%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN058+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 01:49:09 PM UTC 2026
% Result : Theorem 4.45s 1.44s
% Output : Refutation 4.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 13 unt; 6 def)
% Number of atoms : 122 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 113 ( 49 ~; 38 |; 13 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 7 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 34 ( 0 sgn 25 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( big_p(X0)
=> ! [X1] : big_q(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel28_1) ).
fof(f2,axiom,
( ! [X0] :
( big_q(X0)
| big_r(X0) )
=> ? [X1] :
( big_q(X1)
& big_s(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel28_2) ).
fof(f3,axiom,
( ? [X0] : big_s(X0)
=> ! [X1] :
( big_f(X1)
=> big_g(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel28_3) ).
fof(f4,conjecture,
! [X0] :
( ( big_p(X0)
& big_f(X0) )
=> big_g(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel28) ).
fof(f5,negated_conjecture,
~ ! [X0] :
( ( big_p(X0)
& big_f(X0) )
=> big_g(X0) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
( ! [X0] : big_q(X0)
=> ? [X1] :
( big_q(X1)
& big_s(X1) ) ),
inference(pure_predicate_removal,[],[f2]) ).
fof(f7,plain,
! [X0] :
( ! [X1] : big_q(X1)
| ~ big_p(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f8,plain,
( ? [X1] :
( big_q(X1)
& big_s(X1) )
| ? [X0] : ~ big_q(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f9,plain,
( ! [X1] :
( big_g(X1)
| ~ big_f(X1) )
| ! [X0] : ~ big_s(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f10,plain,
? [X0] :
( ~ big_g(X0)
& big_p(X0)
& big_f(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f11,plain,
? [X0] :
( ~ big_g(X0)
& big_p(X0)
& big_f(X0) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
( ? [X0] :
( big_q(X0)
& big_s(X0) )
| ? [X1] : ~ big_q(X1) ),
inference(rectify,[],[f8]) ).
fof(f13,plain,
( ( big_q(sK0)
& big_s(sK0) )
| ~ big_q(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
fof(f14,plain,
( ! [X0] :
( big_g(X0)
| ~ big_f(X0) )
| ! [X1] : ~ big_s(X1) ),
inference(rectify,[],[f9]) ).
fof(f15,plain,
( ~ big_g(sK2)
& big_p(sK2)
& big_f(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f11]) ).
fof(f16,plain,
! [X0,X1] :
( big_q(X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f17,plain,
( big_s(sK0)
| ~ big_q(sK1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f19,plain,
! [X0,X1] :
( big_g(X0)
| ~ big_f(X0)
| ~ big_s(X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f20,plain,
big_f(sK2),
inference(cnf_transformation,[],[f15]) ).
fof(f21,plain,
big_p(sK2),
inference(cnf_transformation,[],[f15]) ).
fof(f22,plain,
~ big_g(sK2),
inference(cnf_transformation,[],[f15]) ).
fof(f24,definition,
( spl3_1
<=> ! [X1] : ~ big_s(X1) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f25,plain,
( ! [X1] : ~ big_s(X1)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f27,definition,
( spl3_2
<=> ! [X0] :
( big_g(X0)
| ~ big_f(X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f28,plain,
( ! [X0] :
( big_g(X0)
| ~ big_f(X0) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f29,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f19,f27,f24]) ).
fof(f31,definition,
( spl3_3
<=> big_q(sK1) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f33,plain,
( ~ big_q(sK1)
| spl3_3 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f35,definition,
( spl3_4
<=> big_s(sK0) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f37,plain,
( big_s(sK0)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f38,plain,
( ~ spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f17,f35,f31]) ).
fof(f45,definition,
( spl3_6
<=> ! [X0] : ~ big_p(X0) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f46,plain,
( ! [X0] : ~ big_p(X0)
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f48,definition,
( spl3_7
<=> ! [X1] : big_q(X1) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f49,plain,
( ! [X1] : big_q(X1)
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f50,plain,
( spl3_6
| spl3_7 ),
inference(avatar_split_clause,[],[f16,f48,f45]) ).
fof(f51,plain,
( $false
| ~ spl3_6 ),
inference(resolution,[],[f46,f21]) ).
fof(f52,plain,
~ spl3_6,
inference(avatar_contradiction_clause,[],[f51]) ).
fof(f53,plain,
( ~ big_f(sK2)
| ~ spl3_2 ),
inference(resolution,[],[f28,f22]) ).
fof(f54,plain,
( $false
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f53,f20]) ).
fof(f55,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f54]) ).
fof(f56,plain,
( $false
| spl3_3
| ~ spl3_7 ),
inference(forward_subsumption_resolution,[],[f33,f49]) ).
fof(f57,plain,
( spl3_3
| ~ spl3_7 ),
inference(avatar_contradiction_clause,[],[f56]) ).
fof(f58,plain,
( $false
| ~ spl3_1
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f37,f25]) ).
fof(f59,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f58]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f29]) ).
cnf(s2,plain,
( ~ spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f38]) ).
cnf(s4,plain,
( spl3_6
| spl3_7 ),
inference(sat_conversion,[],[f50]) ).
cnf(s5,plain,
~ spl3_6,
inference(sat_conversion,[],[f52]) ).
cnf(s6,plain,
~ spl3_2,
inference(sat_conversion,[],[f55]) ).
cnf(s7,plain,
( spl3_3
| ~ spl3_7 ),
inference(sat_conversion,[],[f57]) ).
cnf(s8,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(sat_conversion,[],[f59]) ).
cnf(s9,plain,
spl3_7,
inference(rat,[],[s4,s5]) ).
cnf(s10,plain,
spl3_3,
inference(rat,[],[s7,s9]) ).
cnf(s12,plain,
spl3_4,
inference(rat,[],[s2,s10]) ).
cnf(s13,plain,
~ spl3_1,
inference(rat,[],[s8,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s1,s6,s13]) ).
fof(f60,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN058+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n009.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 15:27:00 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.45/1.44 % (3147349)Detected formulas, will run a generic FOF schedule.
% 4.45/1.44 % (3147484)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2887987692:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.45/1.44 % (3147487)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=398476808:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.45/1.44 % (3147485)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=4095127544:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.45/1.44 % (3147487)Refutation not found, incomplete strategy
% 4.45/1.44 % (3147487)------------------------------
% 4.45/1.44 % (3147487)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.44 % (3147487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.44 % (3147487)CaDiCaL version: 2.1.3
% 4.45/1.44 % (3147487)Termination reason: Refutation not found, incomplete strategy
% 4.45/1.44 % (3147487)Time elapsed: 0.001 s
% 4.45/1.44 % (3147487)Peak memory usage: 86 MB
% 4.45/1.44 % (3147486)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2532368076:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.45/1.44 % (3147488)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=518478581:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.45/1.44 % (3147488)Refutation not found, incomplete strategy
% 4.45/1.44 % (3147488)------------------------------
% 4.45/1.44 % (3147488)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.44 % (3147488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.44 % (3147488)CaDiCaL version: 2.1.3
% 4.45/1.44 % (3147488)Termination reason: Refutation not found, incomplete strategy
% 4.45/1.44 % (3147488)Time elapsed: 0.0000 s
% 4.45/1.44 % (3147488)Peak memory usage: 86 MB
% 4.45/1.44 % (3147490)dis-21_1_sil=8000:lcm=predicate:random_seed=852449885:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.45/1.44 % (3147489)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1565016268:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.45/1.44 % (3147490)Also succeeded, but the first one will report.
% 4.45/1.44 % (3147489)First to succeed.
% 4.45/1.44 % (3147489)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3147349"
% 4.45/1.44 % (3147488)------------------------------
% 4.45/1.44 % (3147488)------------------------------
% 4.45/1.44 % (3147487)------------------------------
% 4.45/1.44 % (3147487)------------------------------
% 4.45/1.44 % (3147489)Refutation found. Thanks to Tanya!
% 4.45/1.44 % SZS status Theorem for theBenchmark
% 4.45/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 4.45/1.44 % (3147489)------------------------------
% 4.45/1.44 % (3147489)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.44 % (3147489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.44 % (3147489)CaDiCaL version: 2.1.3
% 4.45/1.44 % (3147489)Termination reason: Refutation
% 4.45/1.44 % (3147489)Time elapsed: 0.003 s
% 4.45/1.44 % (3147489)Peak memory usage: 89 MB
% 4.45/1.44 % (3147489)Instructions burned: 1 (million)
% 4.45/1.44 % (3147489)------------------------------
% 4.45/1.44 % (3147489)------------------------------
% 4.45/1.44 % (3147349)Success in time 0.542 s
% 4.45/1.44 % Vampire exiting
%------------------------------------------------------------------------------