%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN364+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 : n019.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 02:07:29 PM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 7 unt; 4 def)
% Number of atoms : 126 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 142 ( 57 ~; 44 |; 28 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 57 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ! [X0] :
( ? [X1] : big_p(X0,X1)
=> ! [X2] : big_p(X2,X2) )
& ! [X3] :
? [X4] :
( big_p(X3,X4)
| ( big_m(X3)
& big_q(f(X3,X4)) ) )
& ! [X5] :
( big_q(X5)
=> ~ big_m(g(X5)) ) )
=> ! [X3] :
? [X4] :
( big_p(g(X3),X4)
& big_p(X3,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2115) ).
fof(f2,negated_conjecture,
~ ( ( ! [X0] :
( ? [X1] : big_p(X0,X1)
=> ! [X2] : big_p(X2,X2) )
& ! [X3] :
? [X4] :
( big_p(X3,X4)
| ( big_m(X3)
& big_q(f(X3,X4)) ) )
& ! [X5] :
( big_q(X5)
=> ~ big_m(g(X5)) ) )
=> ! [X3] :
? [X4] :
( big_p(g(X3),X4)
& big_p(X3,X3) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ( ! [X0] :
( ? [X1] : big_p(X0,X1)
=> ! [X2] : big_p(X2,X2) )
& ! [X3] :
? [X4] :
( big_p(X3,X4)
| ( big_m(X3)
& big_q(f(X3,X4)) ) )
& ! [X5] :
( big_q(X5)
=> ~ big_m(g(X5)) ) )
=> ! [X6] :
? [X7] :
( big_p(g(X6),X7)
& big_p(X6,X6) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ? [X6] :
! [X7] :
( ~ big_p(g(X6),X7)
| ~ big_p(X6,X6) )
& ! [X0] :
( ! [X2] : big_p(X2,X2)
| ! [X1] : ~ big_p(X0,X1) )
& ! [X3] :
? [X4] :
( big_p(X3,X4)
| ( big_m(X3)
& big_q(f(X3,X4)) ) )
& ! [X5] :
( ~ big_m(g(X5))
| ~ big_q(X5) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ? [X6] :
! [X7] :
( ~ big_p(g(X6),X7)
| ~ big_p(X6,X6) )
& ! [X0] :
( ! [X2] : big_p(X2,X2)
| ! [X1] : ~ big_p(X0,X1) )
& ! [X3] :
? [X4] :
( big_p(X3,X4)
| ( big_m(X3)
& big_q(f(X3,X4)) ) )
& ! [X5] :
( ~ big_m(g(X5))
| ~ big_q(X5) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
( ? [X0] :
! [X1] :
( ~ big_p(g(X0),X1)
| ~ big_p(X0,X0) )
& ! [X2] :
( ! [X3] : big_p(X3,X3)
| ! [X4] : ~ big_p(X2,X4) )
& ! [X5] :
? [X6] :
( big_p(X5,X6)
| ( big_m(X5)
& big_q(f(X5,X6)) ) )
& ! [X7] :
( ~ big_m(g(X7))
| ~ big_q(X7) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ! [X1] :
( ~ big_p(g(sK0),X1)
| ~ big_p(sK0,sK0) )
& ! [X2] :
( ! [X3] : big_p(X3,X3)
| ! [X4] : ~ big_p(X2,X4) )
& ! [X5] :
( big_p(X5,sK1(X5))
| ( big_m(X5)
& big_q(f(X5,sK1(X5))) ) )
& ! [X7] :
( ~ big_m(g(X7))
| ~ big_q(X7) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X6,sK1(X5))],[f6]) ).
fof(f8,plain,
! [X7] :
( ~ big_m(g(X7))
| ~ big_q(X7) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X5] :
( big_p(X5,sK1(X5))
| big_q(f(X5,sK1(X5))) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X5] :
( big_p(X5,sK1(X5))
| big_m(X5) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X2,X3,X4] :
( big_p(X3,X3)
| ~ big_p(X2,X4) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X1] :
( ~ big_p(g(sK0),X1)
| ~ big_p(sK0,sK0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,definition,
( spl2_1
<=> ! [X4,X2] : ~ big_p(X2,X4) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f15,plain,
( ! [X2,X4] : ~ big_p(X2,X4)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f14]) ).
fof(f17,definition,
( spl2_2
<=> ! [X3] : big_p(X3,X3) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f18,plain,
( ! [X3] : big_p(X3,X3)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f19,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f11,f17,f14]) ).
fof(f21,definition,
( spl2_3
<=> big_p(sK0,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f23,plain,
( ~ big_p(sK0,sK0)
| spl2_3 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f25,definition,
( spl2_4
<=> ! [X1] : ~ big_p(g(sK0),X1) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f26,plain,
( ! [X1] : ~ big_p(g(sK0),X1)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f27,plain,
( ~ spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f12,f25,f21]) ).
fof(f28,plain,
( $false
| ~ spl2_2
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f23,f18]) ).
fof(f29,plain,
( ~ spl2_2
| spl2_3 ),
inference(avatar_contradiction_clause,[],[f28]) ).
fof(f30,plain,
( ! [X5] : big_m(X5)
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f10,f15]) ).
fof(f31,plain,
( ! [X0] : ~ big_q(X0)
| ~ spl2_1 ),
inference(resolution,[],[f30,f8]) ).
fof(f32,plain,
( ! [X5] : big_q(f(X5,sK1(X5)))
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f9,f15]) ).
fof(f33,plain,
( $false
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f32,f31]) ).
fof(f34,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f33]) ).
fof(f35,plain,
( $false
| ~ spl2_2
| ~ spl2_4 ),
inference(resolution,[],[f26,f18]) ).
fof(f36,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f35]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f19]) ).
cnf(s2,plain,
( ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f27]) ).
cnf(s3,plain,
( ~ spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f29]) ).
cnf(s4,plain,
~ spl2_1,
inference(sat_conversion,[],[f34]) ).
cnf(s5,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(sat_conversion,[],[f36]) ).
cnf(s6,plain,
spl2_2,
inference(rat,[],[s1,s4]) ).
cnf(s7,plain,
~ spl2_4,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
spl2_3,
inference(rat,[],[s3,s6]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s2,s7,s8]) ).
fof(f37,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN364+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n019.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 15:48:48 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.20/0.27 % (4114318)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (4114323)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2155424819_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.27 % TRYING [1]
% 0.20/0.27 % TRYING [2]
% 0.20/0.27 % TRYING [3]
% 0.20/0.27 % TRYING [4]
% 0.20/0.27 % TRYING [5]
% 0.20/0.27 % TRYING [6]
% 0.20/0.27 % (4114324)% WARNING: option uhcvi not known.
% 0.20/0.27 % TRYING [7]
% 0.20/0.27 % TRYING [8]
% 0.20/0.27 % (4114326)dis+10_1_sil=32000:sp=arity:random_seed=1686019094:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.27 % (4114324)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1440228641:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.27 % (4114327)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=176826179:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.27 % (4114325)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3786135718:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.27 % (4114329)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=797384493:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.27 % (4114328)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=920746884:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.27 % (4114326) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4114318-4114326"...
% 0.20/0.27 % (4114324) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4114318-4114324"...
% 0.20/0.27 % (4114327) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4114318-4114327"...
% 0.20/0.27 % (4114329) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4114318-4114329"...
% 0.20/0.27 % (4114328) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4114318-4114328"...
% 0.20/0.27 % (4114325) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4114318-4114325"...
% 0.20/0.27 % TRYING [9]
% 0.20/0.27 % (4114326)...printing done.
% 0.20/0.27 % (4114324)...printing done.
% 0.20/0.27 % (4114327)...printing done.
% 0.20/0.27 % (4114329)...printing done.
% 0.20/0.27 % (4114328)...printing done.
% 0.20/0.27 % (4114326)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (4114326)------------------------------
% 0.20/0.27 % (4114326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (4114326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (4114326)CaDiCaL version: 2.1.3
% 0.20/0.27 % (4114326)Termination reason: Refutation
% 0.20/0.27 % (4114326)Time elapsed: 0.002 s
% 0.20/0.27 % (4114326)Peak memory usage: 12 MB
% 0.20/0.27 % (4114326)Instructions burned: 1 (million)
% 0.20/0.27 % (4114318)Success in time 0.032 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------