%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU157+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 : Tue Sep 29 12:47:28 PM UTC 2026
% Result : Theorem 2.56s 1.32s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 42 ( 4 unt; 0 def)
% Number of atoms : 164 ( 44 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 202 ( 80 ~; 82 |; 34 &)
% ( 4 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 146 ( 122 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( X2 = cartesian_product2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f10,conjecture,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f14,axiom,
! [X0,X1,X2,X3] :
( ordered_pair(X0,X1) = ordered_pair(X2,X3)
=> ( X0 = X2
& X1 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(f15,plain,
? [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<~> ( in(X0,X2)
& in(X1,X3) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( ( X0 = X2
& X1 = X3 )
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f14]) ).
fof(f18,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X0,X2)
| ~ in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) )
& ( ( in(X0,X2)
& in(X1,X3) )
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f19,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X0,X2)
| ~ in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) )
& ( ( in(X0,X2)
& in(X1,X3) )
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
( ( ~ in(sK0,sK2)
| ~ in(sK1,sK3)
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) )
& ( ( in(sK0,sK2)
& in(sK1,sK3) )
| in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ? [X3] :
( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,X2) )
& ( ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 ) )
& ( ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) )
| ~ in(X3,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ? [X3] :
( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( in(X6,X0)
& in(X7,X1)
& ordered_pair(X6,X7) = X3 )
| in(X3,X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ~ in(X9,X0)
| ~ in(X10,X1)
| ordered_pair(X9,X10) != X8 ) )
& ( ? [X11,X12] :
( in(X11,X0)
& in(X12,X1)
& ordered_pair(X11,X12) = X8 )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(rectify,[],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != sK4(X0,X1,X2) )
| ~ in(sK4(X0,X1,X2),X2) )
& ( ( in(sK5(X0,X1,X2),X0)
& in(sK6(X0,X1,X2),X1)
& sK4(X0,X1,X2) = ordered_pair(sK5(X0,X1,X2),sK6(X0,X1,X2)) )
| in(sK4(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ~ in(X9,X0)
| ~ in(X10,X1)
| ordered_pair(X9,X10) != X8 ) )
& ( ( in(sK7(X0,X1,X8),X0)
& in(sK8(X0,X1,X8),X1)
& ordered_pair(sK7(X0,X1,X8),sK8(X0,X1,X8)) = X8 )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8]),skolemize(X3,sK4(X0,X1,X2)),skolemize(X6,sK5(X0,X1,X2)),skolemize(X7,sK6(X0,X1,X2)),skolemize(X11,sK7(X0,X1,X8)),skolemize(X12,sK8(X0,X1,X8))],[f22]) ).
fof(f24,plain,
( in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3))
| in(sK1,sK3) ),
inference(cnf_transformation,[],[f20]) ).
fof(f25,plain,
( in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3))
| in(sK0,sK2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f26,plain,
( ~ in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3))
| ~ in(sK1,sK3)
| ~ in(sK0,sK2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f28,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK7(X0,X1,X8),sK8(X0,X1,X8)) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f29,plain,
! [X2,X0,X1,X8] :
( in(sK8(X0,X1,X8),X1)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f30,plain,
! [X2,X0,X1,X8] :
( in(sK7(X0,X1,X8),X0)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f31,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| ~ in(X9,X0)
| ~ in(X10,X1)
| ordered_pair(X9,X10) != X8
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(X2,X3)
| X1 = X3 ),
inference(cnf_transformation,[],[f17]) ).
fof(f37,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(X2,X3)
| X0 = X2 ),
inference(cnf_transformation,[],[f17]) ).
fof(f38,plain,
! [X2,X10,X0,X1,X9] :
( in(ordered_pair(X9,X10),X2)
| ~ in(X9,X0)
| ~ in(X10,X1)
| cartesian_product2(X0,X1) != X2 ),
inference(equality_resolution,[],[f31]) ).
fof(f39,plain,
! [X10,X0,X1,X9] :
( in(ordered_pair(X9,X10),cartesian_product2(X0,X1))
| ~ in(X9,X0)
| ~ in(X10,X1) ),
inference(equality_resolution,[],[f38]) ).
fof(f40,plain,
! [X0,X1,X8] :
( in(sK7(X0,X1,X8),X0)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f30]) ).
fof(f41,plain,
! [X0,X1,X8] :
( in(sK8(X0,X1,X8),X1)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f29]) ).
fof(f42,plain,
! [X0,X1,X8] :
( ordered_pair(sK7(X0,X1,X8),sK8(X0,X1,X8)) = X8
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f28]) ).
fof(f52,plain,
( ~ in(sK0,sK2)
| ~ in(sK1,sK3)
| ~ in(sK1,sK3)
| ~ in(sK0,sK2) ),
inference(resolution,[],[f39,f26]) ).
fof(f54,plain,
( ~ in(sK1,sK3)
| ~ in(sK0,sK2) ),
inference(duplicate_literal_removal,[],[f52]) ).
fof(f56,plain,
! [X2,X3,X0,X1,X4] :
( ordered_pair(X1,X2) != X0
| sK7(X3,X4,X0) = X1
| ~ in(X0,cartesian_product2(X3,X4)) ),
inference(superposition,[],[f37,f42]) ).
fof(f58,plain,
! [X2,X3,X0,X1,X4] :
( ordered_pair(X1,X2) != X0
| sK8(X3,X4,X0) = X2
| ~ in(X0,cartesian_product2(X3,X4)) ),
inference(superposition,[],[f36,f42]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( sK7(X0,X1,ordered_pair(X2,X3)) = X2
| ~ in(ordered_pair(X2,X3),cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f56]) ).
fof(f68,plain,
! [X2,X3,X0,X1] :
( in(X0,X1)
| ~ in(ordered_pair(X0,X3),cartesian_product2(X1,X2))
| ~ in(ordered_pair(X0,X3),cartesian_product2(X1,X2)) ),
inference(superposition,[],[f40,f64]) ).
fof(f69,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X3),cartesian_product2(X1,X2))
| in(X0,X1) ),
inference(duplicate_literal_removal,[],[f68]) ).
fof(f80,plain,
( in(sK0,sK2)
| in(sK0,sK2) ),
inference(resolution,[],[f69,f25]) ).
fof(f85,plain,
in(sK0,sK2),
inference(duplicate_literal_removal,[],[f80]) ).
fof(f91,plain,
! [X2,X3,X0,X1] :
( sK8(X0,X1,ordered_pair(X2,X3)) = X3
| ~ in(ordered_pair(X2,X3),cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f58]) ).
fof(f102,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X3,X0),cartesian_product2(X1,X2))
| ~ in(ordered_pair(X3,X0),cartesian_product2(X1,X2)) ),
inference(superposition,[],[f41,f91]) ).
fof(f103,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X3,X0),cartesian_product2(X1,X2))
| in(X0,X2) ),
inference(duplicate_literal_removal,[],[f102]) ).
fof(f107,plain,
( in(sK1,sK3)
| in(sK1,sK3) ),
inference(resolution,[],[f103,f24]) ).
fof(f111,plain,
in(sK1,sK3),
inference(duplicate_literal_removal,[],[f107]) ).
fof(f113,plain,
~ in(sK0,sK2),
inference(resolution,[],[f111,f54]) ).
fof(f115,plain,
$false,
inference(forward_subsumption_resolution,[],[f113,f85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU157+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:49:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.56/1.32 % (2975521)Detected formulas, will run a generic FOF schedule.
% 2.56/1.32 % (2975530)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2791818502:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.56/1.32 % (2975530)First to succeed.
% 2.56/1.32 % (2975530)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2975521"
% 2.56/1.32 % (2975528)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1304182765:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.56/1.32 % (2975526)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3222698912:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.56/1.32 % (2975527)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3281671875:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.56/1.32 % (2975529)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2404978347:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.56/1.32 % (2975531)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1034668388:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.56/1.32 % (2975529)Refutation not found, incomplete strategy
% 2.56/1.32 % (2975529)------------------------------
% 2.56/1.32 % (2975529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.32 % (2975529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.32 % (2975529)CaDiCaL version: 2.1.3
% 2.56/1.32 % (2975529)Termination reason: Refutation not found, incomplete strategy
% 2.56/1.32 % (2975529)Time elapsed: 0.002 s
% 2.56/1.32 % (2975529)Peak memory usage: 88 MB
% 2.56/1.32 % (2975529)Instructions burned: 1 (million)
% 2.56/1.32 % (2975532)dis-21_1_sil=8000:lcm=predicate:random_seed=629563743:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.56/1.32 % (2975532)Refutation not found, incomplete strategy
% 2.56/1.32 % (2975532)------------------------------
% 2.56/1.32 % (2975532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.32 % (2975532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.32 % (2975532)CaDiCaL version: 2.1.3
% 2.56/1.32 % (2975532)Termination reason: Refutation not found, incomplete strategy
% 2.56/1.32 % (2975532)Time elapsed: 0.003 s
% 2.56/1.32 % (2975532)Peak memory usage: 88 MB
% 2.56/1.32 % (2975532)Instructions burned: 3 (million)
% 2.56/1.32 % (2975531)Also succeeded, but the first one will report.
% 2.56/1.32 % (2975530)Refutation found. Thanks to Tanya!
% 2.56/1.32 % SZS status Theorem for theBenchmark
% 2.56/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.32 % (2975530)------------------------------
% 2.56/1.32 % (2975530)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.32 % (2975530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.32 % (2975530)CaDiCaL version: 2.1.3
% 2.56/1.32 % (2975530)Termination reason: Refutation
% 2.56/1.32 % (2975530)Time elapsed: 0.003 s
% 2.56/1.32 % (2975530)Peak memory usage: 88 MB
% 2.56/1.32 % (2975530)Instructions burned: 6 (million)
% 2.56/1.32 % (2975530)------------------------------
% 2.56/1.32 % (2975530)------------------------------
% 2.56/1.32 % (2975521)Success in time 0.276 s
% 2.56/1.32 % Vampire exiting
%------------------------------------------------------------------------------