%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU156+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n010.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 02:51:08 PM UTC 2026
% Result : Theorem 148.41s 22.28s
% Output : Proof 148.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 6
% Syntax : Number of formulae : 90 ( 29 unt; 0 def)
% Number of atoms : 190 ( 189 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 144 ( 44 ~; 91 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 95 ( 7 sgn 44 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,conjecture,
! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(f7_neg,negated_conjecture,
~ ! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_nnf,plain,
? [A,B,C,D] :
( ( B != D
| A != C )
& ordered_pair(A,B) = ordered_pair(C,D) ),
inference(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,plain,
( ( sk3 != sk5
| sk2 != sk4 )
& ordered_pair(sk2,sk3) = ordered_pair(sk4,sk5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4,sk5])],[f7_nnf]) ).
cnf(c7,plain,
ordered_pair(sk2,sk3) = ordered_pair(sk4,sk5),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f1,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f1_nnf,plain,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f0,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f0_nnf,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p15,plain,
unordered_pair(singleton(X0),unordered_pair(X0,X1)) = ordered_pair(X0,X1),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(p58,plain,
ordered_pair(sk4,sk5) = ordered_pair(sk2,sk3),
inference(superposition,[status(thm)],[c7,p15]) ).
fof(f6,axiom,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(f6_nnf,plain,
! [A,B,C,D] :
( A = D
| A = C
| unordered_pair(A,B) != unordered_pair(C,D) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C,D] :
( A = D
| A = C
| unordered_pair(A,B) != unordered_pair(C,D) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p63,plain,
( singleton(X0) = X3
| singleton(X0) = X2
| ordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(superposition,[status(thm)],[p15,c6]) ).
cnf(p1018,plain,
( singleton(sk4) = X1
| singleton(sk4) = X0
| ordered_pair(sk2,sk3) != unordered_pair(X0,X1) ),
inference(superposition,[status(thm)],[p58,p63]) ).
cnf(p3748,plain,
( singleton(sk4) = singleton(sk2)
| singleton(sk4) = unordered_pair(sk2,sk3) ),
inference(resolution,[status(thm)],[p1018,c1]) ).
fof(f10,axiom,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f10_nnf,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c11,plain,
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p3771,plain,
( sk4 = sk2
| singleton(sk4) = singleton(sk2) ),
inference(resolution,[status(thm)],[p3748,c11]) ).
fof(f8,axiom,
! [A] : unordered_pair(A,A) = singleton(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f8_nnf,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c9,plain,
unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p44,plain,
( X0 = X1
| singleton(X0) != singleton(X1) ),
inference(superposition,[status(thm)],[c9,c11]) ).
cnf(p3846,plain,
( sk4 = sk2
| sk4 = sk2 ),
inference(resolution,[status(thm)],[p3771,p44]) ).
cnf(p3986,plain,
sk4 = sk2,
inference(factoring,[status(thm)],[p3846]) ).
cnf(p31,plain,
( unordered_pair(X0,X1) = X3
| unordered_pair(X0,X1) = X2
| ordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(superposition,[status(thm)],[c1,c6]) ).
cnf(p218,plain,
( unordered_pair(sk4,sk5) = X1
| unordered_pair(sk4,sk5) = X0
| ordered_pair(sk2,sk3) != unordered_pair(X0,X1) ),
inference(superposition,[status(thm)],[p58,p31]) ).
cnf(p224,plain,
( unordered_pair(sk4,sk5) = singleton(sk2)
| unordered_pair(sk4,sk5) = unordered_pair(sk2,sk3) ),
inference(resolution,[status(thm)],[p218,c1]) ).
cnf(p237,plain,
( sk4 = sk3
| sk4 = sk2
| unordered_pair(sk4,sk5) = singleton(sk2) ),
inference(resolution,[status(thm)],[p224,c6]) ).
cnf(p27,plain,
( X0 = X2
| unordered_pair(X0,X1) != singleton(X2) ),
inference(factoring,[status(thm)],[c6]) ).
cnf(p275,plain,
( sk4 = sk2
| sk4 = sk3
| sk4 = sk2 ),
inference(resolution,[status(thm)],[p237,p27]) ).
cnf(p297,plain,
( sk4 = sk3
| sk4 = sk2 ),
inference(factoring,[status(thm)],[p275]) ).
cnf(p235,plain,
( unordered_pair(sk2,sk3) = unordered_pair(sk4,sk5)
| unordered_pair(sk4,sk5) = singleton(sk2) ),
inference(superposition,[status(thm)],[p224,c0]) ).
cnf(p30,plain,
( X1 = X3
| X1 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(superposition,[status(thm)],[c0,c6]) ).
cnf(p267,plain,
( sk3 = sk5
| sk3 = sk4
| unordered_pair(sk4,sk5) = singleton(sk2) ),
inference(resolution,[status(thm)],[p235,p30]) ).
cnf(p499,plain,
( sk4 = sk2
| sk3 = sk5
| sk3 = sk4 ),
inference(resolution,[status(thm)],[p267,p27]) ).
cnf(p521,plain,
( sk4 != sk5
| sk4 = sk2
| sk3 = sk4 ),
inference(equality_factoring,[status(thm)],[p499]) ).
cnf(p529,plain,
( sk3 != sk5
| sk4 = sk2
| sk3 = sk4
| sk4 = sk2 ),
inference(superposition,[status(thm)],[p297,p521]) ).
cnf(p1049,plain,
( sk3 != sk5
| sk3 = sk4
| sk4 = sk2 ),
inference(factoring,[status(thm)],[p529]) ).
cnf(p492,plain,
( singleton(sk2) = unordered_pair(sk4,sk5)
| sk3 = sk5
| sk3 = sk4 ),
inference(superposition,[status(thm)],[p267,c0]) ).
cnf(p43,plain,
( X0 = X2
| singleton(X0) != unordered_pair(X1,X2) ),
inference(superposition,[status(thm)],[c0,c11]) ).
cnf(p624,plain,
( sk2 = sk5
| sk3 = sk5
| sk3 = sk4 ),
inference(resolution,[status(thm)],[p492,p43]) ).
cnf(p1053,plain,
( sk2 = sk5
| sk3 = sk4
| sk3 = sk4
| sk4 = sk2 ),
inference(resolution,[status(thm)],[p1049,p624]) ).
cnf(p1590,plain,
( sk2 = sk5
| sk3 = sk4
| sk4 = sk2 ),
inference(factoring,[status(thm)],[p1053]) ).
cnf(c8,plain,
( sk3 != sk5
| sk2 != sk4 ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p1591,plain,
( sk3 != sk5
| sk2 != sk2
| sk2 = sk5
| sk3 = sk4 ),
inference(superposition,[status(thm)],[p1590,c8]) ).
cnf(p2122,plain,
( sk3 != sk5
| sk2 = sk5
| sk3 = sk4 ),
inference(equality_resolution,[status(thm)],[p1591]) ).
cnf(p2124,plain,
( sk2 = sk5
| sk3 = sk4
| sk2 = sk5
| sk3 = sk4 ),
inference(resolution,[status(thm)],[p2122,p624]) ).
cnf(p2224,plain,
( sk2 = sk5
| sk2 = sk5
| sk3 = sk4 ),
inference(factoring,[status(thm)],[p2124]) ).
cnf(p2226,plain,
( sk2 = sk5
| sk3 = sk4 ),
inference(factoring,[status(thm)],[p2224]) ).
cnf(p264,plain,
( sk2 = sk5
| sk2 = sk4
| unordered_pair(sk4,sk5) = singleton(sk2) ),
inference(resolution,[status(thm)],[p235,c6]) ).
cnf(p367,plain,
( singleton(sk2) = unordered_pair(sk4,sk5)
| sk2 = sk5
| sk2 = sk4 ),
inference(superposition,[status(thm)],[p264,c0]) ).
cnf(p552,plain,
( sk2 = sk4
| sk2 = sk5
| sk2 = sk4 ),
inference(resolution,[status(thm)],[p367,c11]) ).
cnf(p561,plain,
( sk2 = sk5
| sk2 = sk4 ),
inference(factoring,[status(thm)],[p552]) ).
cnf(p563,plain,
( sk5 != sk4
| sk2 = sk5 ),
inference(equality_factoring,[status(thm)],[p561]) ).
cnf(p2241,plain,
( sk5 != sk3
| sk2 = sk5
| sk2 = sk5 ),
inference(superposition,[status(thm)],[p2226,p563]) ).
cnf(p2285,plain,
( sk5 != sk3
| sk2 = sk5 ),
inference(factoring,[status(thm)],[p2241]) ).
cnf(p256,plain,
( sk5 = sk3
| sk5 = sk2
| unordered_pair(sk4,sk5) = singleton(sk2) ),
inference(resolution,[status(thm)],[p224,p30]) ).
cnf(p75,plain,
( X1 = X2
| unordered_pair(X0,X1) != singleton(X2) ),
inference(superposition,[status(thm)],[c0,p27]) ).
cnf(p330,plain,
( sk5 = sk2
| sk5 = sk3
| sk5 = sk2 ),
inference(resolution,[status(thm)],[p256,p75]) ).
cnf(p350,plain,
( sk5 = sk3
| sk5 = sk2 ),
inference(factoring,[status(thm)],[p330]) ).
cnf(p2296,plain,
( sk5 = sk2
| sk2 = sk5 ),
inference(resolution,[status(thm)],[p2285,p350]) ).
cnf(p2302,plain,
( sk2 != sk4
| sk2 = sk5
| sk2 = sk5 ),
inference(superposition,[status(thm)],[p2296,p563]) ).
cnf(p2345,plain,
( sk2 != sk4
| sk2 = sk5 ),
inference(factoring,[status(thm)],[p2302]) ).
cnf(p4329,plain,
( sk2 != sk2
| sk2 = sk5 ),
inference(demodulation,[status(thm)],[p3986,p2345]) ).
cnf(p4725,plain,
sk2 = sk5,
inference(equality_resolution,[status(thm)],[p4329]) ).
cnf(p3988,plain,
ordered_pair(sk2,sk5) = ordered_pair(sk2,sk3),
inference(demodulation,[status(thm)],[p3986,p58]) ).
cnf(p4728,plain,
ordered_pair(sk2,sk2) = ordered_pair(sk2,sk3),
inference(superposition,[status(thm)],[p4725,p3988]) ).
cnf(p5018,plain,
ordered_pair(sk2,sk3) = ordered_pair(sk2,sk2),
inference(superposition,[status(thm)],[p4728,p15]) ).
cnf(p45,plain,
( X0 = unordered_pair(X1,X2)
| singleton(X0) != ordered_pair(X1,X2) ),
inference(superposition,[status(thm)],[c1,c11]) ).
cnf(p5092,plain,
( X0 = unordered_pair(sk2,sk3)
| singleton(X0) != ordered_pair(sk2,sk2) ),
inference(superposition,[status(thm)],[p5018,p45]) ).
cnf(p18,plain,
ordered_pair(X0,X0) = singleton(singleton(X0)),
inference(superposition,[status(thm)],[c9,c1]) ).
cnf(p20,plain,
singleton(singleton(X0)) = ordered_pair(X0,X0),
inference(superposition,[status(thm)],[p18,c9]) ).
cnf(p5101,plain,
singleton(sk2) = unordered_pair(sk2,sk3),
inference(resolution,[status(thm)],[p5092,p20]) ).
cnf(p5112,plain,
unordered_pair(sk2,sk3) = singleton(sk2),
inference(superposition,[status(thm)],[p5101,c0]) ).
cnf(p5122,plain,
sk3 = sk2,
inference(resolution,[status(thm)],[p5112,p75]) ).
cnf(p3987,plain,
( sk3 != sk5
| sk2 != sk2 ),
inference(demodulation,[status(thm)],[p3986,c8]) ).
cnf(p4593,plain,
sk3 != sk5,
inference(equality_resolution,[status(thm)],[p3987]) ).
cnf(p4727,plain,
sk3 != sk2,
inference(superposition,[status(thm)],[p4725,p4593]) ).
cnf(p5123,plain,
sk2 != sk2,
inference(demodulation,[status(thm)],[p5122,p4727]) ).
cnf(p5126,plain,
$false,
inference(equality_resolution,[status(thm)],[p5123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU156+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 12:58:59 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 148.41/22.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 148.41/22.28 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------