%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET085-7 : TPTP v9.2.1. Bugfixed v2.1.0.
% 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 : n012.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 05:07:14 PM UTC 2026
% Result : Unsatisfiable 1.41s 1.72s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 32 ( 16 unt; 5 nHn; 21 RR)
% Number of literals : 50 ( 21 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 30 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_singleton_in_unordered_pair3_1,negated_conjecture,
unordered_pair(y,z) = singleton(x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_1) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(only_member_in_singleton,axiom,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).
cnf(unordered_pair3,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
cnf(unordered_pair_equals_singleton1,axiom,
( member(X1,universal_class)
| unordered_pair(X2,X1) = singleton(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_equals_singleton1) ).
cnf(prove_singleton_in_unordered_pair3_4,negated_conjecture,
x != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_4) ).
cnf(unordered_pair2,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
cnf(prove_singleton_in_unordered_pair3_3,negated_conjecture,
x != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_3) ).
cnf(null_unordered_pair,axiom,
( unordered_pair(X1,X2) = null_class
| member(X1,universal_class)
| member(X2,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_unordered_pair) ).
cnf(corollary_to_unordered_pair_axiom2,axiom,
( ~ member(X1,universal_class)
| unordered_pair(X2,X1) != null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom2) ).
cnf(prove_singleton_in_unordered_pair3_2,negated_conjecture,
member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_2) ).
cnf(c_0_11,negated_conjecture,
unordered_pair(y,z) = singleton(x),
prove_singleton_in_unordered_pair3_1 ).
cnf(c_0_12,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_13,axiom,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
only_member_in_singleton ).
cnf(c_0_14,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
unordered_pair3 ).
cnf(c_0_15,negated_conjecture,
unordered_pair(x,x) = unordered_pair(y,z),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,axiom,
( member(X1,universal_class)
| unordered_pair(X2,X1) = singleton(X2) ),
unordered_pair_equals_singleton1 ).
cnf(c_0_17,plain,
( X1 = X2
| ~ member(X1,unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_18,negated_conjecture,
( member(z,unordered_pair(x,x))
| ~ member(z,universal_class) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
x != z,
prove_singleton_in_unordered_pair3_4 ).
cnf(c_0_20,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2 ).
cnf(c_0_21,plain,
( unordered_pair(X2,X1) = unordered_pair(X2,X2)
| member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_16,c_0_12]) ).
cnf(c_0_22,negated_conjecture,
~ member(z,universal_class),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( member(y,unordered_pair(x,x))
| ~ member(y,universal_class) ),
inference(spm,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_24,negated_conjecture,
x != y,
prove_singleton_in_unordered_pair3_3 ).
cnf(c_0_25,axiom,
( unordered_pair(X1,X2) = null_class
| member(X1,universal_class)
| member(X2,universal_class) ),
null_unordered_pair ).
cnf(c_0_26,negated_conjecture,
unordered_pair(y,y) = unordered_pair(x,x),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_21]),c_0_22]) ).
cnf(c_0_27,negated_conjecture,
~ member(y,universal_class),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_23]),c_0_24]) ).
cnf(c_0_28,axiom,
( ~ member(X1,universal_class)
| unordered_pair(X2,X1) != null_class ),
corollary_to_unordered_pair_axiom2 ).
cnf(c_0_29,negated_conjecture,
unordered_pair(x,x) = null_class,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_30,negated_conjecture,
member(x,universal_class),
prove_singleton_in_unordered_pair3_2 ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SET085-7 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.08 % 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
% 0.08/0.26 % Computer : n012.cluster.edu
% 0.08/0.26 % Model : x86_64 x86_64
% 0.08/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.26 % Memory : 8042.1875MB
% 0.08/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.26 % CPULimit : 300
% 0.08/0.26 % WCLimit : 300
% 0.08/0.26 % DateTime : Tue May 5 02:09:46 EDT 2026
% 0.08/0.27 % CPUTime :
% 0.08/0.27 % start to proof: theBenchmark
% 1.41/1.72 % Version : CSE_E---1.7
% 1.41/1.72 % Problem : theBenchmark.p
% 1.41/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.41/1.72 % SZS output start CNFRefutation
% See solution above
% 1.41/1.72 % Total time : 1.362s
%------------------------------------------------------------------------------