%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET018-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:41:31 PM UTC 2026
% Result : Unsatisfiable 5.42s 1.15s
% Output : Proof 5.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 8
% Syntax : Number of formulae : 74 ( 39 unt; 0 def)
% Number of atoms : 118 ( 74 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 67 ( 23 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 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 : 65 ( 5 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,axiom,
ordered_pair(X,Y) = unordered_pair(singleton_set(X),unordered_pair(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
fof(f5_nnf,plain,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton_set(X),unordered_pair(X,Y)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton_set(X),unordered_pair(X,Y)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
ordered_pair(X0,X1) = unordered_pair(singleton_set(X0),unordered_pair(X0,X1)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f4,axiom,
( X = Z
| X = Y
| ~ member(X,unordered_pair(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_3) ).
fof(f4_nnf,plain,
! [X,Y,Z] :
( X = Z
| X = Y
| ~ member(X,unordered_pair(Y,Z)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Z] :
( X = Z
| X = Y
| ~ member(X,unordered_pair(Y,Z)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p15,plain,
( X0 = unordered_pair(X1,X2)
| X0 = singleton_set(X1)
| ~ member(X0,ordered_pair(X1,X2)) ),
inference(superposition,[status(thm)],[c5,c4]) ).
cnf(f6,hypothesis,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_ordered_pairs) ).
fof(f6_nnf,plain,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(f2,axiom,
member(X,unordered_pair(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_1) ).
fof(f2_nnf,plain,
! [X,Y] : member(X,unordered_pair(X,Y)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] : member(X,unordered_pair(X,Y)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
member(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p8,plain,
member(singleton_set(X0),ordered_pair(X0,X1)),
inference(superposition,[status(thm)],[c5,c2]) ).
cnf(p11,plain,
member(singleton_set(m2),ordered_pair(m1,r1)),
inference(superposition,[status(thm)],[c6,p8]) ).
cnf(p34,plain,
( singleton_set(m2) = unordered_pair(m1,r1)
| singleton_set(m2) = singleton_set(m1) ),
inference(resolution,[status(thm)],[p15,p11]) ).
cnf(p39,plain,
( member(m1,singleton_set(m2))
| singleton_set(m2) = singleton_set(m1) ),
inference(superposition,[status(thm)],[p34,c2]) ).
cnf(f0,axiom,
member(X,singleton_set(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_1) ).
fof(f0_nnf,plain,
! [X] : member(X,singleton_set(X)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : member(X,singleton_set(X)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
member(X0,singleton_set(X0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p48,plain,
( member(m2,singleton_set(m1))
| member(m1,singleton_set(m2)) ),
inference(superposition,[status(thm)],[p39,c0]) ).
cnf(f1,axiom,
( X = Y
| ~ member(X,singleton_set(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_2) ).
fof(f1_nnf,plain,
! [X,Y] :
( X = Y
| ~ member(X,singleton_set(Y)) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( X = Y
| ~ member(X,singleton_set(Y)) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( X0 = X1
| ~ member(X0,singleton_set(X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p57,plain,
( m2 = m1
| member(m1,singleton_set(m2)) ),
inference(resolution,[status(thm)],[p48,c1]) ).
cnf(p58,plain,
( m1 = m2
| m2 = m1 ),
inference(resolution,[status(thm)],[p57,c1]) ).
cnf(p13,plain,
( X1 != X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(equality_factoring,[status(thm)],[c4]) ).
cnf(f3,axiom,
member(Y,unordered_pair(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_2) ).
fof(f3_nnf,plain,
! [Y,X] : member(Y,unordered_pair(X,Y)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [Y,X] : member(Y,unordered_pair(X,Y)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
member(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p23,plain,
( X1 != X0
| X0 = X1 ),
inference(resolution,[status(thm)],[p13,c3]) ).
cnf(p65,plain,
( m1 = m2
| m1 = m2 ),
inference(resolution,[status(thm)],[p58,p23]) ).
cnf(p69,plain,
m1 = m2,
inference(factoring,[status(thm)],[p65]) ).
cnf(p73,plain,
m2 = m1,
inference(resolution,[status(thm)],[p69,p23]) ).
cnf(p9,plain,
member(unordered_pair(X0,X1),ordered_pair(X0,X1)),
inference(superposition,[status(thm)],[c5,c3]) ).
cnf(p16,plain,
member(unordered_pair(m2,r2),ordered_pair(m1,r1)),
inference(superposition,[status(thm)],[c6,p9]) ).
cnf(p35,plain,
( unordered_pair(m2,r2) = unordered_pair(m1,r1)
| unordered_pair(m2,r2) = singleton_set(m1) ),
inference(resolution,[status(thm)],[p15,p16]) ).
cnf(p81,plain,
( unordered_pair(m1,r2) = unordered_pair(m1,r1)
| unordered_pair(m1,r2) = singleton_set(m1) ),
inference(demodulation,[status(thm)],[p73,p35]) ).
cnf(p95,plain,
( member(r2,unordered_pair(m1,r1))
| unordered_pair(m1,r2) = singleton_set(m1) ),
inference(superposition,[status(thm)],[p81,c3]) ).
cnf(p106,plain,
( member(r2,singleton_set(m1))
| member(r2,unordered_pair(m1,r1)) ),
inference(superposition,[status(thm)],[p95,c3]) ).
cnf(p114,plain,
( r2 = r1
| r2 = m1
| member(r2,singleton_set(m1)) ),
inference(resolution,[status(thm)],[p106,c4]) ).
cnf(p117,plain,
( r2 = m1
| r2 = r1
| r2 = m1 ),
inference(resolution,[status(thm)],[p114,c1]) ).
cnf(p128,plain,
( r2 = r1
| r2 = m1 ),
inference(factoring,[status(thm)],[p117]) ).
cnf(f7,negated_conjecture,
r1 != r2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_second_components_equal) ).
fof(f7_nnf,plain,
r1 != r2,
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
r1 != r2,
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
r1 != r2,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p131,plain,
( r1 != r1
| r2 = m1 ),
inference(superposition,[status(thm)],[p128,c7]) ).
cnf(p136,plain,
r2 = m1,
inference(equality_resolution,[status(thm)],[p131]) ).
cnf(p148,plain,
( unordered_pair(m1,m1) = unordered_pair(m1,r1)
| unordered_pair(m1,m1) = singleton_set(m1) ),
inference(demodulation,[status(thm)],[p136,p81]) ).
cnf(p198,plain,
( member(r1,unordered_pair(m1,m1))
| unordered_pair(m1,m1) = singleton_set(m1) ),
inference(superposition,[status(thm)],[p148,c3]) ).
cnf(p211,plain,
( singleton_set(m1) = unordered_pair(m1,m1)
| member(r1,unordered_pair(m1,m1)) ),
inference(resolution,[status(thm)],[p198,p23]) ).
cnf(p10,plain,
ordered_pair(m1,r1) = unordered_pair(singleton_set(m2),unordered_pair(m2,r2)),
inference(superposition,[status(thm)],[c6,c5]) ).
cnf(p18,plain,
ordered_pair(m2,r2) = ordered_pair(m1,r1),
inference(superposition,[status(thm)],[p10,c5]) ).
cnf(p71,plain,
ordered_pair(m1,r2) = ordered_pair(m1,r1),
inference(superposition,[status(thm)],[p69,p18]) ).
cnf(p139,plain,
ordered_pair(m1,m1) = ordered_pair(m1,r1),
inference(demodulation,[status(thm)],[p136,p71]) ).
cnf(p168,plain,
member(unordered_pair(m1,r1),ordered_pair(m1,m1)),
inference(superposition,[status(thm)],[p139,p9]) ).
cnf(p24,plain,
( singleton_set(X1) != unordered_pair(X1,X2)
| X0 = singleton_set(X1)
| ~ member(X0,ordered_pair(X1,X2)) ),
inference(superposition,[status(thm)],[c5,p13]) ).
cnf(p178,plain,
( singleton_set(m1) != unordered_pair(m1,m1)
| unordered_pair(m1,r1) = singleton_set(m1) ),
inference(resolution,[status(thm)],[p168,p24]) ).
cnf(p221,plain,
( unordered_pair(m1,r1) = singleton_set(m1)
| member(r1,unordered_pair(m1,m1)) ),
inference(resolution,[status(thm)],[p211,p178]) ).
cnf(p222,plain,
( member(r1,singleton_set(m1))
| member(r1,unordered_pair(m1,m1)) ),
inference(superposition,[status(thm)],[p221,c3]) ).
cnf(p12,plain,
( X0 = X1
| ~ member(X0,unordered_pair(X1,X1)) ),
inference(factoring,[status(thm)],[c4]) ).
cnf(p226,plain,
( r1 = m1
| member(r1,singleton_set(m1)) ),
inference(resolution,[status(thm)],[p222,p12]) ).
cnf(p231,plain,
( r1 = m1
| r1 = m1 ),
inference(resolution,[status(thm)],[p226,c1]) ).
cnf(p232,plain,
r1 = m1,
inference(factoring,[status(thm)],[p231]) ).
cnf(p137,plain,
r1 != m1,
inference(demodulation,[status(thm)],[p136,c7]) ).
cnf(p233,plain,
m1 != m1,
inference(demodulation,[status(thm)],[p232,p137]) ).
cnf(p235,plain,
$false,
inference(equality_resolution,[status(thm)],[p233]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET018-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 09:14:40 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.42/1.15 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.42/1.15 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------