%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET991+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 : n002.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 0.10s 0.44s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 6 unt; 0 def)
% Number of atoms : 112 ( 33 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 141 ( 51 ~; 49 |; 30 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 41 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f30,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( in(X0,relation_dom(X1))
=> in(apply(X1,X0),relation_rng(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_1) ).
fof(f31,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( in(X0,relation_dom(X1))
=> in(apply(X1,X0),relation_rng(X1)) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f32,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f57,plain,
? [X0,X1] :
( ~ in(apply(X1,X0),relation_rng(X1))
& in(X0,relation_dom(X1))
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f58,plain,
? [X0,X1] :
( ~ in(apply(X1,X0),relation_rng(X1))
& in(X0,relation_dom(X1))
& relation(X1)
& function(X1) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f59]) ).
fof(f70,plain,
( ~ in(apply(sK10,sK9),relation_rng(sK10))
& in(sK9,relation_dom(sK10))
& relation(sK10)
& function(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X0,sK9),skolemize(X1,sK10)],[f58]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f60]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& apply(X0,X4) = X2 )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ? [X7] :
( in(X7,relation_dom(X0))
& apply(X0,X7) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK11(X0,X1) )
| ~ in(sK11(X0,X1),X1) )
& ( ( in(sK12(X0,X1),relation_dom(X0))
& sK11(X0,X1) = apply(X0,sK12(X0,X1)) )
| in(sK11(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK13(X0,X5),relation_dom(X0))
& apply(X0,sK13(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X2,sK11(X0,X1)),skolemize(X4,sK12(X0,X1)),skolemize(X7,sK13(X0,X5))],[f72]) ).
fof(f112,plain,
function(sK10),
inference(cnf_transformation,[],[f70]) ).
fof(f113,plain,
relation(sK10),
inference(cnf_transformation,[],[f70]) ).
fof(f114,plain,
in(sK9,relation_dom(sK10)),
inference(cnf_transformation,[],[f70]) ).
fof(f115,plain,
~ in(apply(sK10,sK9),relation_rng(sK10)),
inference(cnf_transformation,[],[f70]) ).
fof(f118,plain,
! [X0,X1,X6,X5] :
( ~ function(X0)
| ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5
| relation_rng(X0) != X1
| ~ relation(X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f393,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(sK10))
| apply(sK10,X0) != X1
| relation_rng(sK10) != X2
| ~ relation(sK10)
| in(X1,X2) ),
inference(resolution,[],[f118,f112]) ).
fof(f394,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(sK10))
| apply(sK10,X0) != X1
| relation_rng(sK10) != X2
| in(X1,X2) ),
inference(forward_subsumption_resolution,[],[f393,f113]) ).
fof(f471,plain,
! [X0,X1] :
( apply(sK10,sK9) != X0
| relation_rng(sK10) != X1
| in(X0,X1) ),
inference(resolution,[],[f394,f114]) ).
fof(f646,plain,
! [X0] :
( relation_rng(sK10) != X0
| in(apply(sK10,sK9),X0) ),
inference(equality_resolution,[],[f471]) ).
fof(f648,plain,
in(apply(sK10,sK9),relation_rng(sK10)),
inference(equality_resolution,[],[f646]) ).
fof(f649,plain,
$false,
inference(forward_subsumption_resolution,[],[f648,f115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET991+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n002.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
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 03:23:52 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 % (4119882)Will run a generic schedule for satisfiability detection.
% 0.10/0.44 % (4119892)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2935568768:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.44 % (4119888)% WARNING: option uhcvi not known.
% 0.10/0.44 % (4119892) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4119882-4119892"...
% 0.10/0.44 % (4119892)...printing done.
% 0.10/0.44 % (4119887)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2677765287_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.44 % (4119889)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1941753132:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.44 % (4119890)dis+10_1_sil=32000:sp=arity:random_seed=3349819600:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.44 % (4119893)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1405224105:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.44 % (4119892)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 % (4119892)------------------------------
% 0.10/0.44 % (4119892)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.44 % (4119892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.44 % (4119892)CaDiCaL version: 2.1.3
% 0.10/0.44 % (4119892)Termination reason: Refutation
% 0.10/0.44 % (4119892)Time elapsed: 0.006 s
% 0.10/0.44 % (4119892)Peak memory usage: 11 MB
% 0.10/0.44 % (4119892)Instructions burned: 16 (million)
% 0.10/0.44 % (4119882)Success in time 0.029 s
% 0.10/0.44 % Vampire exiting
%------------------------------------------------------------------------------