%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET950+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 : 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 : Tue Sep 29 12:42:24 PM UTC 2026
% Result : Theorem 2.03s 0.87s
% Output : Refutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 7 unt; 1 def)
% Number of atoms : 146 ( 36 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 188 ( 80 ~; 66 |; 35 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 121 ( 105 !; 16 ?)
% 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(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f10,conjecture,
! [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(f11,negated_conjecture,
~ ! [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(negated_conjecture,[status(cth)],[f10]) ).
fof(f13,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f15,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
? [X0,X1,X2,X3] :
( subset(X0,cartesian_product2(X1,X2))
& in(X3,X0)
& ! [X4,X5] :
( ~ in(X4,X1)
| ~ in(X5,X2)
| ordered_pair(X4,X5) != X3 ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f17,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(f18,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,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != sK0(X0,X1,X2) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK1(X0,X1,X2),X0)
& in(sK2(X0,X1,X2),X1)
& sK0(X0,X1,X2) = ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2)) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ~ in(X9,X0)
| ~ in(X10,X1)
| ordered_pair(X9,X10) != X8 ) )
& ( ( in(sK3(X0,X1,X8),X0)
& in(sK4(X0,X1,X8),X1)
& ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8 )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X6,sK1(X0,X1,X2)),skolemize(X7,sK2(X0,X1,X2)),skolemize(X11,sK3(X0,X1,X8)),skolemize(X12,sK4(X0,X1,X8))],[f18]) ).
fof(f22,plain,
( subset(sK7,cartesian_product2(sK8,sK9))
& in(sK10,sK7)
& ! [X4,X5] :
( ~ in(X4,sK8)
| ~ in(X5,sK9)
| ordered_pair(X4,X5) != sK10 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10)],[f16]) ).
fof(f25,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f26,plain,
! [X2,X0,X1,X8] :
( in(sK4(X0,X1,X8),X1)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f27,plain,
! [X2,X0,X1,X8] :
( in(sK3(X0,X1,X8),X0)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f34,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f39,plain,
! [X4,X5] :
( ~ in(X4,sK8)
| ~ in(X5,sK9)
| ordered_pair(X4,X5) != sK10 ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
in(sK10,sK7),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
subset(sK7,cartesian_product2(sK8,sK9)),
inference(cnf_transformation,[],[f22]) ).
fof(f45,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(definition_unfolding,[],[f25,f34]) ).
fof(f47,plain,
! [X4,X5] :
( ~ in(X4,sK8)
| ~ in(X5,sK9)
| sK10 != unordered_pair(unordered_pair(X4,X5),singleton(X4)) ),
inference(definition_unfolding,[],[f39,f34]) ).
fof(f50,plain,
! [X0,X1,X8] :
( in(sK3(X0,X1,X8),X0)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f27]) ).
fof(f51,plain,
! [X0,X1,X8] :
( in(sK4(X0,X1,X8),X1)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f26]) ).
fof(f52,plain,
! [X0,X1,X8] :
( unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f45]) ).
fof(f53,definition,
! [X0,X1] :
( sQ11_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ11_eqProxy])],[equality_proxy_definition]) ).
fof(f59,plain,
! [X0,X1,X8] :
( sQ11_eqProxy(unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))),X8)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_proxy_replacement,[],[f52,f53]) ).
fof(f60,plain,
! [X4,X5] :
( ~ sQ11_eqProxy(sK10,unordered_pair(unordered_pair(X4,X5),singleton(X4)))
| ~ in(X5,sK9)
| ~ in(X4,sK8) ),
inference(equality_proxy_replacement,[],[f47,f53]) ).
fof(f62,plain,
! [X0,X1] :
( sQ11_eqProxy(X1,X0)
| ~ sQ11_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f53]) ).
fof(f66,plain,
! [X0,X1] :
( ~ sQ11_eqProxy(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK10)
| ~ in(X1,sK9)
| ~ in(X0,sK8) ),
inference(resolution,[],[f62,f60]) ).
fof(f68,plain,
! [X0] :
( in(X0,cartesian_product2(sK8,sK9))
| ~ in(X0,sK7) ),
inference(resolution,[],[f33,f41]) ).
fof(f81,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1,sK10),sK9)
| ~ in(sK10,cartesian_product2(X0,X1))
| ~ in(sK3(X0,X1,sK10),sK8) ),
inference(resolution,[],[f59,f66]) ).
fof(f82,plain,
! [X0] :
( ~ in(sK10,cartesian_product2(X0,sK9))
| ~ in(sK3(X0,sK9,sK10),sK8)
| ~ in(sK10,cartesian_product2(X0,sK9)) ),
inference(resolution,[],[f81,f51]) ).
fof(f83,plain,
! [X0] :
( ~ in(sK3(X0,sK9,sK10),sK8)
| ~ in(sK10,cartesian_product2(X0,sK9)) ),
inference(duplicate_literal_removal,[],[f82]) ).
fof(f85,plain,
( ~ in(sK10,cartesian_product2(sK8,sK9))
| ~ in(sK10,cartesian_product2(sK8,sK9)) ),
inference(resolution,[],[f83,f50]) ).
fof(f86,plain,
~ in(sK10,cartesian_product2(sK8,sK9)),
inference(duplicate_literal_removal,[],[f85]) ).
fof(f89,plain,
~ in(sK10,sK7),
inference(resolution,[],[f86,f68]) ).
fof(f90,plain,
$false,
inference(resolution,[],[f89,f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET950+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 28 03:15:34 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 2.03/0.87 % (2982489)Detected formulas, will run a generic FOF schedule.
% 2.03/0.87 % (2982497)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1594328435:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.03/0.87 % (2982498)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1397386681:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.03/0.87 % (2982500)dis-21_1_sil=8000:lcm=predicate:random_seed=3701645479: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)
% 2.03/0.87 % (2982495)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=750640985:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.03/0.87 % (2982496)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=2182592207:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.03/0.87 % (2982494)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=3348938070:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.03/0.87 % (2982499)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1770444646:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.03/0.87 % (2982500)First to succeed.
% 2.03/0.87 % (2982497)Also succeeded, but the first one will report.
% 2.03/0.87 % (2982498)Also succeeded, but the first one will report.
% 2.03/0.87 % (2982500)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2982489"
% 2.03/0.87 % (2982499)Also succeeded, but the first one will report.
% 2.03/0.87 % (2982500)Refutation found. Thanks to Tanya!
% 2.03/0.87 % SZS status Theorem for theBenchmark
% 2.03/0.87 % SZS output start Proof for theBenchmark
% See solution above
% 2.03/0.87 % (2982500)------------------------------
% 2.03/0.87 % (2982500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.03/0.87 % (2982500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.87 % (2982500)CaDiCaL version: 2.1.3
% 2.03/0.87 % (2982500)Termination reason: Refutation
% 2.03/0.87 % (2982500)Time elapsed: 0.002 s
% 2.03/0.87 % (2982500)Peak memory usage: 88 MB
% 2.03/0.87 % (2982500)Instructions burned: 3 (million)
% 2.03/0.87 % (2982500)------------------------------
% 2.03/0.87 % (2982500)------------------------------
% 2.03/0.87 % (2982489)Success in time 0.263 s
% 2.03/0.87 % Vampire exiting
%------------------------------------------------------------------------------