%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN076+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 02:06:41 PM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 56 ( 2 unt; 1 def)
% Number of atoms : 310 ( 159 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 388 ( 134 ~; 189 |; 44 &)
% ( 19 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 159 ( 117 !; 42 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0,X1] :
( X0 != X1
& ! [X2] :
( X2 = X0
| X2 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel53_1) ).
fof(f2,conjecture,
( ? [X0] :
! [X1] :
( ? [X2] :
! [X3] :
( big_f(X1,X3)
<=> X3 = X2 )
<=> X1 = X0 )
<=> ? [X4] :
! [X5] :
( ? [X6] :
! [X7] :
( big_f(X7,X5)
<=> X7 = X6 )
<=> X5 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel53) ).
fof(f3,negated_conjecture,
~ ( ? [X0] :
! [X1] :
( ? [X2] :
! [X3] :
( big_f(X1,X3)
<=> X3 = X2 )
<=> X1 = X0 )
<=> ? [X4] :
! [X5] :
( ? [X6] :
! [X7] :
( big_f(X7,X5)
<=> X7 = X6 )
<=> X5 = X4 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
( ? [X0] :
! [X1] :
( ? [X2] :
! [X3] :
( big_f(X1,X3)
<=> X3 = X2 )
<=> X1 = X0 )
<~> ? [X4] :
! [X5] :
( ? [X6] :
! [X7] :
( big_f(X7,X5)
<=> X7 = X6 )
<=> X5 = X4 ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,definition,
( sP0
<=> ? [X0] :
! [X1] :
( ? [X2] :
! [X3] :
( big_f(X1,X3)
<=> X3 = X2 )
<=> X1 = X0 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f6,plain,
( sP0
<~> ? [X4] :
! [X5] :
( ? [X6] :
! [X7] :
( big_f(X7,X5)
<=> X7 = X6 )
<=> X5 = X4 ) ),
inference(definition_folding,[],[f4,f5]) ).
fof(f7,plain,
( sK1 != sK2
& ! [X2] :
( sK1 = X2
| sK2 = X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f1]) ).
fof(f8,plain,
( ( sP0
| ! [X0] :
? [X1] :
( ( X0 != X1
| ! [X2] :
? [X3] :
( ( X2 != X3
| ~ big_f(X1,X3) )
& ( X3 = X2
| big_f(X1,X3) ) ) )
& ( X1 = X0
| ? [X2] :
! [X3] :
( ( big_f(X1,X3)
| X2 != X3 )
& ( X3 = X2
| ~ big_f(X1,X3) ) ) ) ) )
& ( ? [X0] :
! [X1] :
( ( ? [X2] :
! [X3] :
( ( big_f(X1,X3)
| X2 != X3 )
& ( X3 = X2
| ~ big_f(X1,X3) ) )
| X0 != X1 )
& ( X1 = X0
| ! [X2] :
? [X3] :
( ( X2 != X3
| ~ big_f(X1,X3) )
& ( X3 = X2
| big_f(X1,X3) ) ) ) )
| ~ sP0 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f9,plain,
( ( sP0
| ! [X0] :
? [X1] :
( ( X0 != X1
| ! [X2] :
? [X3] :
( ( X2 != X3
| ~ big_f(X1,X3) )
& ( X3 = X2
| big_f(X1,X3) ) ) )
& ( X1 = X0
| ? [X4] :
! [X5] :
( ( big_f(X1,X5)
| X4 != X5 )
& ( X4 = X5
| ~ big_f(X1,X5) ) ) ) ) )
& ( ? [X6] :
! [X7] :
( ( ? [X8] :
! [X9] :
( ( big_f(X7,X9)
| X8 != X9 )
& ( X8 = X9
| ~ big_f(X7,X9) ) )
| X6 != X7 )
& ( X6 = X7
| ! [X10] :
? [X11] :
( ( X10 != X11
| ~ big_f(X7,X11) )
& ( X10 = X11
| big_f(X7,X11) ) ) ) )
| ~ sP0 ) ),
inference(rectify,[],[f8]) ).
fof(f10,plain,
( ( sP0
| ! [X0] :
( ( sK3(X0) != X0
| ! [X2] :
( ( sK4(X0,X2) != X2
| ~ big_f(sK3(X0),sK4(X0,X2)) )
& ( sK4(X0,X2) = X2
| big_f(sK3(X0),sK4(X0,X2)) ) ) )
& ( sK3(X0) = X0
| ! [X5] :
( ( big_f(sK3(X0),X5)
| sK5(X0) != X5 )
& ( sK5(X0) = X5
| ~ big_f(sK3(X0),X5) ) ) ) ) )
& ( ! [X7] :
( ( ! [X9] :
( ( big_f(X7,X9)
| sK7(X7) != X9 )
& ( sK7(X7) = X9
| ~ big_f(X7,X9) ) )
| sK6 != X7 )
& ( sK6 = X7
| ! [X10] :
( ( sK8(X7,X10) != X10
| ~ big_f(X7,sK8(X7,X10)) )
& ( sK8(X7,X10) = X10
| big_f(X7,sK8(X7,X10)) ) ) ) )
| ~ sP0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(X1,sK3(X0)),skolemize(X3,sK4(X0,X2)),skolemize(X4,sK5(X0)),skolemize(X6,sK6),skolemize(X8,sK7(X7)),skolemize(X11,sK8(X7,X10))],[f9]) ).
fof(f11,plain,
( ( ! [X4] :
? [X5] :
( ( X4 != X5
| ! [X6] :
? [X7] :
( ( X6 != X7
| ~ big_f(X7,X5) )
& ( X7 = X6
| big_f(X7,X5) ) ) )
& ( X5 = X4
| ? [X6] :
! [X7] :
( ( big_f(X7,X5)
| X6 != X7 )
& ( X7 = X6
| ~ big_f(X7,X5) ) ) ) )
| ~ sP0 )
& ( ? [X4] :
! [X5] :
( ( ? [X6] :
! [X7] :
( ( big_f(X7,X5)
| X6 != X7 )
& ( X7 = X6
| ~ big_f(X7,X5) ) )
| X4 != X5 )
& ( X5 = X4
| ! [X6] :
? [X7] :
( ( X6 != X7
| ~ big_f(X7,X5) )
& ( X7 = X6
| big_f(X7,X5) ) ) ) )
| sP0 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f12,plain,
( ( ! [X0] :
? [X1] :
( ( X0 != X1
| ! [X2] :
? [X3] :
( ( X2 != X3
| ~ big_f(X3,X1) )
& ( X2 = X3
| big_f(X3,X1) ) ) )
& ( X0 = X1
| ? [X4] :
! [X5] :
( ( big_f(X5,X1)
| X4 != X5 )
& ( X4 = X5
| ~ big_f(X5,X1) ) ) ) )
| ~ sP0 )
& ( ? [X6] :
! [X7] :
( ( ? [X8] :
! [X9] :
( ( big_f(X9,X7)
| X8 != X9 )
& ( X8 = X9
| ~ big_f(X9,X7) ) )
| X6 != X7 )
& ( X6 = X7
| ! [X10] :
? [X11] :
( ( X10 != X11
| ~ big_f(X11,X7) )
& ( X10 = X11
| big_f(X11,X7) ) ) ) )
| sP0 ) ),
inference(rectify,[],[f11]) ).
fof(f13,plain,
( ( ! [X0] :
( ( sK9(X0) != X0
| ! [X2] :
( ( sK10(X0,X2) != X2
| ~ big_f(sK10(X0,X2),sK9(X0)) )
& ( sK10(X0,X2) = X2
| big_f(sK10(X0,X2),sK9(X0)) ) ) )
& ( sK9(X0) = X0
| ! [X5] :
( ( big_f(X5,sK9(X0))
| sK11(X0) != X5 )
& ( sK11(X0) = X5
| ~ big_f(X5,sK9(X0)) ) ) ) )
| ~ sP0 )
& ( ! [X7] :
( ( ! [X9] :
( ( big_f(X9,X7)
| sK13(X7) != X9 )
& ( sK13(X7) = X9
| ~ big_f(X9,X7) ) )
| sK12 != X7 )
& ( sK12 = X7
| ! [X10] :
( ( sK14(X7,X10) != X10
| ~ big_f(sK14(X7,X10),X7) )
& ( sK14(X7,X10) = X10
| big_f(sK14(X7,X10),X7) ) ) ) )
| sP0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13,sK14]),skolemize(X1,sK9(X0)),skolemize(X3,sK10(X0,X2)),skolemize(X4,sK11(X0)),skolemize(X6,sK12),skolemize(X8,sK13(X7)),skolemize(X11,sK14(X7,X10))],[f12]) ).
fof(f14,plain,
! [X0] :
( sK1 = X0
| sK2 = X0 ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
sK1 != sK2,
inference(cnf_transformation,[],[f7]) ).
fof(f16,plain,
! [X10,X7] :
( sK6 = X7
| sK8(X7,X10) = X10
| big_f(X7,sK8(X7,X10))
| ~ sP0 ),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
! [X10,X7] :
( sK6 = X7
| sK8(X7,X10) != X10
| ~ big_f(X7,sK8(X7,X10))
| ~ sP0 ),
inference(cnf_transformation,[],[f10]) ).
fof(f18,plain,
! [X9,X7] :
( sK7(X7) = X9
| ~ big_f(X7,X9)
| sK6 != X7
| ~ sP0 ),
inference(cnf_transformation,[],[f10]) ).
fof(f19,plain,
! [X9,X7] :
( big_f(X7,X9)
| sK7(X7) != X9
| sK6 != X7
| ~ sP0 ),
inference(cnf_transformation,[],[f10]) ).
fof(f20,plain,
! [X0,X5] :
( sP0
| sK3(X0) = X0
| sK5(X0) = X5
| ~ big_f(sK3(X0),X5) ),
inference(cnf_transformation,[],[f10]) ).
fof(f21,plain,
! [X0,X5] :
( sP0
| sK3(X0) = X0
| big_f(sK3(X0),X5)
| sK5(X0) != X5 ),
inference(cnf_transformation,[],[f10]) ).
fof(f22,plain,
! [X2,X0] :
( sP0
| sK3(X0) != X0
| sK4(X0,X2) = X2
| big_f(sK3(X0),sK4(X0,X2)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f23,plain,
! [X2,X0] :
( sP0
| sK3(X0) != X0
| sK4(X0,X2) != X2
| ~ big_f(sK3(X0),sK4(X0,X2)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f24,plain,
! [X10,X7] :
( sK12 = X7
| sK14(X7,X10) = X10
| big_f(sK14(X7,X10),X7)
| sP0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f25,plain,
! [X10,X7] :
( sK12 = X7
| sK14(X7,X10) != X10
| ~ big_f(sK14(X7,X10),X7)
| sP0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f26,plain,
! [X9,X7] :
( sK13(X7) = X9
| ~ big_f(X9,X7)
| sK12 != X7
| sP0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f27,plain,
! [X9,X7] :
( big_f(X9,X7)
| sK13(X7) != X9
| sK12 != X7
| sP0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f28,plain,
! [X0,X5] :
( sK9(X0) = X0
| sK11(X0) = X5
| ~ big_f(X5,sK9(X0))
| ~ sP0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f29,plain,
! [X0,X5] :
( sK9(X0) = X0
| big_f(X5,sK9(X0))
| sK11(X0) != X5
| ~ sP0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f30,plain,
! [X2,X0] :
( sK9(X0) != X0
| sK10(X0,X2) = X2
| big_f(sK10(X0,X2),sK9(X0))
| ~ sP0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f31,plain,
! [X2,X0] :
( sK9(X0) != X0
| sK10(X0,X2) != X2
| ~ big_f(sK10(X0,X2),sK9(X0))
| ~ sP0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f32,plain,
! [X0] :
( sP0
| sK3(X0) = X0
| big_f(sK3(X0),sK5(X0)) ),
inference(equality_resolution,[],[f21]) ).
fof(f33,plain,
! [X7] :
( big_f(X7,sK7(X7))
| sK6 != X7
| ~ sP0 ),
inference(equality_resolution,[],[f19]) ).
fof(f34,plain,
( big_f(sK6,sK7(sK6))
| ~ sP0 ),
inference(equality_resolution,[],[f33]) ).
fof(f35,plain,
! [X9] :
( sK7(sK6) = X9
| ~ big_f(sK6,X9)
| ~ sP0 ),
inference(equality_resolution,[],[f18]) ).
fof(f36,plain,
! [X0] :
( sK9(X0) = X0
| big_f(sK11(X0),sK9(X0))
| ~ sP0 ),
inference(equality_resolution,[],[f29]) ).
fof(f37,plain,
! [X7] :
( big_f(sK13(X7),X7)
| sK12 != X7
| sP0 ),
inference(equality_resolution,[],[f27]) ).
fof(f38,plain,
( big_f(sK13(sK12),sK12)
| sP0 ),
inference(equality_resolution,[],[f37]) ).
fof(f39,plain,
! [X9] :
( sK13(sK12) = X9
| ~ big_f(X9,sK12)
| sP0 ),
inference(equality_resolution,[],[f26]) ).
fof(f40,plain,
! [X2,X0] :
( ~ sP0
| sK3(X0) != X0
| sK4(X0,X2) != X2
| big_f(sK3(X0),sK4(X0,X2)) ),
inference(consistent_polarity_flipping,[],[f23]) ).
fof(f41,plain,
! [X2,X0] :
( ~ sP0
| sK3(X0) != X0
| sK4(X0,X2) = X2
| ~ big_f(sK3(X0),sK4(X0,X2)) ),
inference(consistent_polarity_flipping,[],[f22]) ).
fof(f42,plain,
! [X0] :
( ~ sP0
| sK3(X0) = X0
| ~ big_f(sK3(X0),sK5(X0)) ),
inference(consistent_polarity_flipping,[],[f32]) ).
fof(f43,plain,
! [X0,X5] :
( ~ sP0
| sK3(X0) = X0
| sK5(X0) = X5
| big_f(sK3(X0),X5) ),
inference(consistent_polarity_flipping,[],[f20]) ).
fof(f44,plain,
( ~ big_f(sK6,sK7(sK6))
| sP0 ),
inference(consistent_polarity_flipping,[],[f34]) ).
fof(f45,plain,
! [X9] :
( sK7(sK6) = X9
| big_f(sK6,X9)
| sP0 ),
inference(consistent_polarity_flipping,[],[f35]) ).
fof(f46,plain,
! [X10,X7] :
( sK6 = X7
| sK8(X7,X10) != X10
| big_f(X7,sK8(X7,X10))
| sP0 ),
inference(consistent_polarity_flipping,[],[f17]) ).
fof(f47,plain,
! [X10,X7] :
( sK6 = X7
| sK8(X7,X10) = X10
| ~ big_f(X7,sK8(X7,X10))
| sP0 ),
inference(consistent_polarity_flipping,[],[f16]) ).
fof(f48,plain,
! [X2,X0] :
( sK9(X0) != X0
| sK10(X0,X2) != X2
| big_f(sK10(X0,X2),sK9(X0))
| sP0 ),
inference(consistent_polarity_flipping,[],[f31]) ).
fof(f49,plain,
! [X2,X0] :
( sK9(X0) != X0
| sK10(X0,X2) = X2
| ~ big_f(sK10(X0,X2),sK9(X0))
| sP0 ),
inference(consistent_polarity_flipping,[],[f30]) ).
fof(f50,plain,
! [X0] :
( sK9(X0) = X0
| ~ big_f(sK11(X0),sK9(X0))
| sP0 ),
inference(consistent_polarity_flipping,[],[f36]) ).
fof(f51,plain,
! [X0,X5] :
( sK9(X0) = X0
| sK11(X0) = X5
| big_f(X5,sK9(X0))
| sP0 ),
inference(consistent_polarity_flipping,[],[f28]) ).
fof(f52,plain,
( ~ big_f(sK13(sK12),sK12)
| ~ sP0 ),
inference(consistent_polarity_flipping,[],[f38]) ).
fof(f53,plain,
! [X9] :
( sK13(sK12) = X9
| big_f(X9,sK12)
| ~ sP0 ),
inference(consistent_polarity_flipping,[],[f39]) ).
fof(f54,plain,
! [X10,X7] :
( sK12 = X7
| sK14(X7,X10) != X10
| big_f(sK14(X7,X10),X7)
| ~ sP0 ),
inference(consistent_polarity_flipping,[],[f25]) ).
fof(f55,plain,
! [X10,X7] :
( sK12 = X7
| sK14(X7,X10) = X10
| ~ big_f(sK14(X7,X10),X7)
| ~ sP0 ),
inference(consistent_polarity_flipping,[],[f24]) ).
fof(f93,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f15,f14,f40,f41,f42,f43,f44,f45,f46,f47,f48,f49,f50,f51,f52,f53,f54,f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN076+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n002.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 15:34:35 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.20 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
% 0.07/0.25 % (452386)Will run a generic schedule for satisfiability detection.
% 0.07/0.25 % (452392)% WARNING: option uhcvi not known.
% 0.07/0.25 % (452392)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3983877133:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.25 % (452391)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2960705633_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.25 % (452393)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=310692866:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.25 % (452396)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3230597154:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.25 % (452394)dis+10_1_sil=32000:sp=arity:random_seed=3800151879:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.25 % (452395)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3947778263:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.25 % (452397)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2405012150:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.25 % Detected minimum model sizes of [1]
% 0.07/0.25 % Detected maximum model sizes of [2]
% 0.07/0.25 % TRYING [1]
% 0.07/0.25 % TRYING [2]
% 0.07/0.25 % (452391) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-452386-452391"...
% 0.07/0.25 % (452391)...printing done.
% 0.07/0.25 % (452391)Refutation found. Thanks to Tanya!
% 0.07/0.25 % SZS status Theorem for theBenchmark
% 0.07/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.25 % (452391)------------------------------
% 0.07/0.25 % (452391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.25 % (452391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.25 % (452391)CaDiCaL version: 2.1.3
% 0.07/0.25 % (452391)Termination reason: Refutation
% 0.07/0.25 % (452391)Time elapsed: 0.004 s
% 0.07/0.25 % (452391)Peak memory usage: 11 MB
% 0.07/0.25 % (452391)Instructions burned: 5 (million)
% 0.07/0.25 % (452386)Success in time 0.037 s
% 0.07/0.25 % Vampire exiting
%------------------------------------------------------------------------------