%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET517-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% 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 : n015.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 05:07:57 PM UTC 2026
% Result : Unsatisfiable 1.43s 1.79s
% Output : CNFRefutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of clauses : 43 ( 17 unt; 15 nHn; 30 RR)
% Number of literals : 77 ( 37 equ; 21 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_not_singleton_of_set_1,negated_conjecture,
singleton(member_of(x)) = x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_not_singleton_of_set_1) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(prove_not_singleton_of_set_2,negated_conjecture,
member_of(x) = x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_not_singleton_of_set_2) ).
cnf(unordered_pair_member,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(regularity2,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
cnf(unordered_pairs_in_universal,axiom,
member(unordered_pair(X1,X2),universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
cnf(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(unordered_pair3,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(c_0_11,negated_conjecture,
singleton(member_of(x)) = x,
prove_not_singleton_of_set_1 ).
cnf(c_0_12,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_13,negated_conjecture,
unordered_pair(member_of(x),member_of(x)) = x,
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,negated_conjecture,
member_of(x) = x,
prove_not_singleton_of_set_2 ).
cnf(c_0_15,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_16,negated_conjecture,
unordered_pair(x,x) = x,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_14]) ).
cnf(c_0_17,negated_conjecture,
( X1 = x
| ~ member(X1,x) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_19,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_20,negated_conjecture,
( regular(x) = x
| x = null_class ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,axiom,
member(unordered_pair(X1,X2),universal_class),
unordered_pairs_in_universal ).
cnf(c_0_22,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_23,negated_conjecture,
( intersection(x,x) = null_class
| x = null_class ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
unordered_pair3 ).
cnf(c_0_25,negated_conjecture,
member(x,universal_class),
inference(spm,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_26,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_27,negated_conjecture,
( x = null_class
| member(X1,null_class)
| ~ member(X1,x) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
member(x,x),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_16]),c_0_25])]) ).
cnf(c_0_29,plain,
( X1 = null_class
| member(X2,X1)
| ~ member(X2,null_class) ),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_30,negated_conjecture,
( x = null_class
| member(x,null_class) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_32,negated_conjecture,
( x = null_class
| X1 = null_class
| member(x,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( complement(X1) = null_class
| x = null_class
| ~ member(x,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_34,negated_conjecture,
( complement(null_class) = null_class
| x = null_class ),
inference(spm,[status(thm)],[c_0_33,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
( x = null_class
| ~ member(X1,null_class) ),
inference(spm,[status(thm)],[c_0_31,c_0_34]) ).
cnf(c_0_36,negated_conjecture,
x = null_class,
inference(spm,[status(thm)],[c_0_35,c_0_30]) ).
cnf(c_0_37,negated_conjecture,
member(null_class,null_class),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_36]),c_0_36]) ).
cnf(c_0_38,negated_conjecture,
( X1 = null_class
| member(null_class,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_37]) ).
cnf(c_0_39,negated_conjecture,
( complement(X1) = null_class
| ~ member(null_class,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_38]) ).
cnf(c_0_40,negated_conjecture,
complement(null_class) = null_class,
inference(spm,[status(thm)],[c_0_39,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
~ member(X1,null_class),
inference(spm,[status(thm)],[c_0_31,c_0_40]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_37,c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET517-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% 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
% 0.17/0.33 % Computer : n015.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 02:25:47 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 1.43/1.79 % Version : CSE_E---1.7
% 1.43/1.79 % Problem : theBenchmark.p
% 1.43/1.79 % SZS status Unsatisfiable for theBenchmark.p
% 1.43/1.79 % SZS output start CNFRefutation
% See solution above
% 1.43/1.79 % Total time : 1.372s
%------------------------------------------------------------------------------