%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU156+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 106.26s 20.58s
% Output : Proof 106.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 7
% Syntax : Number of formulae : 100 ( 25 unt; 0 def)
% Number of atoms : 201 ( 200 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 157 ( 56 ~; 91 |; 6 &)
% ( 0 <=>; 4 =>; 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 : 129 ( 15 sgn 53 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [A] : unordered_pair(A,A) = singleton(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f11_nnf,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c12,plain,
unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
fof(f1,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('/export/starexec/sandbox/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]) ).
cnf(p21,plain,
ordered_pair(X0,X0) = singleton(singleton(X0)),
inference(superposition,[status(thm)],[c12,c1]) ).
fof(f10,conjecture,
! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(f10_neg,negated_conjecture,
~ ! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f10_nnf,plain,
? [A,B,C,D] :
( ( B != D
| A != C )
& ordered_pair(A,B) = ordered_pair(C,D) ),
inference(nnf_transformation,[status(thm)],[f10_neg]) ).
fof(f10_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])],[f10_nnf]) ).
cnf(c10,plain,
ordered_pair(sk2,sk3) = ordered_pair(sk4,sk5),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f0,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox/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(p18,plain,
unordered_pair(singleton(X0),unordered_pair(X0,X1)) = ordered_pair(X0,X1),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(p61,plain,
ordered_pair(sk4,sk5) = ordered_pair(sk2,sk3),
inference(superposition,[status(thm)],[c10,p18]) ).
fof(f9,axiom,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(f9_nnf,plain,
! [A,B,C,D] :
( A = D
| A = C
| unordered_pair(A,B) != unordered_pair(C,D) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B,C,D] :
( A = D
| A = C
| unordered_pair(A,B) != unordered_pair(C,D) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p30,plain,
( unordered_pair(X0,X1) = X3
| unordered_pair(X0,X1) = X2
| ordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(superposition,[status(thm)],[c1,c9]) ).
cnf(p207,plain,
( unordered_pair(sk4,sk5) = X1
| unordered_pair(sk4,sk5) = X0
| ordered_pair(sk2,sk3) != unordered_pair(X0,X1) ),
inference(superposition,[status(thm)],[p61,p30]) ).
cnf(p214,plain,
( unordered_pair(sk4,sk5) = singleton(sk2)
| unordered_pair(sk4,sk5) = unordered_pair(sk2,sk3) ),
inference(resolution,[status(thm)],[p207,c1]) ).
cnf(p29,plain,
( X1 = X3
| X1 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(superposition,[status(thm)],[c0,c9]) ).
cnf(p247,plain,
( sk5 = sk3
| sk5 = sk2
| unordered_pair(sk4,sk5) = singleton(sk2) ),
inference(resolution,[status(thm)],[p214,p29]) ).
cnf(p26,plain,
( X0 = X2
| unordered_pair(X0,X1) != singleton(X2) ),
inference(factoring,[status(thm)],[c9]) ).
cnf(p78,plain,
( X1 = X2
| unordered_pair(X0,X1) != singleton(X2) ),
inference(superposition,[status(thm)],[c0,p26]) ).
cnf(p369,plain,
( sk5 = sk2
| sk5 = sk3
| sk5 = sk2 ),
inference(resolution,[status(thm)],[p247,p78]) ).
cnf(p401,plain,
( sk5 = sk3
| sk5 = sk2 ),
inference(factoring,[status(thm)],[p369]) ).
cnf(p27,plain,
( X2 != X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(equality_factoring,[status(thm)],[c9]) ).
cnf(p134,plain,
( X1 != X0
| X0 = X1 ),
inference(resolution,[status(thm)],[p27,c0]) ).
cnf(p405,plain,
( sk3 = sk5
| sk5 = sk2 ),
inference(resolution,[status(thm)],[p401,p134]) ).
cnf(p415,plain,
( sk2 = sk5
| sk3 = sk5 ),
inference(resolution,[status(thm)],[p405,p134]) ).
cnf(p226,plain,
( unordered_pair(sk2,sk3) = unordered_pair(sk4,sk5)
| unordered_pair(sk4,sk5) = singleton(sk2) ),
inference(superposition,[status(thm)],[p214,c0]) ).
cnf(p276,plain,
( sk2 = sk5
| sk2 = sk4
| unordered_pair(sk4,sk5) = singleton(sk2) ),
inference(resolution,[status(thm)],[p226,c9]) ).
cnf(p550,plain,
( sk4 = sk2
| sk2 = sk5
| sk2 = sk4 ),
inference(resolution,[status(thm)],[p276,p26]) ).
cnf(p588,plain,
( sk2 = sk4
| sk2 = sk5
| sk2 = sk4 ),
inference(resolution,[status(thm)],[p550,p134]) ).
cnf(p607,plain,
( sk2 = sk5
| sk2 = sk4 ),
inference(factoring,[status(thm)],[p588]) ).
cnf(p609,plain,
( sk5 != sk4
| sk2 = sk5 ),
inference(equality_factoring,[status(thm)],[p607]) ).
cnf(p622,plain,
( sk3 != sk4
| sk2 = sk5
| sk2 = sk5 ),
inference(superposition,[status(thm)],[p415,p609]) ).
cnf(p656,plain,
( sk3 != sk4
| sk2 = sk5 ),
inference(factoring,[status(thm)],[p622]) ).
cnf(p228,plain,
( sk4 = sk3
| sk4 = sk2
| unordered_pair(sk4,sk5) = singleton(sk2) ),
inference(resolution,[status(thm)],[p214,c9]) ).
cnf(p287,plain,
( sk4 = sk2
| sk4 = sk3
| sk4 = sk2 ),
inference(resolution,[status(thm)],[p228,p26]) ).
cnf(p305,plain,
( sk4 = sk3
| sk4 = sk2 ),
inference(factoring,[status(thm)],[p287]) ).
cnf(p309,plain,
( sk3 = sk4
| sk4 = sk2 ),
inference(resolution,[status(thm)],[p305,p134]) ).
cnf(c11,plain,
( sk3 != sk5
| sk2 != sk4 ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p316,plain,
( sk3 != sk5
| sk2 != sk2
| sk3 = sk4 ),
inference(superposition,[status(thm)],[p309,c11]) ).
cnf(p338,plain,
( sk3 != sk5
| sk3 = sk4 ),
inference(equality_resolution,[status(thm)],[p316]) ).
cnf(p430,plain,
( sk3 = sk4
| sk2 = sk5 ),
inference(resolution,[status(thm)],[p415,p338]) ).
cnf(p683,plain,
( sk2 = sk5
| sk2 = sk5 ),
inference(resolution,[status(thm)],[p656,p430]) ).
cnf(p684,plain,
sk2 = sk5,
inference(factoring,[status(thm)],[p683]) ).
cnf(p686,plain,
sk5 = sk2,
inference(resolution,[status(thm)],[p684,p134]) ).
fof(f14,axiom,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(f14_nnf,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c15,plain,
( X1 = X2
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p59,plain,
( unordered_pair(X1,X2) = singleton(X1)
| singleton(X0) != ordered_pair(X1,X2) ),
inference(superposition,[status(thm)],[c1,c15]) ).
cnf(p640,plain,
( unordered_pair(sk4,sk5) = singleton(sk4)
| singleton(X0) != ordered_pair(sk2,sk3) ),
inference(superposition,[status(thm)],[p61,p59]) ).
cnf(p760,plain,
( unordered_pair(sk4,sk2) = singleton(sk4)
| singleton(X0) != ordered_pair(sk2,sk3) ),
inference(demodulation,[status(thm)],[p686,p640]) ).
cnf(p960,plain,
( unordered_pair(sk2,sk4) = singleton(sk4)
| ordered_pair(X0,X0) != ordered_pair(sk2,sk3) ),
inference(superposition,[status(thm)],[p21,p760]) ).
cnf(p317,plain,
( ordered_pair(sk2,sk5) = ordered_pair(sk2,sk3)
| sk3 = sk4 ),
inference(superposition,[status(thm)],[p309,p61]) ).
cnf(p725,plain,
( ordered_pair(sk2,sk2) = ordered_pair(sk2,sk3)
| sk3 = sk4 ),
inference(demodulation,[status(thm)],[p686,p317]) ).
cnf(p1344,plain,
( sk3 = sk4
| unordered_pair(sk2,sk4) = singleton(sk4) ),
inference(resolution,[status(thm)],[p960,p725]) ).
cnf(p62,plain,
unordered_pair(singleton(X0),unordered_pair(X1,X0)) = ordered_pair(X0,X1),
inference(superposition,[status(thm)],[c0,p18]) ).
cnf(p1351,plain,
( ordered_pair(sk4,sk4) = ordered_pair(sk2,sk3)
| sk3 = sk4 ),
inference(superposition,[status(thm)],[p1344,p62]) ).
cnf(p60,plain,
( X1 = X2
| ordered_pair(X0,X0) != unordered_pair(X1,X2) ),
inference(superposition,[status(thm)],[p21,c15]) ).
cnf(p1391,plain,
( X0 = X1
| ordered_pair(sk2,sk3) != unordered_pair(X0,X1)
| sk3 = sk4 ),
inference(superposition,[status(thm)],[p1351,p60]) ).
cnf(p3194,plain,
( unordered_pair(sk2,sk3) = singleton(sk2)
| sk3 = sk4 ),
inference(resolution,[status(thm)],[p1391,c1]) ).
fof(f13,axiom,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f13_nnf,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c14,plain,
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p69,plain,
( X0 = singleton(X1)
| singleton(X0) != ordered_pair(X1,X2) ),
inference(superposition,[status(thm)],[p18,c14]) ).
cnf(p189,plain,
( X0 = singleton(sk4)
| singleton(X0) != ordered_pair(sk2,sk3) ),
inference(superposition,[status(thm)],[p61,p69]) ).
cnf(p192,plain,
( singleton(X0) = singleton(sk4)
| ordered_pair(X0,X0) != ordered_pair(sk2,sk3) ),
inference(superposition,[status(thm)],[p21,p189]) ).
cnf(p834,plain,
( singleton(sk2) = singleton(sk4)
| sk3 = sk4 ),
inference(resolution,[status(thm)],[p725,p192]) ).
cnf(p858,plain,
( X0 = sk4
| unordered_pair(X0,X1) != singleton(sk2)
| sk3 = sk4 ),
inference(superposition,[status(thm)],[p834,p26]) ).
cnf(p1303,plain,
( unordered_pair(sk3,X0) != singleton(sk2)
| sk3 = sk4 ),
inference(factoring,[status(thm)],[p858]) ).
cnf(p1308,plain,
( unordered_pair(X0,sk3) != singleton(sk2)
| sk3 = sk4 ),
inference(superposition,[status(thm)],[c0,p1303]) ).
cnf(p3224,plain,
( sk3 = sk4
| sk3 = sk4 ),
inference(resolution,[status(thm)],[p3194,p1308]) ).
cnf(p3275,plain,
sk3 = sk4,
inference(factoring,[status(thm)],[p3224]) ).
cnf(p3276,plain,
sk4 = sk3,
inference(resolution,[status(thm)],[p3275,p134]) ).
cnf(p685,plain,
ordered_pair(sk4,sk2) = ordered_pair(sk2,sk3),
inference(superposition,[status(thm)],[p684,p61]) ).
cnf(p66,plain,
( singleton(X0) = X3
| singleton(X0) = X2
| ordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(superposition,[status(thm)],[p18,c9]) ).
cnf(p893,plain,
( singleton(sk4) = X1
| singleton(sk4) = X0
| ordered_pair(sk2,sk3) != unordered_pair(X0,X1) ),
inference(superposition,[status(thm)],[p685,p66]) ).
cnf(p3320,plain,
( singleton(sk3) = X1
| singleton(sk3) = X0
| ordered_pair(sk2,sk3) != unordered_pair(X0,X1) ),
inference(demodulation,[status(thm)],[p3276,p893]) ).
cnf(p3556,plain,
( singleton(sk3) = singleton(sk2)
| singleton(sk3) = unordered_pair(sk2,sk3) ),
inference(resolution,[status(thm)],[p3320,c1]) ).
cnf(p3571,plain,
( sk3 = sk2
| singleton(sk3) = singleton(sk2) ),
inference(resolution,[status(thm)],[p3556,c14]) ).
cnf(p46,plain,
( X0 = X1
| singleton(X0) != singleton(X1) ),
inference(superposition,[status(thm)],[c12,c14]) ).
cnf(p3610,plain,
( sk3 = sk2
| sk3 = sk2 ),
inference(resolution,[status(thm)],[p3571,p46]) ).
cnf(p3703,plain,
sk3 = sk2,
inference(factoring,[status(thm)],[p3610]) ).
cnf(p687,plain,
( sk3 != sk2
| sk2 != sk4 ),
inference(demodulation,[status(thm)],[p686,c11]) ).
cnf(p3297,plain,
( sk3 != sk2
| sk2 != sk3 ),
inference(demodulation,[status(thm)],[p3276,p687]) ).
cnf(p3713,plain,
( sk2 != sk2
| sk2 != sk2 ),
inference(demodulation,[status(thm)],[p3703,p3297]) ).
cnf(p3772,plain,
sk2 != sk2,
inference(factoring,[status(thm)],[p3713]) ).
cnf(p3790,plain,
$false,
inference(equality_resolution,[status(thm)],[p3772]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU156+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.05/5.30 % Computer : n012.cluster.edu
% 0.05/5.30 % Model : x86_64 x86_64
% 0.05/5.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/5.30 % Memory : 8046.5625MB
% 0.05/5.30 % OS : Linux 6.8.0-71-generic
% 0.08/5.30 % CPULimit : 300
% 0.08/5.30 % WCLimit : 300
% 0.08/5.30 % DateTime : Thu Sep 24 12:58:25 UTC 2026
% 0.08/5.30 % CPUTime :
% 0.08/5.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 106.26/20.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 106.26/20.58 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------