2,X2) = c_inter(X1,X3,X2),
cls_Relation_OImage__diag_0 ).
cnf(c_0_33,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 ).
cnf(c_0_34,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X2,X1,tc_set(X3)) ),
cls_Set_Osubset__antisym_0 ).
cnf(c_0_35,plain,
c_lessequals(X1,c_union(X2,X1,X3),tc_set(X3)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
( c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(c_UNIV,X2,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_28,c_0_30]) ).
cnf(c_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)],[c_0_31,c_0_32]) ).
cnf(c_0_38,axiom,
( c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
cls_Set_OsubsetI_0 ).
cnf(c_0_39,plain,
c_lessequals(X1,c_union(X1,X2,X3),tc_set(X3)),
inference(spm,[status(thm)],[c_0_33,c_0_29]) ).
cnf(c_0_40,plain,
( c_union(X1,X2,X3) = X2
| ~ c_lessequals(c_union(X1,X2,X3),X2,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,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 ).
cnf(c_0_42,axiom,
c_inter(c_UNIV,X1,X2) = X1,
cls_Set_OInt__UNIV__left_0 ).
cnf(c_0_43,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_44,plain,
c_lessequals(X1,c_UNIV,tc_set(X2)),
inference(spm,[status(thm)],[c_0_36,c_0_29]) ).
cnf(c_0_45,axiom,
c_lessequals(c_emptyset,X1,tc_set(X2)),
cls_Set_Oempty__subsetI_0 ).
cnf(c_0_46,axiom,
~ c_in(X1,c_emptyset,X2),
cls_Set_Oempty__iff_0 ).
cnf(c_0_47,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_37,c_0_38]) ).
cnf(c_0_48,plain,
( c_union(X1,X2,X3) = X1
| ~ c_lessequals(c_union(X1,X2,X3),X1,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_34,c_0_39]) ).
cnf(c_0_49,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_40,c_0_41]),c_0_29])]) ).
cnf(c_0_50,plain,
c_Relation_OImage(c_Relation_Odiag(c_UNIV,X2),X1,X2,X2) = X1,
inference(rw,[status(thm)],[c_0_42,c_0_32]) ).
cnf(c_0_51,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)],[c_0_43,c_0_32]) ).
cnf(c_0_52,plain,
( c_UNIV = X1
| ~ c_lessequals(c_UNIV,X1,tc_set(X2)) ),
inference(spm,[status(thm)],[c_0_34,c_0_44]) ).
cnf(c_0_53,plain,
( X1 = c_emptyset
| ~ c_lessequals(X1,c_emptyset,tc_set(X2)) ),
inference(spm,[status(thm)],[c_0_34,c_0_45]) ).
cnf(c_0_54,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_46,c_0_47]) ).
cnf(c_0_55,axiom,
c_uminus(c_uminus(X1,tc_set(X2)),tc_set(X2)) = X1,
cls_Set_Odouble__complement_0 ).
cnf(c_0_56,axiom,
c_uminus(c_UNIV,tc_set(X1)) = c_emptyset,
cls_Set_OCompl__UNIV__eq_0 ).
cnf(c_0_57,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_58,negated_conjecture,
c_inter(c_union(v_a,v_t,t_a),v_u,t_a) = c_emptyset,
cls_conjecture_4 ).
cnf(c_0_59,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_48,c_0_41]),c_0_29])]) ).
cnf(c_0_60,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_61,plain,
c_union(X1,c_union(X2,X1,X3),X3) = c_union(X2,X1,X3),
inference(spm,[status(thm)],[c_0_49,c_0_35]) ).
cnf(c_0_62,plain,
c_minus(c_UNIV,c_uminus(X1,tc_set(X2)),tc_set(X2)) = X1,
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_63,plain,
c_union(X1,c_UNIV,X2) = c_UNIV,
inference(spm,[status(thm)],[c_0_52,c_0_35]) ).
cnf(c_0_64,plain,
c_Relation_OImage(c_Relation_Odiag(X1,X2),c_emptyset,X2,X2) = c_emptyset,
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_65,plain,
c_uminus(c_emptyset,tc_set(X1)) = c_UNIV,
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_66,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_57,c_0_51]) ).
cnf(c_0_67,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)],[c_0_58,c_0_32]) ).
cnf(c_0_68,axiom,
c_union(X1,c_emptyset,X2) = X1,
cls_Set_OUn__empty__right_0 ).
cnf(c_0_69,plain,
c_union(X1,X2,X3) = c_union(X2,X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_39]),c_0_60]),c_0_61]) ).
cnf(c_0_70,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_57,c_0_60]),c_0_60]) ).
cnf(c_0_71,plain,
c_union(c_uminus(X1,tc_set(X2)),X1,X2) = c_UNIV,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_62]),c_0_63]) ).
cnf(c_0_72,plain,
c_minus(X1,c_UNIV,tc_set(X2)) = c_emptyset,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_64]),c_0_65]) ).
cnf(c_0_73,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_69]),c_0_69]),c_0_60]) ).
cnf(c_0_74,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_75,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_70,c_0_71]),c_0_72]),c_0_68]),c_0_71]) ).
cnf(c_0_76,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_40,c_0_73]),c_0_35])]) ).
cnf(c_0_77,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_78,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_55,c_0_74]) ).
cnf(c_0_79,negated_conjecture,
c_union(c_uminus(v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a) = c_UNIV,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_69]) ).
cnf(c_0_80,plain,
c_union(X1,c_uminus(X1,tc_set(X2)),X2) = c_UNIV,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_62]),c_0_30]) ).
cnf(c_0_81,negated_conjecture,
c_Relation_OImage(c_Relation_Odiag(v_u,t_a),v_a,t_a,t_a) = c_emptyset,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_56]),c_0_51]) ).
cnf(c_0_82,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(c_0_83,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_70,c_0_80]),c_0_72]),c_0_68]),c_0_80]) ).
cnf(c_0_84,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_81]),c_0_68]),c_0_69]) ).
cnf(c_0_85,negated_conjecture,
c_inter(v_a,v_t,t_a) = c_emptyset,
cls_conjecture_2 ).
cnf(c_0_86,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 ).
cnf(c_0_87,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(c_0_88,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)],[c_0_82,c_0_32]) ).
cnf(c_0_89,negated_conjecture,
c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
cls_conjecture_3 ).
cnf(c_0_90,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_78,c_0_83]),c_0_56]),c_0_55]) ).
cnf(c_0_91,plain,
( c_union(X1,c_union(X2,X3,X4),X4) = X3
| ~ c_lessequals(X1,X3,tc_set(X4))
| ~ c_lessequals(X2,X3,tc_set(X4)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_41]),c_0_60]) ).
cnf(c_0_92,negated_conjecture,
( c_lessequals(v_u,X1,tc_set(t_a))
| ~ c_lessequals(c_uminus(v_a,tc_set(t_a)),X1,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_33,c_0_84]) ).
cnf(c_0_93,axiom,
c_union(X1,X1,X2) = X1,
cls_Set_OUn__absorb_0 ).
cnf(c_0_94,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_74,c_0_51]) ).
cnf(c_0_95,negated_conjecture,
c_Relation_OImage(c_Relation_Odiag(v_a,t_a),v_t,t_a,t_a) = c_emptyset,
inference(rw,[status(thm)],[c_0_85,c_0_32]) ).
cnf(c_0_96,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_86,c_0_60]) ).
cnf(c_0_97,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)],[c_0_87,c_0_32]) ).
cnf(c_0_98,negated_conjecture,
c_in(v_a,v_A,tc_set(t_a)),
cls_conjecture_0 ).
cnf(c_0_99,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_88,c_0_89])]) ).
cnf(c_0_100,plain,
( c_minus(X1,X2,tc_set(X3)) = c_emptyset
| ~ c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X4,X2,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_101,plain,
c_union(X1,c_union(X2,c_union(X1,X3,X4),X4),X4) = c_union(X2,c_union(X1,X3,X4),X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_60]),c_0_60]) ).
cnf(c_0_102,negated_conjecture,
c_lessequals(v_u,c_union(X1,c_uminus(v_a,tc_set(t_a)),t_a),tc_set(t_a)),
inference(spm,[status(thm)],[c_0_92,c_0_35]) ).
cnf(c_0_103,plain,
c_union(X1,c_union(X1,X2,X3),X3) = c_union(X1,X2,X3),
inference(spm,[status(thm)],[c_0_60,c_0_93]) ).
cnf(c_0_104,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)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_65]),c_0_69]) ).
cnf(c_0_105,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_96,c_0_97]),c_0_98])]) ).
cnf(c_0_106,negated_conjecture,
( c_in(c_union(v_u,v_t,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(rw,[status(thm)],[c_0_99,c_0_69]) ).
cnf(c_0_107,negated_conjecture,
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_90,c_0_73]),c_0_51]) ).
cnf(c_0_108,plain,
( c_minus(X1,X2,tc_set(X3)) = c_emptyset
| ~ c_lessequals(X1,X2,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_100,c_0_45]) ).
cnf(c_0_109,plain,
c_minus(X1,c_union(X2,c_union(c_uminus(X1,tc_set(X3)),X4,X3),X3),tc_set(X3)) = c_uminus(c_union(X2,c_union(c_uminus(X1,tc_set(X3)),X4,X3),X3),tc_set(X3)),
inference(spm,[status(thm)],[c_0_78,c_0_101]) ).
cnf(c_0_110,negated_conjecture,
c_union(v_u,c_union(X1,c_uminus(v_a,tc_set(t_a)),t_a),t_a) = c_union(X1,c_uminus(v_a,tc_set(t_a)),t_a),
inference(spm,[status(thm)],[c_0_49,c_0_102]) ).
cnf(c_0_111,plain,
c_minus(X1,c_union(c_uminus(X1,tc_set(X2)),X3,X2),tc_set(X2)) = c_minus(X1,X3,tc_set(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_103]),c_0_78]) ).
cnf(c_0_112,plain,
c_uminus(c_union(X1,c_uminus(X2,tc_set(X3)),X3),tc_set(X3)) = c_minus(X2,X1,tc_set(X3)),
inference(spm,[status(thm)],[c_0_78,c_0_69]) ).
cnf(c_0_113,plain,
c_lessequals(c_union(X1,X2,X3),c_union(X1,c_union(X2,X4,X3),X3),tc_set(X3)),
inference(spm,[status(thm)],[c_0_39,c_0_60]) ).
cnf(c_0_114,negated_conjecture,
c_Relation_OImage(c_Relation_Odiag(v_t,t_a),v_a,t_a,t_a) = c_emptyset,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_104]),c_0_56]),c_0_51]) ).
cnf(c_0_115,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_in(c_union(v_u,v_t,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_69]),c_0_69]) ).
cnf(c_0_116,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)],[c_0_106,c_0_107])]) ).
cnf(c_0_117,plain,
( c_Relation_OImage(c_Relation_Odiag(X1,X2),X3,X2,X2) = c_emptyset
| ~ c_lessequals(X1,c_uminus(X3,tc_set(X2)),tc_set(X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_108]) ).
cnf(c_0_118,negated_conjecture,
c_Relation_OImage(c_Relation_Odiag(X1,t_a),v_a,t_a,t_a) = c_Relation_OImage(c_Relation_Odiag(v_a,t_a),X1,t_a,t_a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_111]),c_0_51]),c_0_112]),c_0_51]) ).
cnf(c_0_119,negated_conjecture,
c_lessequals(c_union(X1,v_u,t_a),c_union(X1,c_uminus(v_a,tc_set(t_a)),t_a),tc_set(t_a)),
inference(spm,[status(thm)],[c_0_113,c_0_84]) ).
cnf(c_0_120,negated_conjecture,
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_66,c_0_114]),c_0_68]),c_0_69]) ).
cnf(c_0_121,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_115,c_0_116])]) ).
cnf(c_0_122,negated_conjecture,
( c_Relation_OImage(c_Relation_Odiag(v_a,t_a),X1,t_a,t_a) = c_emptyset
| ~ c_lessequals(X1,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_123,negated_conjecture,
c_lessequals(c_union(v_u,v_t,t_a),c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_69]) ).
cnf(c_0_124,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : PUZ064-2 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 22:20:54 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 8.55/8.66 % Version : CSE_E---1.5
% 8.55/8.66 % Problem : theBenchmark.p
% 8.55/8.66 % Proof found
% 8.55/8.66 % SZS status Theorem for theBenchmark.p
% 8.55/8.66 % SZS output start Proof
% See solution above
% 8.55/8.67 % Total time : 8.090000 s
% 8.55/8.67 % SZS output end Proof
% 8.55/8.67 % Total time : 8.094000 s
%------------------------------------------------------------------------------