%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET018-3 : TPTP v9.2.1. Released v1.0.0.
% 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 : n026.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 05:06:52 PM UTC 2026
% Result : Unsatisfiable 2.17s 2.01s
% Output : CNFRefutation 2.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of clauses : 52 ( 28 unt; 16 nHn; 39 RR)
% Number of literals : 90 ( 52 equ; 25 neg)
% Maximal clause size : 4 ( 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 : 43 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ordered_pair,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',singleton_set) ).
cnf(non_ordered_pair3,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X3 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',non_ordered_pair3) ).
cnf(equal_ordered_pair,hypothesis,
ordered_pair(a,b) = ordered_pair(c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_ordered_pair) ).
cnf(non_ordered_pair4,axiom,
little_set(non_ordered_pair(X1,X2)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SET003-0.ax',non_ordered_pair1) ).
cnf(d_little_set,hypothesis,
little_set(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_little_set) ).
cnf(prove_second_components_equal,negated_conjecture,
b != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_second_components_equal) ).
cnf(non_ordered_pair2,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',non_ordered_pair2) ).
cnf(a_little_set,hypothesis,
little_set(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_little_set) ).
cnf(left_cancellation,axiom,
( X1 = X2
| ~ little_set(X1)
| ~ little_set(X2)
| non_ordered_pair(X3,X1) != non_ordered_pair(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_cancellation) ).
cnf(c_little_set,hypothesis,
little_set(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_little_set) ).
cnf(b_little_set,hypothesis,
little_set(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_little_set) ).
cnf(c_0_13,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
ordered_pair ).
cnf(c_0_14,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
singleton_set ).
cnf(c_0_15,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X3 ),
non_ordered_pair3 ).
cnf(c_0_16,hypothesis,
ordered_pair(a,b) = ordered_pair(c,d),
equal_ordered_pair ).
cnf(c_0_17,plain,
ordered_pair(X1,X2) = non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( member(X1,non_ordered_pair(X2,X1))
| ~ little_set(X1) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_19,hypothesis,
non_ordered_pair(non_ordered_pair(c,c),non_ordered_pair(c,d)) = non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17]) ).
cnf(c_0_20,axiom,
little_set(non_ordered_pair(X1,X2)),
non_ordered_pair4 ).
cnf(c_0_21,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,non_ordered_pair(X2,X3)) ),
non_ordered_pair1 ).
cnf(c_0_22,hypothesis,
member(non_ordered_pair(c,d),non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_23,hypothesis,
( non_ordered_pair(c,d) = non_ordered_pair(a,a)
| non_ordered_pair(c,d) = non_ordered_pair(a,b) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,hypothesis,
little_set(d),
d_little_set ).
cnf(c_0_25,hypothesis,
( non_ordered_pair(c,d) = non_ordered_pair(a,a)
| member(d,non_ordered_pair(a,b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_23]),c_0_24])]) ).
cnf(c_0_26,negated_conjecture,
b != d,
prove_second_components_equal ).
cnf(c_0_27,hypothesis,
( non_ordered_pair(c,d) = non_ordered_pair(a,a)
| d = a ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_25]),c_0_26]) ).
cnf(c_0_28,hypothesis,
( X1 = non_ordered_pair(c,c)
| X1 = non_ordered_pair(c,d)
| ~ member(X1,non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b))) ),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_29,hypothesis,
( d = a
| member(d,non_ordered_pair(a,a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_27]),c_0_24])]) ).
cnf(c_0_30,hypothesis,
( non_ordered_pair(c,d) = non_ordered_pair(a,b)
| non_ordered_pair(c,c) = non_ordered_pair(a,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_18]),c_0_20])]) ).
cnf(c_0_31,hypothesis,
d = a,
inference(spm,[status(thm)],[c_0_21,c_0_29]) ).
cnf(c_0_32,hypothesis,
( non_ordered_pair(c,c) = non_ordered_pair(a,b)
| non_ordered_pair(c,a) = non_ordered_pair(a,b) ),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X2 ),
non_ordered_pair2 ).
cnf(c_0_34,hypothesis,
( non_ordered_pair(c,a) = non_ordered_pair(a,b)
| X1 = c
| ~ member(X1,non_ordered_pair(a,b)) ),
inference(spm,[status(thm)],[c_0_21,c_0_32]) ).
cnf(c_0_35,plain,
( member(X1,non_ordered_pair(X1,X2))
| ~ little_set(X1) ),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_36,hypothesis,
little_set(a),
a_little_set ).
cnf(c_0_37,axiom,
( X1 = X2
| ~ little_set(X1)
| ~ little_set(X2)
| non_ordered_pair(X3,X1) != non_ordered_pair(X3,X2) ),
left_cancellation ).
cnf(c_0_38,hypothesis,
( non_ordered_pair(c,a) = non_ordered_pair(a,b)
| c = a ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_39,hypothesis,
member(non_ordered_pair(c,c),non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_19]),c_0_20])]) ).
cnf(c_0_40,hypothesis,
( c = a
| a = X1
| non_ordered_pair(c,X1) != non_ordered_pair(a,b)
| ~ little_set(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_36])]) ).
cnf(c_0_41,hypothesis,
( non_ordered_pair(c,c) = non_ordered_pair(a,a)
| non_ordered_pair(c,c) = non_ordered_pair(a,b) ),
inference(spm,[status(thm)],[c_0_21,c_0_39]) ).
cnf(c_0_42,hypothesis,
little_set(c),
c_little_set ).
cnf(c_0_43,hypothesis,
( non_ordered_pair(c,c) = non_ordered_pair(a,a)
| c = a ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_44,hypothesis,
little_set(b),
b_little_set ).
cnf(c_0_45,hypothesis,
( c = a
| member(c,non_ordered_pair(a,a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_43]),c_0_42])]) ).
cnf(c_0_46,hypothesis,
( non_ordered_pair(c,a) = non_ordered_pair(a,b)
| b = c ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_18]),c_0_44])]) ).
cnf(c_0_47,hypothesis,
c = a,
inference(spm,[status(thm)],[c_0_21,c_0_45]) ).
cnf(c_0_48,negated_conjecture,
b != a,
inference(rw,[status(thm)],[c_0_26,c_0_31]) ).
cnf(c_0_49,hypothesis,
non_ordered_pair(a,b) = non_ordered_pair(a,a),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47]),c_0_47]),c_0_48]) ).
cnf(c_0_50,hypothesis,
member(b,non_ordered_pair(a,a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_49]),c_0_44])]) ).
cnf(c_0_51,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_50]),c_0_48]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET018-3 : TPTP v9.2.1. Released v1.0.0.
% 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 : n026.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 02:04:53 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 2.17/2.01 % Version : CSE_E---1.7
% 2.17/2.01 % Problem : theBenchmark.p
% 2.17/2.01 % SZS status Unsatisfiable for theBenchmark.p
% 2.17/2.01 % SZS output start CNFRefutation
% See solution above
% 2.17/2.02 % Total time : 1.368s
%------------------------------------------------------------------------------