%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET956+1 : TPTP v9.3.1. Released v3.2.0.
% 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 12:42:25 PM UTC 2026
% Result : Theorem 2.56s 1.21s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 4 unt; 0 def)
% Number of atoms : 85 ( 4 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 94 ( 35 ~; 30 |; 22 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 76 ( 64 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,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/sandbox2/benchmark/theBenchmark.p',t103_zfmisc_1) ).
fof(f10,conjecture,
! [X0,X1,X2,X3] :
( ( subset(X0,cartesian_product2(X1,X2))
& ! [X4,X5] :
( in(ordered_pair(X4,X5),X0)
=> in(ordered_pair(X4,X5),X3) ) )
=> subset(X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( subset(X0,cartesian_product2(X1,X2))
& ! [X4,X5] :
( in(ordered_pair(X4,X5),X0)
=> in(ordered_pair(X4,X5),X3) ) )
=> subset(X0,X3) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f13,plain,
? [X0,X1,X2,X3] :
( ~ subset(X0,X3)
& subset(X0,cartesian_product2(X1,X2))
& ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
| ~ in(ordered_pair(X4,X5),X0) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f14,plain,
? [X0,X1,X2,X3] :
( ~ subset(X0,X3)
& subset(X0,cartesian_product2(X1,X2))
& ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
| ~ in(ordered_pair(X4,X5),X0) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f3]) ).
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,[],[f9]) ).
fof(f18,plain,
( ~ subset(sK0,sK3)
& subset(sK0,cartesian_product2(sK1,sK2))
& ! [X4,X5] :
( in(ordered_pair(X4,X5),sK3)
| ~ in(ordered_pair(X4,X5),sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f14]) ).
fof(f19,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f20,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK4(X0,X1),X1)
& in(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f20]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ~ subset(X0,cartesian_product2(X1,X2))
| ~ in(X3,X0)
| ( in(sK5(X1,X2,X3),X1)
& in(sK6(X1,X2,X3),X2)
& ordered_pair(sK5(X1,X2,X3),sK6(X1,X2,X3)) = X3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X4,sK5(X1,X2,X3)),skolemize(X5,sK6(X1,X2,X3))],[f17]) ).
fof(f23,plain,
! [X4,X5] :
( in(ordered_pair(X4,X5),sK3)
| ~ in(ordered_pair(X4,X5),sK0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f24,plain,
subset(sK0,cartesian_product2(sK1,sK2)),
inference(cnf_transformation,[],[f18]) ).
fof(f25,plain,
~ subset(sK0,sK3),
inference(cnf_transformation,[],[f18]) ).
fof(f27,plain,
! [X0,X1] :
( in(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f28,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f31,plain,
! [X2,X3,X0,X1] :
( ordered_pair(sK5(X1,X2,X3),sK6(X1,X2,X3)) = X3
| ~ in(X3,X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( ~ subset(X3,cartesian_product2(X1,X2))
| ~ in(X0,sK0)
| ~ in(X0,X3)
| in(X0,sK3) ),
inference(superposition,[],[f23,f31]) ).
fof(f54,plain,
! [X0] :
( ~ in(X0,sK0)
| ~ in(X0,sK0)
| in(X0,sK3) ),
inference(resolution,[],[f52,f24]) ).
fof(f56,plain,
! [X0] :
( in(X0,sK3)
| ~ in(X0,sK0) ),
inference(duplicate_literal_removal,[],[f54]) ).
fof(f60,plain,
! [X0] :
( ~ in(sK4(X0,sK3),sK0)
| subset(X0,sK3) ),
inference(resolution,[],[f56,f28]) ).
fof(f76,plain,
( subset(sK0,sK3)
| subset(sK0,sK3) ),
inference(resolution,[],[f60,f27]) ).
fof(f78,plain,
subset(sK0,sK3),
inference(duplicate_literal_removal,[],[f76]) ).
fof(f79,plain,
$false,
inference(forward_subsumption_resolution,[],[f78,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET956+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n018.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 : Mon Sep 28 03:18:24 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.39 Running first-order theorem proving
% 0.08/0.39 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
% 2.56/1.21 % (2964720)Detected formulas, will run a generic FOF schedule.
% 2.56/1.21 % (2964729)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4043652484:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.56/1.21 % (2964729)First to succeed.
% 2.56/1.21 % (2964729)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2964720"
% 2.56/1.21 % (2964727)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=1076804462:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.56/1.21 % (2964725)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=102805062:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.56/1.21 % (2964730)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3424440764:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.56/1.21 % (2964726)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=3883472267:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.56/1.21 % (2964728)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1748074969:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.56/1.21 % (2964731)dis-21_1_sil=8000:lcm=predicate:random_seed=1182126547: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)
% 2.56/1.21 % (2964728)Also succeeded, but the first one will report.
% 2.56/1.21 % (2964730)Also succeeded, but the first one will report.
% 2.56/1.21 % (2964731)Instruction limit reached!
% 2.56/1.21 % (2964731)------------------------------
% 2.56/1.21 % (2964731)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.21 % (2964731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.21 % (2964731)CaDiCaL version: 2.1.3
% 2.56/1.21 % (2964731)Termination reason: Instruction limit
% 2.56/1.21 % (2964731)Termination phase: Saturation
% 2.56/1.21 % (2964731)Time elapsed: 0.079 s
% 2.56/1.21 % (2964731)Peak memory usage: 88 MB
% 2.56/1.21 % (2964731)Instructions burned: 130 (million)
% 2.56/1.21 % (2964729)Refutation found. Thanks to Tanya!
% 2.56/1.21 % SZS status Theorem for theBenchmark
% 2.56/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.21 % (2964729)------------------------------
% 2.56/1.21 % (2964729)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.21 % (2964729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.21 % (2964729)CaDiCaL version: 2.1.3
% 2.56/1.21 % (2964729)Termination reason: Refutation
% 2.56/1.21 % (2964729)Time elapsed: 0.002 s
% 2.56/1.21 % (2964729)Peak memory usage: 88 MB
% 2.56/1.21 % (2964729)Instructions burned: 3 (million)
% 2.56/1.21 % (2964729)------------------------------
% 2.56/1.21 % (2964729)------------------------------
% 2.56/1.21 % (2964720)Success in time 0.289 s
% 2.56/1.21 % Vampire exiting
%------------------------------------------------------------------------------