%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET950+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:45:04 PM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 16 unt; 2 def)
% Number of atoms : 166 ( 39 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 191 ( 78 ~; 70 |; 35 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 120 ( 0 sgn 104 !; 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/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,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(f59,plain,
! [X0,X1,X8] :
( in(X8,cartesian_product2(X0,X1))
| ~ in(sK3(X0,X1,X8),X0) ),
inference(consistent_polarity_flipping,[],[f50]) ).
fof(f60,plain,
! [X0,X1,X8] :
( in(X8,cartesian_product2(X0,X1))
| ~ in(sK4(X0,X1,X8),X1) ),
inference(consistent_polarity_flipping,[],[f51]) ).
fof(f61,plain,
! [X0,X1,X8] :
( in(X8,cartesian_product2(X0,X1))
| unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8 ),
inference(consistent_polarity_flipping,[],[f52]) ).
fof(f62,plain,
! [X2,X0,X1] :
( subset(X0,X1)
| in(X2,X0)
| ~ in(X2,X1) ),
inference(consistent_polarity_flipping,[],[f33]) ).
fof(f67,plain,
~ subset(sK7,cartesian_product2(sK8,sK9)),
inference(consistent_polarity_flipping,[],[f41]) ).
fof(f68,plain,
~ in(sK10,sK7),
inference(consistent_polarity_flipping,[],[f40]) ).
fof(f69,plain,
! [X4,X5] :
( sK10 != unordered_pair(unordered_pair(X4,X5),singleton(X4))
| in(X5,sK9)
| in(X4,sK8) ),
inference(consistent_polarity_flipping,[],[f47]) ).
fof(f95,plain,
! [X0] :
( in(X0,sK7)
| ~ in(X0,cartesian_product2(sK8,sK9)) ),
inference(resolution,[],[f62,f67]) ).
fof(f97,plain,
~ in(sK10,cartesian_product2(sK8,sK9)),
inference(resolution,[],[f95,f68]) ).
fof(f98,plain,
~ in(sK3(sK8,sK9,sK10),sK8),
inference(resolution,[],[f97,f59]) ).
fof(f101,plain,
~ in(sK4(sK8,sK9,sK10),sK9),
inference(resolution,[],[f60,f97]) ).
fof(f194,plain,
sK10 = unordered_pair(unordered_pair(sK3(sK8,sK9,sK10),sK4(sK8,sK9,sK10)),singleton(sK3(sK8,sK9,sK10))),
inference(resolution,[],[f61,f97]) ).
fof(f199,plain,
( sK10 != sK10
| in(sK4(sK8,sK9,sK10),sK9)
| in(sK3(sK8,sK9,sK10),sK8) ),
inference(superposition,[],[f69,f194]) ).
fof(f226,plain,
( in(sK4(sK8,sK9,sK10),sK9)
| in(sK3(sK8,sK9,sK10),sK8) ),
inference(trivial_inequality_removal,[],[f199]) ).
fof(f296,definition,
( spl11_17
<=> in(sK3(sK8,sK9,sK10),sK8) ),
introduced(definition,[new_symbols(definition,[spl11_17])],[avatar_definition]) ).
fof(f298,plain,
( in(sK3(sK8,sK9,sK10),sK8)
| ~ spl11_17 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f300,definition,
( spl11_18
<=> in(sK4(sK8,sK9,sK10),sK9) ),
introduced(definition,[new_symbols(definition,[spl11_18])],[avatar_definition]) ).
fof(f302,plain,
( in(sK4(sK8,sK9,sK10),sK9)
| ~ spl11_18 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f303,plain,
( spl11_17
| spl11_18 ),
inference(avatar_split_clause,[],[f226,f300,f296]) ).
fof(f304,plain,
( $false
| ~ spl11_17 ),
inference(resolution,[],[f298,f98]) ).
fof(f305,plain,
~ spl11_17,
inference(avatar_contradiction_clause,[],[f304]) ).
fof(f306,plain,
( $false
| ~ spl11_18 ),
inference(resolution,[],[f302,f101]) ).
fof(f307,plain,
~ spl11_18,
inference(avatar_contradiction_clause,[],[f306]) ).
cnf(s10,plain,
( spl11_17
| spl11_18 ),
inference(sat_conversion,[],[f303]) ).
cnf(s11,plain,
~ spl11_17,
inference(sat_conversion,[],[f305]) ).
cnf(s12,plain,
~ spl11_18,
inference(sat_conversion,[],[f307]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s10,s12,s11]) ).
fof(f308,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET950+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 03:15:40 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.44 % (3547220)Will run a generic schedule for satisfiability detection.
% 0.10/0.44 % (3547231)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4094902783:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.44 % (3547226)% WARNING: option uhcvi not known.
% 0.10/0.44 % (3547231) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3547220-3547231"...
% 0.10/0.44 % (3547225)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1804318990_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.44 % (3547231)...printing done.
% 0.10/0.44 % (3547226)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1935081308:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.44 % (3547228)dis+10_1_sil=32000:sp=arity:random_seed=1983688419:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.44 % (3547227)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3683101636:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.44 % (3547229)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1507905089:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.44 % (3547231)Refutation found. Thanks to Tanya!
% 0.10/0.44 % SZS status Theorem for theBenchmark
% 0.10/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.44 % (3547231)------------------------------
% 0.10/0.44 % (3547231)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.44 % (3547231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.44 % (3547231)CaDiCaL version: 2.1.3
% 0.10/0.44 % (3547231)Termination reason: Refutation
% 0.10/0.44 % (3547231)Time elapsed: 0.006 s
% 0.10/0.44 % (3547231)Peak memory usage: 12 MB
% 0.10/0.44 % (3547231)Instructions burned: 13 (million)
% 0.10/0.44 % (3547220)Success in time 0.031 s
% 0.10/0.44 % Vampire exiting
%------------------------------------------------------------------------------