%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET018-1 : 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 : n002.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 1.25s 1.71s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of clauses : 44 ( 23 unt; 15 nHn; 36 RR)
% Number of literals : 72 ( 50 equ; 15 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(equal_ordered_pairs,hypothesis,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_ordered_pairs) ).
cnf(ordered_pair,axiom,
ordered_pair(X1,X2) = unordered_pair(singleton_set(X1),unordered_pair(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
cnf(unordered_pair_1,axiom,
member(X1,unordered_pair(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_1) ).
cnf(unordered_pair_3,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_3) ).
cnf(singleton_2,axiom,
( X1 = X2
| ~ member(X1,singleton_set(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_2) ).
cnf(singleton_1,axiom,
member(X1,singleton_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_1) ).
cnf(unordered_pair_2,axiom,
member(X1,unordered_pair(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_2) ).
cnf(prove_second_components_equal,negated_conjecture,
r1 != r2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_second_components_equal) ).
cnf(c_0_8,hypothesis,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
equal_ordered_pairs ).
cnf(c_0_9,axiom,
ordered_pair(X1,X2) = unordered_pair(singleton_set(X1),unordered_pair(X1,X2)),
ordered_pair ).
cnf(c_0_10,axiom,
member(X1,unordered_pair(X1,X2)),
unordered_pair_1 ).
cnf(c_0_11,hypothesis,
unordered_pair(singleton_set(m2),unordered_pair(m2,r2)) = unordered_pair(singleton_set(m1),unordered_pair(m1,r1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_9]) ).
cnf(c_0_12,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_3 ).
cnf(c_0_13,hypothesis,
member(singleton_set(m1),unordered_pair(singleton_set(m2),unordered_pair(m2,r2))),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,axiom,
( X1 = X2
| ~ member(X1,singleton_set(X2)) ),
singleton_2 ).
cnf(c_0_15,hypothesis,
( singleton_set(m1) = unordered_pair(m2,r2)
| singleton_set(m1) = singleton_set(m2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,hypothesis,
( singleton_set(m1) = unordered_pair(m2,r2)
| X1 = m1
| ~ member(X1,singleton_set(m2)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,axiom,
member(X1,singleton_set(X1)),
singleton_1 ).
cnf(c_0_18,hypothesis,
( singleton_set(m1) = unordered_pair(m2,r2)
| m1 = m2 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,hypothesis,
( m1 = m2
| X1 = m1
| ~ member(X1,unordered_pair(m2,r2)) ),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_20,hypothesis,
( singleton_set(m1) = unordered_pair(m2,r2)
| singleton_set(m2) != unordered_pair(m2,r2) ),
inference(ef,[status(thm)],[c_0_15]) ).
cnf(c_0_21,hypothesis,
m1 = m2,
inference(spm,[status(thm)],[c_0_19,c_0_10]) ).
cnf(c_0_22,hypothesis,
( X1 = m1
| singleton_set(m2) != unordered_pair(m2,r2)
| ~ member(X1,unordered_pair(m2,r2)) ),
inference(spm,[status(thm)],[c_0_14,c_0_20]) ).
cnf(c_0_23,axiom,
member(X1,unordered_pair(X2,X1)),
unordered_pair_2 ).
cnf(c_0_24,hypothesis,
unordered_pair(singleton_set(m2),unordered_pair(m2,r1)) = unordered_pair(singleton_set(m2),unordered_pair(m2,r2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_21]),c_0_21]) ).
cnf(c_0_25,hypothesis,
( m1 = r2
| singleton_set(m2) != unordered_pair(m2,r2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,hypothesis,
( X1 = unordered_pair(m2,r1)
| X1 = singleton_set(m2)
| ~ member(X1,unordered_pair(singleton_set(m2),unordered_pair(m2,r2))) ),
inference(spm,[status(thm)],[c_0_12,c_0_24]) ).
cnf(c_0_27,hypothesis,
( m2 = r2
| singleton_set(m2) != unordered_pair(m2,r2) ),
inference(rw,[status(thm)],[c_0_25,c_0_21]) ).
cnf(c_0_28,hypothesis,
( unordered_pair(m2,r1) = unordered_pair(m2,r2)
| singleton_set(m2) = unordered_pair(m2,r2) ),
inference(spm,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_29,hypothesis,
( unordered_pair(m2,r1) = unordered_pair(m2,r2)
| m2 = r2 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,hypothesis,
( m2 = r2
| member(r1,unordered_pair(m2,r2)) ),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
r1 != r2,
prove_second_components_equal ).
cnf(c_0_32,hypothesis,
( m2 = r2
| m2 = r1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_30]),c_0_31]) ).
cnf(c_0_33,hypothesis,
( unordered_pair(r1,r1) = unordered_pair(r1,r2)
| m2 = r2 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_32]),c_0_31]) ).
cnf(c_0_34,hypothesis,
member(unordered_pair(m1,r1),unordered_pair(singleton_set(m2),unordered_pair(m2,r2))),
inference(spm,[status(thm)],[c_0_23,c_0_11]) ).
cnf(c_0_35,hypothesis,
( m2 = r2
| X1 = r1
| ~ member(X1,unordered_pair(r1,r2)) ),
inference(spm,[status(thm)],[c_0_12,c_0_33]) ).
cnf(c_0_36,hypothesis,
member(unordered_pair(m2,r1),unordered_pair(singleton_set(m2),unordered_pair(m2,r2))),
inference(rw,[status(thm)],[c_0_34,c_0_21]) ).
cnf(c_0_37,hypothesis,
m2 = r2,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_23]),c_0_31]) ).
cnf(c_0_38,hypothesis,
member(unordered_pair(r2,r1),unordered_pair(singleton_set(r2),unordered_pair(r2,r2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_37]),c_0_37]) ).
cnf(c_0_39,hypothesis,
( unordered_pair(r2,r1) = unordered_pair(r2,r2)
| singleton_set(r2) = unordered_pair(r2,r2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_37]),c_0_37]),c_0_37]),c_0_37]) ).
cnf(c_0_40,hypothesis,
( unordered_pair(r2,r1) = unordered_pair(r2,r2)
| singleton_set(r2) = unordered_pair(r2,r1) ),
inference(spm,[status(thm)],[c_0_12,c_0_38]) ).
cnf(c_0_41,hypothesis,
unordered_pair(r2,r1) = unordered_pair(r2,r2),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_42,hypothesis,
member(r1,unordered_pair(r2,r2)),
inference(spm,[status(thm)],[c_0_23,c_0_41]) ).
cnf(c_0_43,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_42]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET018-1 : 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
% 0.14/0.33 % Computer : n002.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:04:46 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.25/1.71 % Version : CSE_E---1.7
% 1.25/1.71 % Problem : theBenchmark.p
% 1.25/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.25/1.71 % SZS output start CNFRefutation
% See solution above
% 1.25/1.71 % Total time : 1.370s
%------------------------------------------------------------------------------