%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN066+1 : TPTP v9.3.1. Bugfixed v3.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 01:49:12 PM UTC 2026
% Result : Theorem 4.57s 1.45s
% Output : Refutation 4.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 11 unt; 2 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 57 ( 26 ~; 19 |; 6 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 41 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
? [X1] :
! [X2] :
? [X3] :
( ( big_p(X2,X0)
=> big_p(X3,X1) )
& big_p(X3,X0)
& ( big_p(X3,X1)
=> ? [X4] : big_q(X4,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel37_1) ).
fof(f2,axiom,
! [X0,X1] :
( ~ big_p(X0,X1)
=> ? [X2] : big_q(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel37_2) ).
fof(f3,axiom,
( ? [X0,X1] : big_q(X0,X1)
=> ! [X2] : big_r(X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel37_3) ).
fof(f4,conjecture,
! [X0] :
? [X1] : big_r(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel37) ).
fof(f5,negated_conjecture,
~ ! [X0] :
? [X1] : big_r(X0,X1),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X0] :
? [X1] :
! [X2] :
? [X3] :
( ( big_p(X3,X1)
| ~ big_p(X2,X0) )
& big_p(X3,X0)
& ( ? [X4] : big_q(X4,X1)
| ~ big_p(X3,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f7,plain,
! [X0,X1] :
( ? [X2] : big_q(X2,X1)
| big_p(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f8,plain,
( ! [X2] : big_r(X2,X2)
| ! [X0,X1] : ~ big_q(X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f9,plain,
? [X0] :
! [X1] : ~ big_r(X0,X1),
inference(ennf_transformation,[],[f5]) ).
fof(f10,plain,
! [X0,X2] :
( ( big_p(sK1(X0,X2),sK0(X0))
| ~ big_p(X2,X0) )
& big_p(sK1(X0,X2),X0)
& ( big_q(sK2(X0),sK0(X0))
| ~ big_p(sK1(X0,X2),sK0(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X1,sK0(X0)),skolemize(X3,sK1(X0,X2)),skolemize(X4,sK2(X0))],[f6]) ).
fof(f11,plain,
! [X0,X1] :
( big_q(sK3(X1),X1)
| big_p(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X1))],[f7]) ).
fof(f12,plain,
( ! [X0] : big_r(X0,X0)
| ! [X1,X2] : ~ big_q(X1,X2) ),
inference(rectify,[],[f8]) ).
fof(f13,plain,
! [X1] : ~ big_r(sK4,X1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4)],[f9]) ).
fof(f14,plain,
! [X2,X0] :
( big_q(sK2(X0),sK0(X0))
| ~ big_p(sK1(X0,X2),sK0(X0)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
! [X0,X1] :
( big_q(sK3(X1),X1)
| big_p(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f18,plain,
! [X2,X0,X1] :
( big_r(X0,X0)
| ~ big_q(X1,X2) ),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X1] : ~ big_r(sK4,X1),
inference(cnf_transformation,[],[f13]) ).
fof(f21,definition,
( spl5_1
<=> ! [X2,X1] : ~ big_q(X1,X2) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f22,plain,
( ! [X2,X1] : ~ big_q(X1,X2)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f24,definition,
( spl5_2
<=> ! [X0] : big_r(X0,X0) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f25,plain,
( ! [X0] : big_r(X0,X0)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f26,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f18,f24,f21]) ).
fof(f27,plain,
( $false
| ~ spl5_2 ),
inference(resolution,[],[f25,f19]) ).
fof(f28,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f27]) ).
fof(f29,plain,
( ! [X0,X1] : big_p(X0,X1)
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f17,f22]) ).
fof(f30,plain,
( ! [X2,X0] : ~ big_p(sK1(X0,X2),sK0(X0))
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f14,f22]) ).
fof(f31,plain,
( $false
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f30,f29]) ).
fof(f32,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f31]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f26]) ).
cnf(s2,plain,
~ spl5_2,
inference(sat_conversion,[],[f28]) ).
cnf(s3,plain,
~ spl5_1,
inference(sat_conversion,[],[f32]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f33,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN066+1 : TPTP v9.3.1. Bugfixed v3.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n006.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 15:27:40 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.57/1.45 % (4054268)Detected formulas, will run a generic FOF schedule.
% 4.57/1.45 % (4054405)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=3237079670:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.57/1.45 % (4054403)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=965003947:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.57/1.45 % (4054409)dis-21_1_sil=8000:lcm=predicate:random_seed=3395994030: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)
% 4.57/1.45 % (4054404)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=937868663:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.57/1.45 % (4054407)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=655464861:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.57/1.45 % (4054408)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1608455140:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.57/1.45 % (4054406)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1001332184:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.57/1.45 % (4054407)Refutation not found, incomplete strategy
% 4.57/1.45 % (4054407)------------------------------
% 4.57/1.45 % (4054407)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.57/1.45 % (4054407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.57/1.45 % (4054407)CaDiCaL version: 2.1.3
% 4.57/1.45 % (4054407)Termination reason: Refutation not found, incomplete strategy
% 4.57/1.45 % (4054407)Time elapsed: 0.0000 s
% 4.57/1.45 % (4054406)Refutation not found, incomplete strategy
% 4.57/1.45 % (4054406)------------------------------
% 4.57/1.45 % (4054406)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.57/1.45 % (4054407)Peak memory usage: 86 MB
% 4.57/1.45 % (4054406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.57/1.45 % (4054406)CaDiCaL version: 2.1.3
% 4.57/1.45 % (4054406)Termination reason: Refutation not found, incomplete strategy
% 4.57/1.45 % (4054406)Time elapsed: 0.0000 s
% 4.57/1.45 % (4054406)Peak memory usage: 87 MB
% 4.57/1.45 % (4054409)Also succeeded, but the first one will report.
% 4.57/1.45 % (4054408)First to succeed.
% 4.57/1.45 % (4054408)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4054268"
% 4.57/1.45 % (4054406)------------------------------
% 4.57/1.45 % (4054406)------------------------------
% 4.57/1.45 % (4054408)Refutation found. Thanks to Tanya!
% 4.57/1.45 % SZS status Theorem for theBenchmark
% 4.57/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 4.57/1.45 % (4054408)------------------------------
% 4.57/1.45 % (4054408)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.57/1.45 % (4054408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.57/1.45 % (4054408)CaDiCaL version: 2.1.3
% 4.57/1.45 % (4054408)Termination reason: Refutation
% 4.57/1.45 % (4054408)Time elapsed: 0.002 s
% 4.57/1.45 % (4054408)Peak memory usage: 89 MB
% 4.57/1.45 % (4054408)Instructions burned: 1 (million)
% 4.57/1.45 % (4054408)------------------------------
% 4.57/1.45 % (4054408)------------------------------
% 4.57/1.45 % (4054268)Success in time 0.56 s
% 4.57/1.45 % Vampire exiting
%------------------------------------------------------------------------------