%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET016-3 : TPTP v9.2.1. Released v1.0.0.
% 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 : n004.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 05:06:51 PM UTC 2026
% Result : Unsatisfiable 1.42s 1.77s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 31 ( 24 unt; 4 nHn; 21 RR)
% Number of literals : 42 ( 23 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ordered_pair,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',singleton_set) ).
cnf(non_ordered_pair2,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair2) ).
cnf(equal_ordered_pairs,hypothesis,
ordered_pair(a,c) = ordered_pair(b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_ordered_pairs) ).
cnf(non_ordered_pair4,axiom,
little_set(non_ordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair4) ).
cnf(non_ordered_pair1,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,non_ordered_pair(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair1) ).
cnf(little_set_b,hypothesis,
little_set(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',little_set_b) ).
cnf(prove_first_components_equal,negated_conjecture,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_first_components_equal) ).
cnf(little_set_a,hypothesis,
little_set(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',little_set_a) ).
cnf(c_0_9,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
ordered_pair ).
cnf(c_0_10,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
singleton_set ).
cnf(c_0_11,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X2 ),
non_ordered_pair2 ).
cnf(c_0_12,hypothesis,
ordered_pair(a,c) = ordered_pair(b,d),
equal_ordered_pairs ).
cnf(c_0_13,plain,
ordered_pair(X1,X2) = non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( member(X1,non_ordered_pair(X1,X2))
| ~ little_set(X1) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_15,hypothesis,
non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,d)) = non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13]) ).
cnf(c_0_16,axiom,
little_set(non_ordered_pair(X1,X2)),
non_ordered_pair4 ).
cnf(c_0_17,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,non_ordered_pair(X2,X3)) ),
non_ordered_pair1 ).
cnf(c_0_18,hypothesis,
member(non_ordered_pair(b,b),non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,c))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_19,hypothesis,
( non_ordered_pair(b,b) = non_ordered_pair(a,a)
| non_ordered_pair(b,b) = non_ordered_pair(a,c) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,hypothesis,
little_set(b),
little_set_b ).
cnf(c_0_21,hypothesis,
( non_ordered_pair(b,b) = non_ordered_pair(a,c)
| member(b,non_ordered_pair(a,a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_19]),c_0_20])]) ).
cnf(c_0_22,negated_conjecture,
a != b,
prove_first_components_equal ).
cnf(c_0_23,hypothesis,
non_ordered_pair(b,b) = non_ordered_pair(a,c),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_21]),c_0_22]) ).
cnf(c_0_24,hypothesis,
member(b,non_ordered_pair(a,c)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_23]),c_0_20])]) ).
cnf(c_0_25,hypothesis,
b = c,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_24]),c_0_22]) ).
cnf(c_0_26,hypothesis,
non_ordered_pair(a,c) = non_ordered_pair(c,c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_25]),c_0_25]) ).
cnf(c_0_27,hypothesis,
little_set(a),
little_set_a ).
cnf(c_0_28,hypothesis,
member(a,non_ordered_pair(c,c)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_26]),c_0_27])]) ).
cnf(c_0_29,negated_conjecture,
a != c,
inference(rw,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_30,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_28]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET016-3 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n004.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 02:05:17 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.42/1.77 % Version : CSE_E---1.7
% 1.42/1.77 % Problem : theBenchmark.p
% 1.42/1.77 % SZS status Unsatisfiable for theBenchmark.p
% 1.42/1.77 % SZS output start CNFRefutation
% See solution above
% 1.42/1.77 % Total time : 1.372s
%------------------------------------------------------------------------------