%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN077+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 02:06:42 PM UTC 2026
% Result : Theorem 0.18s 0.27s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 50 ( 6 unt; 2 def)
% Number of atoms : 171 ( 9 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 219 ( 98 ~; 90 |; 21 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 65 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
? [X1] :
! [X2] :
( big_f(X2,X1)
<=> X2 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel54_1) ).
fof(f2,conjecture,
~ ? [X0] :
! [X1] :
( big_f(X1,X0)
<=> ! [X2] :
( big_f(X1,X2)
=> ? [X3] :
( big_f(X3,X2)
& ~ ? [X4] :
( big_f(X4,X2)
& big_f(X4,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel54) ).
fof(f3,negated_conjecture,
~ ~ ? [X0] :
! [X1] :
( big_f(X1,X0)
<=> ! [X2] :
( big_f(X1,X2)
=> ? [X3] :
( big_f(X3,X2)
& ~ ? [X4] :
( big_f(X4,X2)
& big_f(X4,X3) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
? [X0] :
! [X1] :
( big_f(X1,X0)
<=> ! [X2] :
( big_f(X1,X2)
=> ? [X3] :
( big_f(X3,X2)
& ~ ? [X4] :
( big_f(X4,X2)
& big_f(X4,X3) ) ) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
? [X0] :
! [X1] :
( big_f(X1,X0)
<=> ! [X2] :
( ? [X3] :
( big_f(X3,X2)
& ! [X4] :
( ~ big_f(X4,X2)
| ~ big_f(X4,X3) ) )
| ~ big_f(X1,X2) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f6,plain,
! [X0] :
? [X1] :
! [X2] :
( ( big_f(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ big_f(X2,X1) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f7,plain,
! [X0,X2] :
( ( big_f(X2,sK0(X0))
| X0 != X2 )
& ( X2 = X0
| ~ big_f(X2,sK0(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f6]) ).
fof(f8,plain,
? [X0] :
! [X1] :
( ( big_f(X1,X0)
| ? [X2] :
( ! [X3] :
( ~ big_f(X3,X2)
| ? [X4] :
( big_f(X4,X2)
& big_f(X4,X3) ) )
& big_f(X1,X2) ) )
& ( ! [X2] :
( ? [X3] :
( big_f(X3,X2)
& ! [X4] :
( ~ big_f(X4,X2)
| ~ big_f(X4,X3) ) )
| ~ big_f(X1,X2) )
| ~ big_f(X1,X0) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f9,plain,
? [X0] :
! [X1] :
( ( big_f(X1,X0)
| ? [X2] :
( ! [X3] :
( ~ big_f(X3,X2)
| ? [X4] :
( big_f(X4,X2)
& big_f(X4,X3) ) )
& big_f(X1,X2) ) )
& ( ! [X5] :
( ? [X6] :
( big_f(X6,X5)
& ! [X7] :
( ~ big_f(X7,X5)
| ~ big_f(X7,X6) ) )
| ~ big_f(X1,X5) )
| ~ big_f(X1,X0) ) ),
inference(rectify,[],[f8]) ).
fof(f10,plain,
! [X1] :
( ( big_f(X1,sK1)
| ( ! [X3] :
( ~ big_f(X3,sK2(X1))
| ( big_f(sK3(X1,X3),sK2(X1))
& big_f(sK3(X1,X3),X3) ) )
& big_f(X1,sK2(X1)) ) )
& ( ! [X5] :
( ( big_f(sK4(X5),X5)
& ! [X7] :
( ~ big_f(X7,X5)
| ~ big_f(X7,sK4(X5)) ) )
| ~ big_f(X1,X5) )
| ~ big_f(X1,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X2,sK2(X1)),skolemize(X4,sK3(X1,X3)),skolemize(X6,sK4(X5))],[f9]) ).
fof(f11,plain,
! [X2,X0] :
( ~ big_f(X2,sK0(X0))
| X0 = X2 ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X2,X0] :
( big_f(X2,sK0(X0))
| X0 != X2 ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X1,X7,X5] :
( ~ big_f(X7,sK4(X5))
| ~ big_f(X7,X5)
| ~ big_f(X1,X5)
| ~ big_f(X1,sK1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f14,plain,
! [X1,X5] :
( ~ big_f(X1,sK1)
| ~ big_f(X1,X5)
| big_f(sK4(X5),X5) ),
inference(cnf_transformation,[],[f10]) ).
fof(f15,plain,
! [X1] :
( big_f(X1,sK2(X1))
| big_f(X1,sK1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f16,plain,
! [X3,X1] :
( big_f(sK3(X1,X3),X3)
| ~ big_f(X3,sK2(X1))
| big_f(X1,sK1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
! [X3,X1] :
( big_f(sK3(X1,X3),sK2(X1))
| ~ big_f(X3,sK2(X1))
| big_f(X1,sK1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f18,plain,
! [X2] : big_f(X2,sK0(X2)),
inference(equality_resolution,[],[f12]) ).
fof(f20,plain,
! [X2,X0,X1] :
( ~ big_f(sK3(X0,sK4(X1)),X1)
| ~ big_f(X2,X1)
| ~ big_f(X2,sK1)
| ~ big_f(sK4(X1),sK2(X0))
| big_f(X0,sK1) ),
inference(resolution,[],[f13,f16]) ).
fof(f32,definition,
( spl5_2
<=> ! [X0] :
( big_f(X0,sK1)
| ~ big_f(sK1,sK2(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f33,plain,
( ! [X0] :
( ~ big_f(sK1,sK2(X0))
| big_f(X0,sK1) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f37,plain,
( big_f(sK1,sK1)
| big_f(sK1,sK1)
| ~ spl5_2 ),
inference(resolution,[],[f33,f15]) ).
fof(f38,plain,
( big_f(sK1,sK1)
| ~ spl5_2 ),
inference(duplicate_literal_removal,[],[f37]) ).
fof(f41,plain,
( ! [X0] :
( big_f(sK4(X0),X0)
| ~ big_f(sK1,X0) )
| ~ spl5_2 ),
inference(resolution,[],[f38,f14]) ).
fof(f42,plain,
! [X0,X1] :
( ~ big_f(X0,sK2(X1))
| ~ big_f(X0,sK1)
| ~ big_f(sK4(sK2(X1)),sK2(X1))
| big_f(X1,sK1)
| ~ big_f(sK4(sK2(X1)),sK2(X1))
| big_f(X1,sK1) ),
inference(resolution,[],[f20,f17]) ).
fof(f43,plain,
! [X0,X1] :
( ~ big_f(X0,sK2(X1))
| ~ big_f(X0,sK1)
| ~ big_f(sK4(sK2(X1)),sK2(X1))
| big_f(X1,sK1) ),
inference(duplicate_literal_removal,[],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ~ big_f(X0,sK2(X1))
| ~ big_f(X0,sK1)
| big_f(X1,sK1) ),
inference(forward_subsumption_resolution,[],[f43,f14]) ).
fof(f50,plain,
! [X0,X1] :
( ~ big_f(sK3(X0,X1),sK1)
| big_f(X0,sK1)
| ~ big_f(X1,sK2(X0))
| big_f(X0,sK1) ),
inference(resolution,[],[f44,f17]) ).
fof(f53,plain,
! [X0,X1] :
( ~ big_f(sK3(X0,X1),sK1)
| big_f(X0,sK1)
| ~ big_f(X1,sK2(X0)) ),
inference(duplicate_literal_removal,[],[f50]) ).
fof(f89,plain,
! [X0] :
( big_f(X0,sK1)
| ~ big_f(sK1,sK2(X0))
| ~ big_f(sK1,sK2(X0))
| big_f(X0,sK1) ),
inference(resolution,[],[f53,f16]) ).
fof(f90,plain,
! [X0] :
( big_f(X0,sK1)
| ~ big_f(sK1,sK2(X0)) ),
inference(duplicate_literal_removal,[],[f89]) ).
fof(f91,plain,
spl5_2,
inference(avatar_split_clause,[],[f90,f32]) ).
fof(f97,plain,
( ! [X0] :
( ~ big_f(sK1,sK0(X0))
| sK4(sK0(X0)) = X0 )
| ~ spl5_2 ),
inference(resolution,[],[f41,f11]) ).
fof(f164,plain,
( sK1 = sK4(sK0(sK1))
| ~ spl5_2 ),
inference(resolution,[],[f97,f18]) ).
fof(f167,plain,
( ! [X0,X1] :
( ~ big_f(X0,sK1)
| ~ big_f(X0,sK0(sK1))
| ~ big_f(X1,sK0(sK1))
| ~ big_f(X1,sK1) )
| ~ spl5_2 ),
inference(superposition,[],[f13,f164]) ).
fof(f169,definition,
( spl5_10
<=> ! [X1] :
( ~ big_f(X1,sK0(sK1))
| ~ big_f(X1,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
fof(f170,plain,
( ! [X1] :
( ~ big_f(X1,sK0(sK1))
| ~ big_f(X1,sK1) )
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f171,plain,
( spl5_10
| spl5_10
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f167,f32,f169,f169]) ).
fof(f194,plain,
( ~ big_f(sK4(sK0(sK1)),sK1)
| ~ big_f(sK1,sK0(sK1))
| ~ spl5_2
| ~ spl5_10 ),
inference(resolution,[],[f170,f41]) ).
fof(f195,plain,
( ~ big_f(sK4(sK0(sK1)),sK1)
| ~ spl5_2
| ~ spl5_10 ),
inference(forward_subsumption_resolution,[],[f194,f18]) ).
fof(f198,plain,
( ~ big_f(sK1,sK1)
| ~ spl5_2
| ~ spl5_10 ),
inference(forward_demodulation,[],[f195,f164]) ).
fof(f199,plain,
( $false
| ~ spl5_2
| ~ spl5_10 ),
inference(forward_subsumption_resolution,[],[f198,f38]) ).
fof(f200,plain,
( ~ spl5_2
| ~ spl5_10 ),
inference(avatar_contradiction_clause,[],[f199]) ).
cnf(s5,plain,
spl5_2,
inference(sat_conversion,[],[f91]) ).
cnf(s17,plain,
( spl5_10
| ~ spl5_2
| spl5_10 ),
inference(sat_conversion,[],[f171]) ).
cnf(s18,plain,
( ~ spl5_2
| spl5_10 ),
inference(rat,[],[s17]) ).
cnf(s21,plain,
( ~ spl5_2
| ~ spl5_10 ),
inference(sat_conversion,[],[f200]) ).
cnf(s22,plain,
~ spl5_10,
inference(rat,[],[s21,s5]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s18,s22,s5]) ).
fof(f201,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN077+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n020.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 15:31:35 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.18/0.27 % (249210)Will run a generic schedule for satisfiability detection.
% 0.18/0.27 % (249215)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1529564609_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.27 % TRYING [1]
% 0.18/0.27 % TRYING [2]
% 0.18/0.27 % TRYING [3]
% 0.18/0.27 % TRYING [4]
% 0.18/0.27 % TRYING [5]
% 0.18/0.27 % TRYING [6]
% 0.18/0.27 % (249216)% WARNING: option uhcvi not known.
% 0.18/0.27 % TRYING [7]
% 0.18/0.27 % (249216)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=242131129:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.27 % (249217)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1772988007:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.27 % (249218)dis+10_1_sil=32000:sp=arity:random_seed=1139117474:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.27 % (249219)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=921532172:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.27 % (249221)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2975614052:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.27 % (249220)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4256318048:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.27 % TRYING [8]
% 0.18/0.27 % (249218) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-249210-249218"...
% 0.18/0.27 % TRYING [9]
% 0.18/0.27 % (249216) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-249210-249216"...
% 0.18/0.27 % (249218)...printing done.
% 0.18/0.27 % (249216)...printing done.
% 0.18/0.27 % (249220) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-249210-249220"...
% 0.18/0.27 % (249218)Refutation found. Thanks to Tanya!
% 0.18/0.27 % SZS status Theorem for theBenchmark
% 0.18/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.27 % (249218)------------------------------
% 0.18/0.27 % (249218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (249218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (249218)CaDiCaL version: 2.1.3
% 0.18/0.27 % (249218)Termination reason: Refutation
% 0.18/0.27 % (249218)Time elapsed: 0.006 s
% 0.18/0.27 % (249218)Peak memory usage: 12 MB
% 0.18/0.27 % (249218)Instructions burned: 7 (million)
% 0.18/0.27 % (249210)Success in time 0.042 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------