%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET962+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 2.55s 1.32s
% Output : Refutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 44 ( 8 unt; 0 def)
% Number of atoms : 115 ( 27 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 132 ( 61 ~; 56 |; 9 &)
% ( 2 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 74 ( 70 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [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(f8,conjecture,
! [X0,X1] :
( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] :
( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f11,plain,
? [X0,X1] :
( X0 != X1
& cartesian_product2(X0,X0) = cartesian_product2(X1,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f12,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f14,plain,
( sK0 != sK1
& cartesian_product2(sK0,sK0) = cartesian_product2(sK1,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f11]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f18,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK2(X0,X1),X1)
| ~ in(sK2(X0,X1),X0) )
& ( in(sK2(X0,X1),X1)
| in(sK2(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f17]) ).
fof(f21,plain,
cartesian_product2(sK0,sK0) = cartesian_product2(sK1,sK1),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f14]) ).
fof(f24,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f25,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f16]) ).
fof(f26,plain,
! [X0,X1] :
( in(sK2(X0,X1),X1)
| X0 = X1
| in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f27,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X1)
| X0 = X1
| ~ in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(sK0,sK0))
| in(X0,sK1) ),
inference(superposition,[],[f24,f21]) ).
fof(f37,plain,
! [X0,X1] :
( in(X0,sK1)
| ~ in(X1,sK0)
| ~ in(X0,sK0) ),
inference(resolution,[],[f25,f34]) ).
fof(f40,plain,
! [X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(sK0,sK0))
| ~ in(X0,sK1)
| ~ in(X1,sK1) ),
inference(superposition,[],[f25,f21]) ).
fof(f46,plain,
! [X0,X1] :
( ~ in(sK2(X0,sK1),sK0)
| ~ in(sK2(X0,sK1),X0)
| ~ in(X1,sK0)
| sK1 = X0 ),
inference(resolution,[],[f27,f37]) ).
fof(f51,plain,
! [X0,X1] :
( in(X0,sK0)
| ~ in(X1,sK1)
| ~ in(X0,sK1) ),
inference(resolution,[],[f40,f24]) ).
fof(f58,plain,
! [X0,X1] :
( ~ in(sK2(X1,sK0),sK1)
| ~ in(X0,sK1)
| sK0 = X1
| ~ in(sK2(X1,sK0),X1) ),
inference(resolution,[],[f51,f27]) ).
fof(f76,plain,
! [X0] :
( ~ in(sK2(sK0,sK1),sK0)
| ~ in(X0,sK0)
| sK0 = sK1 ),
inference(factoring,[],[f46]) ).
fof(f79,plain,
! [X0] :
( ~ in(sK2(sK0,sK1),sK0)
| ~ in(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f76,f22]) ).
fof(f81,plain,
! [X0,X1] :
( ~ in(sK2(sK0,sK1),sK1)
| ~ in(X1,sK1)
| ~ in(X0,sK0) ),
inference(resolution,[],[f79,f51]) ).
fof(f82,plain,
~ in(sK2(sK0,sK1),sK0),
inference(factoring,[],[f79]) ).
fof(f86,plain,
! [X0] :
( ~ in(sK2(sK0,sK1),sK1)
| ~ in(X0,sK1) ),
inference(resolution,[],[f82,f51]) ).
fof(f91,plain,
! [X0] :
( ~ in(sK2(sK1,sK0),sK1)
| ~ in(X0,sK1)
| sK0 = sK1 ),
inference(factoring,[],[f58]) ).
fof(f93,plain,
! [X0] :
( ~ in(sK2(sK1,sK0),sK1)
| ~ in(X0,sK1) ),
inference(forward_subsumption_resolution,[],[f91,f22]) ).
fof(f98,plain,
~ in(sK2(sK1,sK0),sK1),
inference(factoring,[],[f93]) ).
fof(f101,plain,
! [X0] :
( ~ in(sK2(sK1,sK0),sK0)
| ~ in(X0,sK0) ),
inference(resolution,[],[f98,f37]) ).
fof(f112,plain,
! [X0,X1] :
( ~ in(X0,sK1)
| ~ in(X1,sK0)
| sK0 = sK1
| in(sK2(sK0,sK1),sK0) ),
inference(resolution,[],[f81,f26]) ).
fof(f115,plain,
! [X0,X1] :
( ~ in(X0,sK1)
| ~ in(X1,sK0)
| sK0 = sK1 ),
inference(forward_subsumption_resolution,[],[f112,f79]) ).
fof(f116,plain,
! [X0,X1] :
( ~ in(X1,sK0)
| ~ in(X0,sK1) ),
inference(forward_subsumption_resolution,[],[f115,f22]) ).
fof(f120,plain,
! [X0] :
( ~ in(X0,sK1)
| sK0 = sK1
| in(sK2(sK0,sK1),sK0) ),
inference(resolution,[],[f86,f26]) ).
fof(f123,plain,
! [X0] :
( ~ in(X0,sK1)
| sK0 = sK1 ),
inference(forward_subsumption_resolution,[],[f120,f116]) ).
fof(f124,plain,
! [X0] : ~ in(X0,sK1),
inference(forward_subsumption_resolution,[],[f123,f22]) ).
fof(f126,plain,
! [X0] :
( in(sK2(X0,sK1),X0)
| sK1 = X0 ),
inference(resolution,[],[f124,f26]) ).
fof(f128,plain,
! [X0] :
( ~ in(X0,sK0)
| sK0 = sK1
| in(sK2(sK1,sK0),sK1) ),
inference(resolution,[],[f101,f26]) ).
fof(f131,plain,
! [X0] :
( ~ in(X0,sK0)
| in(sK2(sK1,sK0),sK1) ),
inference(forward_subsumption_resolution,[],[f128,f22]) ).
fof(f132,plain,
! [X0] : ~ in(X0,sK0),
inference(forward_subsumption_resolution,[],[f131,f124]) ).
fof(f142,plain,
sK0 = sK1,
inference(resolution,[],[f126,f132]) ).
fof(f148,plain,
$false,
inference(forward_subsumption_resolution,[],[f142,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET962+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n007.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:14:26 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 2.55/1.31 % (1993325)Detected formulas, will run a generic FOF schedule.
% 2.55/1.31 % (1993334)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2850153015:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.55/1.31 % (1993334)First to succeed.
% 2.55/1.31 % (1993334)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1993325"
% 2.55/1.31 % (1993336)dis-21_1_sil=8000:lcm=predicate:random_seed=2516048139: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)
% 2.55/1.31 % (1993333)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2573164141:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.55/1.31 % (1993330)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=152061000:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.55/1.31 % (1993331)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=3923297140:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.55/1.31 % (1993332)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=880407881:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.55/1.31 % (1993336)Refutation not found, incomplete strategy
% 2.55/1.31 % (1993336)------------------------------
% 2.55/1.31 % (1993336)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.31 % (1993336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.31 % (1993336)CaDiCaL version: 2.1.3
% 2.55/1.31 % (1993336)Termination reason: Refutation not found, incomplete strategy
% 2.55/1.31 % (1993336)Time elapsed: 0.002 s
% 2.55/1.31 % (1993336)Peak memory usage: 88 MB
% 2.55/1.31 % (1993336)Instructions burned: 1 (million)
% 2.55/1.31 % (1993333)Refutation not found, incomplete strategy
% 2.55/1.31 % (1993333)------------------------------
% 2.55/1.31 % (1993333)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.32 % (1993333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.32 % (1993333)CaDiCaL version: 2.1.3
% 2.55/1.32 % (1993333)Termination reason: Refutation not found, incomplete strategy
% 2.55/1.32 % (1993333)Time elapsed: 0.001 s
% 2.55/1.32 % (1993333)Peak memory usage: 88 MB
% 2.55/1.32 % (1993335)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3021511167:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.55/1.32 % (1993334)Refutation found. Thanks to Tanya!
% 2.55/1.32 % SZS status Theorem for theBenchmark
% 2.55/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.55/1.32 % (1993334)------------------------------
% 2.55/1.32 % (1993334)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.32 % (1993334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.32 % (1993334)CaDiCaL version: 2.1.3
% 2.55/1.32 % (1993334)Termination reason: Refutation
% 2.55/1.32 % (1993334)Time elapsed: 0.003 s
% 2.55/1.32 % (1993334)Peak memory usage: 88 MB
% 2.55/1.32 % (1993334)Instructions burned: 5 (million)
% 2.55/1.32 % (1993334)------------------------------
% 2.55/1.32 % (1993334)------------------------------
% 2.55/1.32 % (1993325)Success in time 0.269 s
% 2.55/1.32 % Vampire exiting
%------------------------------------------------------------------------------