%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : PUZ064-1 : 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 : n020.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 48.48s 28.84s
% Output : CNFRefutation 48.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of clauses : 59 ( 34 unt; 0 nHn; 46 RR)
% Number of literals : 100 ( 39 equ; 48 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 : 14 ( 14 usr; 6 con; 0-4 aty)
% Number of variables : 103 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',cls_Mutil_Otiling_OUn_0) ).
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/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Relation_OImage__diag_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/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Set_ODiff__Compl_0) ).
cnf(cls_Set_OCompl__Un_0,axiom,
c_uminus(c_union(X1,X2,X3),tc_set(X3)) = c_inter(c_uminus(X1,tc_set(X3)),c_uminus(X2,tc_set(X3)),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Set_OCompl__Un_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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
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_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_Odouble__complement_0,axiom,
c_uminus(c_uminus(X1,tc_set(X2)),tc_set(X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Set_Odouble__complement_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_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_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(cls_Set_OInt__subset__iff_2,axiom,
( c_lessequals(X1,c_inter(X4,X2,X3),tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X1,X4,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Set_OInt__subset__iff_2) ).
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_Set_ODiff__eq__empty__iff_0,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| c_minus(X1,X2,tc_set(X3)) != c_emptyset ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Set_ODiff__eq__empty__iff_0) ).
cnf(cls_Set_ODiff__eq__empty__iff_1,axiom,
( c_minus(X1,X2,tc_set(X3)) = c_emptyset
| ~ c_lessequals(X1,X2,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Set_ODiff__eq__empty__iff_1) ).
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/sandbox2/benchmark/Axioms/MSC001-1.ax',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/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Set_OUn__subset__iff_1) ).
cnf(c_0_17,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_18,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_19,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_20,axiom,
c_uminus(c_union(X1,X2,X3),tc_set(X3)) = c_inter(c_uminus(X1,tc_set(X3)),c_uminus(X2,tc_set(X3)),X3),
cls_Set_OCompl__Un_0 ).
cnf(c_0_21,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_22,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_23,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_24,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_17,c_0_18]) ).
cnf(c_0_25,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_19,c_0_18]) ).
cnf(c_0_26,plain,
c_uminus(c_union(X1,X2,X3),tc_set(X3)) = c_Relation_OImage(c_Relation_Odiag(c_uminus(X1,tc_set(X3)),X3),c_uminus(X2,tc_set(X3)),X3,X3),
inference(rw,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_27,axiom,
c_uminus(c_uminus(X1,tc_set(X2)),tc_set(X2)) = X1,
cls_Set_Odouble__complement_0 ).
cnf(c_0_28,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_21,c_0_18]) ).
cnf(c_0_29,negated_conjecture,
c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
cls_conjecture_3 ).
cnf(c_0_30,negated_conjecture,
c_inter(c_union(v_a,v_t,t_a),v_u,t_a) = c_emptyset,
cls_conjecture_4 ).
cnf(c_0_31,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_22,c_0_23]) ).
cnf(c_0_32,plain,
( c_in(c_union(X1,X2,X3),c_Mutil_Otiling(X4,X3),tc_set(X3))
| c_minus(X1,c_uminus(X2,tc_set(X3)),tc_set(X3)) != c_emptyset
| ~ c_in(X2,c_Mutil_Otiling(X4,X3),tc_set(X3))
| ~ c_in(X1,X4,tc_set(X3)) ),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,plain,
c_uminus(c_union(X1,X2,X3),tc_set(X3)) = c_minus(c_uminus(X1,tc_set(X3)),X2,tc_set(X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_25]),c_0_27]) ).
cnf(c_0_34,negated_conjecture,
c_in(v_a,v_A,tc_set(t_a)),
cls_conjecture_0 ).
cnf(c_0_35,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_28,c_0_29])]) ).
cnf(c_0_36,axiom,
( c_lessequals(X1,c_inter(X4,X2,X3),tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X1,X4,tc_set(X3)) ),
cls_Set_OInt__subset__iff_2 ).
cnf(c_0_37,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_30,c_0_18]) ).
cnf(c_0_38,negated_conjecture,
c_inter(v_a,v_t,t_a) = c_emptyset,
cls_conjecture_2 ).
cnf(c_0_39,negated_conjecture,
( c_minus(v_a,c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34])]) ).
cnf(c_0_40,negated_conjecture,
( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| c_minus(v_t,c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) != c_emptyset ),
inference(rw,[status(thm)],[c_0_35,c_0_25]) ).
cnf(c_0_41,plain,
( c_lessequals(X1,c_Relation_OImage(c_Relation_Odiag(X4,X3),X2,X3,X3),tc_set(X3))
| ~ c_lessequals(X1,X4,tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3)) ),
inference(rw,[status(thm)],[c_0_36,c_0_18]) ).
cnf(c_0_42,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| c_minus(X1,X2,tc_set(X3)) != c_emptyset ),
cls_Set_ODiff__eq__empty__iff_0 ).
cnf(c_0_43,negated_conjecture,
c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) = c_emptyset,
inference(rw,[status(thm)],[c_0_37,c_0_25]) ).
cnf(c_0_44,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_38,c_0_18]) ).
cnf(c_0_45,negated_conjecture,
( c_minus(v_a,c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)) != c_emptyset
| c_minus(v_t,c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) != c_emptyset ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,axiom,
( c_minus(X1,X2,tc_set(X3)) = c_emptyset
| ~ c_lessequals(X1,X2,tc_set(X3)) ),
cls_Set_ODiff__eq__empty__iff_1 ).
cnf(c_0_47,plain,
( c_lessequals(X1,c_minus(X2,c_uminus(X3,tc_set(X4)),tc_set(X4)),tc_set(X4))
| ~ c_lessequals(X1,X2,tc_set(X4))
| ~ c_lessequals(X1,X3,tc_set(X4)) ),
inference(rw,[status(thm)],[c_0_41,c_0_25]) ).
cnf(c_0_48,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_49,negated_conjecture,
c_lessequals(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,negated_conjecture,
c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) = c_emptyset,
inference(rw,[status(thm)],[c_0_44,c_0_25]) ).
cnf(c_0_51,negated_conjecture,
( c_minus(v_t,c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) != c_emptyset
| ~ c_lessequals(v_a,c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,plain,
( c_lessequals(X1,c_minus(X2,X3,tc_set(X4)),tc_set(X4))
| ~ c_lessequals(X1,c_uminus(X3,tc_set(X4)),tc_set(X4))
| ~ c_lessequals(X1,X2,tc_set(X4)) ),
inference(spm,[status(thm)],[c_0_47,c_0_27]) ).
cnf(c_0_53,negated_conjecture,
c_lessequals(v_a,c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,negated_conjecture,
c_lessequals(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),
inference(spm,[status(thm)],[c_0_42,c_0_50]) ).
cnf(c_0_55,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_56,negated_conjecture,
c_minus(v_t,c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) != c_emptyset,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_54])]) ).
cnf(c_0_57,negated_conjecture,
c_lessequals(v_t,c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),
inference(spm,[status(thm)],[c_0_55,c_0_49]) ).
cnf(c_0_58,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_46]),c_0_57])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ064-1 : 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
% 0.15/0.33 % Computer : n020.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:35:35 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 48.48/28.84 % Version : CSE_E---1.7
% 48.48/28.84 % Problem : theBenchmark.p
% 48.48/28.84 % SZS status Unsatisfiable for theBenchmark.p
% 48.48/28.84 % SZS output start CNFRefutation
% See solution above
% 48.71/29.05 % Total time : 21.612s
%------------------------------------------------------------------------------