%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET995+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 : n026.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 12:45:09 PM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 60 ( 13 unt; 0 def)
% Number of atoms : 296 ( 112 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 389 ( 153 ~; 154 |; 63 &)
% ( 8 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 100 ( 81 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f5,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/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f25,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( relation_dom(X1) = relation_dom(X2)
& relation_rng(X1) = singleton(X0)
& relation_rng(X2) = singleton(X0) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_1) ).
fof(f26,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( relation_dom(X1) = relation_dom(X2)
& relation_rng(X1) = singleton(X0)
& relation_rng(X2) = singleton(X0) )
=> X1 = X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f35,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( relation_dom(X0) = relation_dom(X1)
& ! [X2] :
( in(X2,relation_dom(X0))
=> apply(X0,X2) = apply(X1,X2) ) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_1) ).
fof(f43,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,[],[f5]) ).
fof(f44,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,[],[f43]) ).
fof(f52,plain,
? [X0,X1] :
( ? [X2] :
( X1 != X2
& relation_dom(X1) = relation_dom(X2)
& relation_rng(X1) = singleton(X0)
& relation_rng(X2) = singleton(X0)
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f53,plain,
? [X0,X1] :
( ? [X2] :
( X1 != X2
& relation_dom(X1) = relation_dom(X2)
& relation_rng(X1) = singleton(X0)
& relation_rng(X2) = singleton(X0)
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(flattening,[],[f52]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| relation_dom(X0) != relation_dom(X1)
| ? [X2] :
( apply(X0,X2) != apply(X1,X2)
& in(X2,relation_dom(X0)) )
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| relation_dom(X0) != relation_dom(X1)
| ? [X2] :
( apply(X0,X2) != apply(X1,X2)
& in(X2,relation_dom(X0)) )
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f67,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f67]) ).
fof(f69,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,[],[f44]) ).
fof(f70,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,[],[f69]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK1(X0,X1) )
| ~ in(sK1(X0,X1),X1) )
& ( ( in(sK2(X0,X1),relation_dom(X0))
& sK1(X0,X1) = apply(X0,sK2(X0,X1)) )
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK3(X0,X5),relation_dom(X0))
& apply(X0,sK3(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X4,sK2(X0,X1)),skolemize(X7,sK3(X0,X5))],[f70]) ).
fof(f81,plain,
( sK14 != sK15
& relation_dom(sK14) = relation_dom(sK15)
& singleton(sK13) = relation_rng(sK14)
& singleton(sK13) = relation_rng(sK15)
& relation(sK15)
& function(sK15)
& relation(sK14)
& function(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15)],[f53]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| relation_dom(X0) != relation_dom(X1)
| ( apply(X0,sK16(X0,X1)) != apply(X1,sK16(X0,X1))
& in(sK16(X0,X1),relation_dom(X0)) )
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X2,sK16(X0,X1))],[f65]) ).
fof(f86,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f68]) ).
fof(f92,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f124,plain,
function(sK14),
inference(cnf_transformation,[],[f81]) ).
fof(f125,plain,
relation(sK14),
inference(cnf_transformation,[],[f81]) ).
fof(f126,plain,
function(sK15),
inference(cnf_transformation,[],[f81]) ).
fof(f127,plain,
relation(sK15),
inference(cnf_transformation,[],[f81]) ).
fof(f128,plain,
singleton(sK13) = relation_rng(sK15),
inference(cnf_transformation,[],[f81]) ).
fof(f129,plain,
singleton(sK13) = relation_rng(sK14),
inference(cnf_transformation,[],[f81]) ).
fof(f130,plain,
relation_dom(sK14) = relation_dom(sK15),
inference(cnf_transformation,[],[f81]) ).
fof(f131,plain,
sK14 != sK15,
inference(cnf_transformation,[],[f81]) ).
fof(f140,plain,
! [X0,X1] :
( relation_dom(X0) != relation_dom(X1)
| X0 = X1
| in(sK16(X0,X1),relation_dom(X0))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f141,plain,
! [X0,X1] :
( apply(X0,sK16(X0,X1)) != apply(X1,sK16(X0,X1))
| relation_dom(X0) != relation_dom(X1)
| X0 = X1
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f144,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f86]) ).
fof(f145,plain,
! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f92]) ).
fof(f146,plain,
! [X0,X6] :
( in(apply(X0,X6),relation_rng(X0))
| ~ in(X6,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f145]) ).
fof(f277,plain,
! [X0] :
( in(apply(sK15,X0),singleton(sK13))
| ~ in(X0,relation_dom(sK15))
| ~ relation(sK15)
| ~ function(sK15) ),
inference(superposition,[],[f146,f128]) ).
fof(f278,plain,
! [X0] :
( in(apply(sK14,X0),singleton(sK13))
| ~ in(X0,relation_dom(sK14))
| ~ relation(sK14)
| ~ function(sK14) ),
inference(superposition,[],[f146,f129]) ).
fof(f279,plain,
! [X0] :
( in(apply(sK14,X0),singleton(sK13))
| ~ in(X0,relation_dom(sK14))
| ~ function(sK14) ),
inference(forward_subsumption_resolution,[],[f278,f125]) ).
fof(f280,plain,
! [X0] :
( in(apply(sK15,X0),singleton(sK13))
| ~ in(X0,relation_dom(sK15))
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f277,f127]) ).
fof(f281,plain,
! [X0] :
( in(apply(sK14,X0),singleton(sK13))
| ~ in(X0,relation_dom(sK14)) ),
inference(forward_subsumption_resolution,[],[f279,f124]) ).
fof(f282,plain,
! [X0] :
( in(apply(sK15,X0),singleton(sK13))
| ~ in(X0,relation_dom(sK15)) ),
inference(forward_subsumption_resolution,[],[f280,f126]) ).
fof(f283,plain,
! [X0] :
( in(apply(sK15,X0),singleton(sK13))
| ~ in(X0,relation_dom(sK14)) ),
inference(forward_demodulation,[],[f282,f130]) ).
fof(f284,plain,
! [X0] :
( ~ in(X0,relation_dom(sK14))
| sK13 = apply(sK14,X0) ),
inference(resolution,[],[f281,f144]) ).
fof(f309,plain,
! [X0] :
( ~ in(X0,relation_dom(sK14))
| sK13 = apply(sK15,X0) ),
inference(resolution,[],[f283,f144]) ).
fof(f352,plain,
! [X0] :
( relation_dom(X0) != relation_dom(sK14)
| sK15 = X0
| in(sK16(X0,sK15),relation_dom(X0))
| ~ relation(sK15)
| ~ function(sK15)
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[],[f140,f130]) ).
fof(f355,plain,
! [X0] :
( relation_dom(X0) != relation_dom(sK14)
| sK15 = X0
| in(sK16(X0,sK15),relation_dom(X0))
| ~ function(sK15)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f352,f127]) ).
fof(f357,plain,
! [X0] :
( relation_dom(X0) != relation_dom(sK14)
| sK15 = X0
| in(sK16(X0,sK15),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f355,f126]) ).
fof(f413,plain,
( sK14 = sK15
| in(sK16(sK14,sK15),relation_dom(sK14))
| ~ relation(sK14)
| ~ function(sK14) ),
inference(equality_resolution,[],[f357]) ).
fof(f414,plain,
( in(sK16(sK14,sK15),relation_dom(sK14))
| ~ relation(sK14)
| ~ function(sK14) ),
inference(forward_subsumption_resolution,[],[f413,f131]) ).
fof(f415,plain,
( in(sK16(sK14,sK15),relation_dom(sK14))
| ~ function(sK14) ),
inference(forward_subsumption_resolution,[],[f414,f125]) ).
fof(f416,plain,
in(sK16(sK14,sK15),relation_dom(sK14)),
inference(forward_subsumption_resolution,[],[f415,f124]) ).
fof(f417,plain,
sK13 = apply(sK15,sK16(sK14,sK15)),
inference(resolution,[],[f416,f309]) ).
fof(f418,plain,
sK13 = apply(sK14,sK16(sK14,sK15)),
inference(resolution,[],[f416,f284]) ).
fof(f534,plain,
( sK13 != apply(sK14,sK16(sK14,sK15))
| relation_dom(sK14) != relation_dom(sK15)
| sK14 = sK15
| ~ relation(sK15)
| ~ function(sK15)
| ~ relation(sK14)
| ~ function(sK14) ),
inference(superposition,[],[f141,f417]) ).
fof(f539,plain,
( sK13 != apply(sK14,sK16(sK14,sK15))
| sK14 = sK15
| ~ relation(sK15)
| ~ function(sK15)
| ~ relation(sK14)
| ~ function(sK14) ),
inference(forward_subsumption_resolution,[],[f534,f130]) ).
fof(f542,plain,
( sK13 != apply(sK14,sK16(sK14,sK15))
| ~ relation(sK15)
| ~ function(sK15)
| ~ relation(sK14)
| ~ function(sK14) ),
inference(forward_subsumption_resolution,[],[f539,f131]) ).
fof(f545,plain,
( sK13 != apply(sK14,sK16(sK14,sK15))
| ~ function(sK15)
| ~ relation(sK14)
| ~ function(sK14) ),
inference(forward_subsumption_resolution,[],[f542,f127]) ).
fof(f547,plain,
( sK13 != apply(sK14,sK16(sK14,sK15))
| ~ relation(sK14)
| ~ function(sK14) ),
inference(forward_subsumption_resolution,[],[f545,f126]) ).
fof(f549,plain,
( sK13 != apply(sK14,sK16(sK14,sK15))
| ~ function(sK14) ),
inference(forward_subsumption_resolution,[],[f547,f125]) ).
fof(f551,plain,
sK13 != apply(sK14,sK16(sK14,sK15)),
inference(forward_subsumption_resolution,[],[f549,f124]) ).
fof(f823,plain,
$false,
inference(forward_subsumption_resolution,[],[f551,f418]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET995+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n026.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 03:23:41 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.10/0.46 % (3434327)Will run a generic schedule for satisfiability detection.
% 0.10/0.46 % (3434335)dis+10_1_sil=32000:sp=arity:random_seed=3111549333:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.46 % (3434333)% WARNING: option uhcvi not known.
% 0.10/0.46 % (3434332)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=968542861_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.46 % (3434333)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3275024833:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.46 % (3434334)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1416377632:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.46 % (3434336)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1062075838:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.46 % (3434338)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=119456088:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.46 % (3434337)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3111153788:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.46 % (3434335) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3434327-3434335"...
% 0.10/0.46 % (3434335)...printing done.
% 0.10/0.46 % TRYING [1]
% 0.10/0.46 % TRYING [2]
% 0.10/0.46 % (3434335)Refutation found. Thanks to Tanya!
% 0.10/0.46 % SZS status Theorem for theBenchmark
% 0.10/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.46 % (3434335)------------------------------
% 0.10/0.46 % (3434335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.46 % (3434335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.46 % (3434335)CaDiCaL version: 2.1.3
% 0.10/0.46 % (3434335)Termination reason: Refutation
% 0.10/0.46 % (3434335)Time elapsed: 0.010 s
% 0.10/0.46 % (3434335)Peak memory usage: 12 MB
% 0.10/0.46 % (3434335)Instructions burned: 26 (million)
% 0.10/0.46 % (3434327)Success in time 0.047 s
% 0.10/0.46 % Vampire exiting
%------------------------------------------------------------------------------