%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET988+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 12:45:08 PM UTC 2026
% Result : Theorem 0.15s 0.46s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 64 ( 10 unt; 2 def)
% Number of atoms : 193 ( 49 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 204 ( 75 ~; 80 |; 35 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-2 aty)
% Number of variables : 132 ( 0 sgn 112 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f30,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(f31,conjecture,
! [X0] :
( ( ! [X1] :
~ ( in(X1,X0)
& ! [X2,X3] : ordered_pair(X2,X3) != X1 )
& ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X1,X3),X0) )
=> X2 = X3 ) )
=> ( relation(X0)
& function(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_funct_1) ).
fof(f32,negated_conjecture,
~ ! [X0] :
( ( ! [X1] :
~ ( in(X1,X0)
& ! [X2,X3] : ordered_pair(X2,X3) != X1 )
& ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X1,X3),X0) )
=> X2 = X3 ) )
=> ( relation(X0)
& function(X0) ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,axiom,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X1,X3),X0) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_1) ).
fof(f34,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( in(X1,X0)
& ! [X2,X3] : X1 != ordered_pair(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f36,plain,
~ ! [X0] :
( ( ! [X1] :
~ ( in(X1,X0)
& ! [X2,X3] : ordered_pair(X2,X3) != X1 )
& ! [X4,X5,X6] :
( ( in(ordered_pair(X4,X5),X0)
& in(ordered_pair(X4,X6),X0) )
=> X5 = X6 ) )
=> ( relation(X0)
& function(X0) ) ),
inference(rectify,[],[f32]) ).
fof(f54,plain,
? [X0] :
( ( ~ relation(X0)
| ~ function(X0) )
& ! [X1] :
( ~ in(X1,X0)
| ? [X2,X3] : ordered_pair(X2,X3) = X1 )
& ! [X4,X5,X6] :
( X5 = X6
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X4,X6),X0) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f55,plain,
? [X0] :
( ( ~ relation(X0)
| ~ function(X0) )
& ! [X1] :
( ~ in(X1,X0)
| ? [X2,X3] : ordered_pair(X2,X3) = X1 )
& ! [X4,X5,X6] :
( X5 = X6
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X4,X6),X0) ) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X1,X3),X0) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f57,plain,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X1,X3),X0) ) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ~ in(X1,X0)
| ? [X2,X3] : ordered_pair(X2,X3) = X1 ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f68,plain,
( ( ~ relation(sK9)
| ~ function(sK9) )
& ! [X1] :
( ~ in(X1,sK9)
| ordered_pair(sK10(X1),sK11(X1)) = X1 )
& ! [X4,X5,X6] :
( X5 = X6
| ~ in(ordered_pair(X4,X5),sK9)
| ~ in(ordered_pair(X4,X6),sK9) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X0,sK9),skolemize(X2,sK10(X1)),skolemize(X3,sK11(X1))],[f55]) ).
fof(f69,plain,
! [X0] :
( ( function(X0)
| ? [X1,X2,X3] :
( X2 != X3
& in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X1,X3),X0) ) )
& ( ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X1,X3),X0) )
| ~ function(X0) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f70,plain,
! [X0] :
( ( function(X0)
| ? [X1,X2,X3] :
( X2 != X3
& in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X1,X3),X0) ) )
& ( ! [X4,X5,X6] :
( X5 = X6
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X4,X6),X0) )
| ~ function(X0) ) ),
inference(rectify,[],[f69]) ).
fof(f71,plain,
! [X0] :
( ( function(X0)
| ( sK13(X0) != sK14(X0)
& in(ordered_pair(sK12(X0),sK13(X0)),X0)
& in(ordered_pair(sK12(X0),sK14(X0)),X0) ) )
& ( ! [X4,X5,X6] :
( X5 = X6
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X4,X6),X0) )
| ~ function(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X1,sK12(X0)),skolemize(X2,sK13(X0)),skolemize(X3,sK14(X0))],[f70]) ).
fof(f72,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( in(X1,X0)
& ! [X2,X3] : ordered_pair(X2,X3) != X1 ) )
& ( ! [X1] :
( ~ in(X1,X0)
| ? [X2,X3] : ordered_pair(X2,X3) = X1 )
| ~ relation(X0) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f73,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( in(X1,X0)
& ! [X2,X3] : ordered_pair(X2,X3) != X1 ) )
& ( ! [X4] :
( ~ in(X4,X0)
| ? [X5,X6] : ordered_pair(X5,X6) = X4 )
| ~ relation(X0) ) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
! [X0] :
( ( relation(X0)
| ( in(sK15(X0),X0)
& ! [X2,X3] : ordered_pair(X2,X3) != sK15(X0) ) )
& ( ! [X4] :
( ~ in(X4,X0)
| ordered_pair(sK16(X4),sK17(X4)) = X4 )
| ~ relation(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17]),skolemize(X1,sK15(X0)),skolemize(X5,sK16(X4)),skolemize(X6,sK17(X4))],[f73]) ).
fof(f81,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f111,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f30]) ).
fof(f112,plain,
! [X6,X4,X5] :
( X5 = X6
| ~ in(ordered_pair(X4,X5),sK9)
| ~ in(ordered_pair(X4,X6),sK9) ),
inference(cnf_transformation,[],[f68]) ).
fof(f113,plain,
! [X1] :
( ~ in(X1,sK9)
| ordered_pair(sK10(X1),sK11(X1)) = X1 ),
inference(cnf_transformation,[],[f68]) ).
fof(f114,plain,
( ~ relation(sK9)
| ~ function(sK9) ),
inference(cnf_transformation,[],[f68]) ).
fof(f116,plain,
! [X0] :
( function(X0)
| in(ordered_pair(sK12(X0),sK14(X0)),X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f117,plain,
! [X0] :
( function(X0)
| in(ordered_pair(sK12(X0),sK13(X0)),X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f118,plain,
! [X0] :
( sK13(X0) != sK14(X0)
| function(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f120,plain,
! [X2,X3,X0] :
( relation(X0)
| ordered_pair(X2,X3) != sK15(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f121,plain,
! [X0] :
( relation(X0)
| in(sK15(X0),X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f123,plain,
! [X1] :
( ~ in(X1,sK9)
| unordered_pair(unordered_pair(sK10(X1),sK11(X1)),singleton(sK10(X1))) = X1 ),
inference(definition_unfolding,[],[f113,f111]) ).
fof(f124,plain,
! [X6,X4,X5] :
( ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),sK9)
| X5 = X6
| ~ in(unordered_pair(unordered_pair(X4,X6),singleton(X4)),sK9) ),
inference(definition_unfolding,[],[f112,f111,f111]) ).
fof(f125,plain,
! [X0] :
( function(X0)
| in(unordered_pair(unordered_pair(sK12(X0),sK13(X0)),singleton(sK12(X0))),X0) ),
inference(definition_unfolding,[],[f117,f111]) ).
fof(f126,plain,
! [X0] :
( function(X0)
| in(unordered_pair(unordered_pair(sK12(X0),sK14(X0)),singleton(sK12(X0))),X0) ),
inference(definition_unfolding,[],[f116,f111]) ).
fof(f128,plain,
! [X2,X3,X0] :
( sK15(X0) != unordered_pair(unordered_pair(X2,X3),singleton(X2))
| relation(X0) ),
inference(definition_unfolding,[],[f120,f111]) ).
fof(f131,definition,
( spl18_1
<=> function(sK9) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
fof(f133,plain,
( ~ function(sK9)
| spl18_1 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f135,definition,
( spl18_2
<=> relation(sK9) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
fof(f137,plain,
( ~ relation(sK9)
| spl18_2 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f138,plain,
( ~ spl18_1
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f114,f135,f131]) ).
fof(f177,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK9)
| X1 = X2
| ~ in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),sK9) ),
inference(superposition,[],[f124,f81]) ).
fof(f239,plain,
! [X2,X0,X1] :
( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK15(X2)
| relation(X2) ),
inference(superposition,[],[f128,f81]) ).
fof(f242,plain,
( in(unordered_pair(unordered_pair(sK12(sK9),sK13(sK9)),singleton(sK12(sK9))),sK9)
| spl18_1 ),
inference(resolution,[],[f125,f133]) ).
fof(f243,plain,
( in(unordered_pair(singleton(sK12(sK9)),unordered_pair(sK12(sK9),sK13(sK9))),sK9)
| spl18_1 ),
inference(forward_demodulation,[],[f242,f81]) ).
fof(f244,plain,
( ! [X0] :
( ~ in(unordered_pair(unordered_pair(sK12(sK9),X0),singleton(sK12(sK9))),sK9)
| sK13(sK9) = X0 )
| spl18_1 ),
inference(resolution,[],[f243,f177]) ).
fof(f250,plain,
( in(unordered_pair(unordered_pair(sK12(sK9),sK14(sK9)),singleton(sK12(sK9))),sK9)
| spl18_1 ),
inference(resolution,[],[f126,f133]) ).
fof(f251,plain,
( in(unordered_pair(singleton(sK12(sK9)),unordered_pair(sK12(sK9),sK14(sK9))),sK9)
| spl18_1 ),
inference(forward_demodulation,[],[f250,f81]) ).
fof(f301,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(sK12(sK9)),unordered_pair(sK12(sK9),X0)),sK9)
| sK13(sK9) = X0 )
| spl18_1 ),
inference(superposition,[],[f244,f81]) ).
fof(f380,plain,
( sK13(sK9) = sK14(sK9)
| spl18_1 ),
inference(resolution,[],[f301,f251]) ).
fof(f397,plain,
( sK13(sK9) != sK13(sK9)
| function(sK9)
| spl18_1 ),
inference(superposition,[],[f118,f380]) ).
fof(f398,plain,
( function(sK9)
| spl18_1 ),
inference(trivial_inequality_removal,[],[f397]) ).
fof(f399,plain,
( $false
| spl18_1 ),
inference(forward_subsumption_resolution,[],[f398,f133]) ).
fof(f400,plain,
spl18_1,
inference(avatar_contradiction_clause,[],[f399]) ).
fof(f403,plain,
( in(sK15(sK9),sK9)
| spl18_2 ),
inference(resolution,[],[f137,f121]) ).
fof(f404,plain,
( sK15(sK9) = unordered_pair(unordered_pair(sK10(sK15(sK9)),sK11(sK15(sK9))),singleton(sK10(sK15(sK9))))
| spl18_2 ),
inference(resolution,[],[f403,f123]) ).
fof(f411,plain,
( sK15(sK9) = unordered_pair(singleton(sK10(sK15(sK9))),unordered_pair(sK10(sK15(sK9)),sK11(sK15(sK9))))
| spl18_2 ),
inference(forward_demodulation,[],[f404,f81]) ).
fof(f475,plain,
( ! [X0] :
( sK15(X0) != sK15(sK9)
| relation(X0) )
| spl18_2 ),
inference(superposition,[],[f239,f411]) ).
fof(f683,plain,
( relation(sK9)
| spl18_2 ),
inference(equality_resolution,[],[f475]) ).
fof(f684,plain,
( $false
| spl18_2 ),
inference(forward_subsumption_resolution,[],[f683,f137]) ).
fof(f685,plain,
spl18_2,
inference(avatar_contradiction_clause,[],[f684]) ).
cnf(s1,plain,
( ~ spl18_1
| ~ spl18_2 ),
inference(sat_conversion,[],[f138]) ).
cnf(s2,plain,
spl18_1,
inference(sat_conversion,[],[f400]) ).
cnf(s14,plain,
spl18_2,
inference(sat_conversion,[],[f685]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s1,s14,s2]) ).
fof(f686,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET988+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 % Computer : n005.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Mon Sep 28 03:19:32 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.46 % (403263)Will run a generic schedule for satisfiability detection.
% 0.15/0.46 % (403273)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1387655284:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.46 % (403269)% WARNING: option uhcvi not known.
% 0.15/0.46 % (403269)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2851271180:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.46 % (403268)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4166938948_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.46 % (403270)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1896825950:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.46 % (403272)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1943152722:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.46 % (403271)dis+10_1_sil=32000:sp=arity:random_seed=806971851:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.46 % (403273) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-403263-403273"...
% 0.15/0.46 % (403274)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1754795343:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.46 % (403273)...printing done.
% 0.15/0.46 % (403273)Refutation found. Thanks to Tanya!
% 0.15/0.46 % SZS status Theorem for theBenchmark
% 0.15/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (403273)------------------------------
% 0.15/0.47 % (403273)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (403273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (403273)CaDiCaL version: 2.1.3
% 0.15/0.47 % (403273)Termination reason: Refutation
% 0.15/0.47 % (403273)Time elapsed: 0.009 s
% 0.15/0.47 % (403273)Peak memory usage: 12 MB
% 0.15/0.47 % (403273)Instructions burned: 20 (million)
% 0.15/0.47 % (403263)Success in time 0.032 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------