%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET957+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:42:25 PM UTC 2026
% Result : Theorem 2.69s 1.26s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 7 unt; 0 def)
% Number of atoms : 110 ( 20 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 119 ( 43 ~; 39 |; 28 &)
% ( 5 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 94 ( 72 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1,X2,X3] :
~ ( subset(X0,cartesian_product2(X1,X2))
& in(X3,X0)
& ! [X4,X5] :
~ ( in(X4,X1)
& in(X5,X2)
& X3 = ordered_pair(X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1,X2,X3,X4,X5] :
( ( subset(X0,cartesian_product2(X1,X2))
& subset(X3,cartesian_product2(X4,X5))
& ! [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<=> in(ordered_pair(X6,X7),X3) ) )
=> X0 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( subset(X0,cartesian_product2(X1,X2))
& subset(X3,cartesian_product2(X4,X5))
& ! [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<=> in(ordered_pair(X6,X7),X3) ) )
=> X0 = X3 ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f13,plain,
? [X0,X1,X2,X3,X4,X5] :
( X0 != X3
& subset(X0,cartesian_product2(X1,X2))
& subset(X3,cartesian_product2(X4,X5))
& ! [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<=> in(ordered_pair(X6,X7),X3) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f14,plain,
? [X0,X1,X2,X3,X4,X5] :
( X0 != X3
& subset(X0,cartesian_product2(X1,X2))
& subset(X3,cartesian_product2(X4,X5))
& ! [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<=> in(ordered_pair(X6,X7),X3) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( ~ subset(X0,cartesian_product2(X1,X2))
| ~ in(X3,X0)
| ? [X4,X5] :
( in(X4,X1)
& in(X5,X2)
& X3 = ordered_pair(X4,X5) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f18,plain,
? [X0,X1,X2,X3,X4,X5] :
( X0 != X3
& subset(X0,cartesian_product2(X1,X2))
& subset(X3,cartesian_product2(X4,X5))
& ! [X6,X7] :
( ( in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X6,X7),X3) )
& ( in(ordered_pair(X6,X7),X3)
| ~ in(ordered_pair(X6,X7),X0) ) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f19,plain,
( sK0 != sK3
& subset(sK0,cartesian_product2(sK1,sK2))
& subset(sK3,cartesian_product2(sK4,sK5))
& ! [X6,X7] :
( ( in(ordered_pair(X6,X7),sK0)
| ~ in(ordered_pair(X6,X7),sK3) )
& ( in(ordered_pair(X6,X7),sK3)
| ~ in(ordered_pair(X6,X7),sK0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f21,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK6(X0,X1),X1)
| ~ in(sK6(X0,X1),X0) )
& ( in(sK6(X0,X1),X1)
| in(sK6(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f20]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ~ subset(X0,cartesian_product2(X1,X2))
| ~ in(X3,X0)
| ( in(sK7(X1,X2,X3),X1)
& in(sK8(X1,X2,X3),X2)
& ordered_pair(sK7(X1,X2,X3),sK8(X1,X2,X3)) = X3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X4,sK7(X1,X2,X3)),skolemize(X5,sK8(X1,X2,X3))],[f17]) ).
fof(f23,plain,
! [X6,X7] :
( in(ordered_pair(X6,X7),sK3)
| ~ in(ordered_pair(X6,X7),sK0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f24,plain,
! [X6,X7] :
( in(ordered_pair(X6,X7),sK0)
| ~ in(ordered_pair(X6,X7),sK3) ),
inference(cnf_transformation,[],[f19]) ).
fof(f25,plain,
subset(sK3,cartesian_product2(sK4,sK5)),
inference(cnf_transformation,[],[f19]) ).
fof(f26,plain,
subset(sK0,cartesian_product2(sK1,sK2)),
inference(cnf_transformation,[],[f19]) ).
fof(f27,plain,
sK0 != sK3,
inference(cnf_transformation,[],[f19]) ).
fof(f28,plain,
! [X0,X1] :
( in(sK6(X0,X1),X1)
| X0 = X1
| in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f29,plain,
! [X0,X1] :
( ~ in(sK6(X0,X1),X1)
| X0 = X1
| ~ in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f32,plain,
! [X2,X3,X0,X1] :
( ordered_pair(sK7(X1,X2,X3),sK8(X1,X2,X3)) = X3
| ~ in(X3,X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f50,plain,
! [X2,X3,X0,X1] :
( ~ subset(X3,cartesian_product2(X1,X2))
| ~ in(X0,sK3)
| ~ in(X0,X3)
| in(X0,sK0) ),
inference(superposition,[],[f24,f32]) ).
fof(f51,plain,
! [X2,X3,X0,X1] :
( ~ subset(X3,cartesian_product2(X1,X2))
| ~ in(X0,sK0)
| ~ in(X0,X3)
| in(X0,sK3) ),
inference(superposition,[],[f23,f32]) ).
fof(f52,plain,
! [X0] :
( ~ in(X0,sK3)
| ~ in(X0,sK3)
| in(X0,sK0) ),
inference(resolution,[],[f50,f25]) ).
fof(f55,plain,
! [X0] :
( in(X0,sK0)
| ~ in(X0,sK3) ),
inference(duplicate_literal_removal,[],[f52]) ).
fof(f57,plain,
! [X0] :
( ~ in(X0,sK0)
| ~ in(X0,sK0)
| in(X0,sK3) ),
inference(resolution,[],[f51,f26]) ).
fof(f59,plain,
! [X0] :
( in(X0,sK3)
| ~ in(X0,sK0) ),
inference(duplicate_literal_removal,[],[f57]) ).
fof(f62,plain,
! [X0] :
( ~ in(sK6(X0,sK0),sK3)
| sK0 = X0
| ~ in(sK6(X0,sK0),X0) ),
inference(resolution,[],[f55,f29]) ).
fof(f78,plain,
( ~ in(sK6(sK3,sK0),sK3)
| sK0 = sK3 ),
inference(factoring,[],[f62]) ).
fof(f80,plain,
~ in(sK6(sK3,sK0),sK3),
inference(forward_subsumption_resolution,[],[f78,f27]) ).
fof(f82,plain,
~ in(sK6(sK3,sK0),sK0),
inference(resolution,[],[f80,f59]) ).
fof(f84,plain,
( sK0 = sK3
| in(sK6(sK3,sK0),sK3) ),
inference(resolution,[],[f82,f28]) ).
fof(f86,plain,
in(sK6(sK3,sK0),sK3),
inference(forward_subsumption_resolution,[],[f84,f27]) ).
fof(f87,plain,
$false,
inference(forward_subsumption_resolution,[],[f86,f80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET957+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n006.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 28 03:15:55 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.69/1.26 % (3547618)Detected formulas, will run a generic FOF schedule.
% 2.69/1.26 % (3547627)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=228825547:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.26 % (3547627)First to succeed.
% 2.69/1.26 % (3547627)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3547618"
% 2.69/1.26 % (3547626)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3552768170:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.26 % (3547623)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=3834979617:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.26 % (3547624)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=206715414:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.26 % (3547625)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=3243814158:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.26 % (3547626)Also succeeded, but the first one will report.
% 2.69/1.26 % (3547629)dis-21_1_sil=8000:lcm=predicate:random_seed=3561014526: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)
% 2.69/1.26 % (3547628)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2814121008:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.26 % (3547629)Refutation not found, incomplete strategy
% 2.69/1.26 % (3547629)------------------------------
% 2.69/1.26 % (3547629)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.26 % (3547629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.26 % (3547629)CaDiCaL version: 2.1.3
% 2.69/1.26 % (3547629)Termination reason: Refutation not found, incomplete strategy
% 2.69/1.26 % (3547629)Time elapsed: 0.003 s
% 2.69/1.26 % (3547629)Peak memory usage: 88 MB
% 2.69/1.26 % (3547629)Instructions burned: 2 (million)
% 2.69/1.26 % (3547628)Also succeeded, but the first one will report.
% 2.69/1.26 % (3547627)Refutation found. Thanks to Tanya!
% 2.69/1.26 % SZS status Theorem for theBenchmark
% 2.69/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.26 % (3547627)------------------------------
% 2.69/1.26 % (3547627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.26 % (3547627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.26 % (3547627)CaDiCaL version: 2.1.3
% 2.69/1.26 % (3547627)Termination reason: Refutation
% 2.69/1.26 % (3547627)Time elapsed: 0.002 s
% 2.69/1.26 % (3547627)Peak memory usage: 88 MB
% 2.69/1.26 % (3547627)Instructions burned: 3 (million)
% 2.69/1.26 % (3547627)------------------------------
% 2.69/1.26 % (3547627)------------------------------
% 2.69/1.26 % (3547618)Success in time 0.31 s
% 2.69/1.26 % Vampire exiting
%------------------------------------------------------------------------------