%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN070+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 01:49:13 PM UTC 2026
% Result : Theorem 0.19s 1.30s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 9 unt; 4 def)
% Number of atoms : 169 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 201 ( 87 ~; 81 |; 22 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 59 ( 0 sgn 53 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( big_f(X0)
& ( ( big_f(X1)
& big_h(X1,X0) )
=> big_g(X1) ) )
=> big_g(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel46_1) ).
fof(f2,axiom,
( ? [X0] :
( big_f(X0)
& ~ big_g(X0) )
=> ? [X1] :
( big_f(X1)
& ~ big_g(X1)
& ! [X2] :
( ( big_f(X2)
& ~ big_g(X2) )
=> big_j(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel46_2) ).
fof(f3,axiom,
! [X0,X1] :
( ( big_f(X0)
& big_f(X1)
& big_h(X0,X1) )
=> ~ big_j(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel46_3) ).
fof(f4,conjecture,
! [X0] :
( big_f(X0)
=> big_g(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel46) ).
fof(f5,negated_conjecture,
~ ! [X0] :
( big_f(X0)
=> big_g(X0) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X0,X1] :
( big_g(X0)
| ~ big_f(X0)
| ( ~ big_g(X1)
& big_f(X1)
& big_h(X1,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f7,plain,
! [X0,X1] :
( big_g(X0)
| ~ big_f(X0)
| ( ~ big_g(X1)
& big_f(X1)
& big_h(X1,X0) ) ),
inference(flattening,[],[f6]) ).
fof(f8,plain,
( ? [X1] :
( big_f(X1)
& ~ big_g(X1)
& ! [X2] :
( big_j(X1,X2)
| ~ big_f(X2)
| big_g(X2) ) )
| ! [X0] :
( ~ big_f(X0)
| big_g(X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
( ? [X1] :
( big_f(X1)
& ~ big_g(X1)
& ! [X2] :
( big_j(X1,X2)
| ~ big_f(X2)
| big_g(X2) ) )
| ! [X0] :
( ~ big_f(X0)
| big_g(X0) ) ),
inference(flattening,[],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( ~ big_j(X1,X0)
| ~ big_f(X0)
| ~ big_f(X1)
| ~ big_h(X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f11,plain,
! [X0,X1] :
( ~ big_j(X1,X0)
| ~ big_f(X0)
| ~ big_f(X1)
| ~ big_h(X0,X1) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
? [X0] :
( ~ big_g(X0)
& big_f(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f13,plain,
( ? [X0] :
( big_f(X0)
& ~ big_g(X0)
& ! [X1] :
( big_j(X0,X1)
| ~ big_f(X1)
| big_g(X1) ) )
| ! [X2] :
( ~ big_f(X2)
| big_g(X2) ) ),
inference(rectify,[],[f9]) ).
fof(f14,plain,
( ( big_f(sK0)
& ~ big_g(sK0)
& ! [X1] :
( big_j(sK0,X1)
| ~ big_f(X1)
| big_g(X1) ) )
| ! [X2] :
( ~ big_f(X2)
| big_g(X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f13]) ).
fof(f15,plain,
( ~ big_g(sK1)
& big_f(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f12]) ).
fof(f16,plain,
! [X0,X1] :
( big_g(X0)
| ~ big_f(X0)
| big_h(X1,X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f17,plain,
! [X0,X1] :
( big_g(X0)
| ~ big_f(X0)
| big_f(X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f18,plain,
! [X0,X1] :
( big_g(X0)
| ~ big_f(X0)
| ~ big_g(X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f19,plain,
! [X2,X1] :
( big_j(sK0,X1)
| ~ big_f(X1)
| big_g(X1)
| ~ big_f(X2)
| big_g(X2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X0,X1] :
( ~ big_j(X1,X0)
| ~ big_f(X0)
| ~ big_f(X1)
| ~ big_h(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f23,plain,
big_f(sK1),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
~ big_g(sK1),
inference(cnf_transformation,[],[f15]) ).
fof(f26,definition,
( spl2_1
<=> ! [X2] :
( ~ big_f(X2)
| big_g(X2) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f27,plain,
( ! [X2] :
( big_g(X2)
| ~ big_f(X2) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f29,definition,
( spl2_2
<=> ! [X1] :
( big_j(sK0,X1)
| big_g(X1)
| ~ big_f(X1) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f30,plain,
( ! [X1] :
( big_j(sK0,X1)
| big_g(X1)
| ~ big_f(X1) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f31,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f19,f29,f26]) ).
fof(f43,definition,
( spl2_5
<=> ! [X1] : big_f(X1) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f44,plain,
( ! [X1] : big_f(X1)
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f45,plain,
( spl2_5
| spl2_1 ),
inference(avatar_split_clause,[],[f17,f26,f43]) ).
fof(f47,definition,
( spl2_6
<=> ! [X1] : ~ big_g(X1) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f48,plain,
( ! [X1] : ~ big_g(X1)
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f49,plain,
( spl2_6
| spl2_1 ),
inference(avatar_split_clause,[],[f18,f26,f47]) ).
fof(f50,plain,
( ! [X0,X1] :
( ~ big_f(X0)
| big_h(X1,X0) )
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f16,f48]) ).
fof(f51,plain,
( ! [X0,X1] : big_h(X1,X0)
| ~ spl2_5
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f50,f44]) ).
fof(f52,plain,
( ! [X1] :
( big_j(sK0,X1)
| ~ big_f(X1) )
| ~ spl2_2
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f30,f48]) ).
fof(f53,plain,
( ! [X1] : big_j(sK0,X1)
| ~ spl2_2
| ~ spl2_5
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f52,f44]) ).
fof(f54,plain,
( ! [X0,X1] :
( ~ big_j(X1,X0)
| ~ big_f(X1)
| ~ big_h(X0,X1) )
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f22,f44]) ).
fof(f55,plain,
( ! [X0,X1] :
( ~ big_j(X1,X0)
| ~ big_h(X0,X1) )
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f54,f44]) ).
fof(f56,plain,
( ! [X0,X1] : ~ big_j(X1,X0)
| ~ spl2_5
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f55,f51]) ).
fof(f57,plain,
( $false
| ~ spl2_2
| ~ spl2_5
| ~ spl2_6 ),
inference(resolution,[],[f56,f53]) ).
fof(f58,plain,
( ~ spl2_2
| ~ spl2_5
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[],[f57]) ).
fof(f67,plain,
( ~ big_f(sK1)
| ~ spl2_1 ),
inference(resolution,[],[f27,f24]) ).
fof(f71,plain,
( $false
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f67,f23]) ).
fof(f72,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f71]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f31]) ).
cnf(s4,plain,
( spl2_1
| spl2_5 ),
inference(sat_conversion,[],[f45]) ).
cnf(s5,plain,
( spl2_1
| spl2_6 ),
inference(sat_conversion,[],[f49]) ).
cnf(s6,plain,
( ~ spl2_2
| ~ spl2_5
| ~ spl2_6 ),
inference(sat_conversion,[],[f58]) ).
cnf(s11,plain,
~ spl2_1,
inference(sat_conversion,[],[f72]) ).
cnf(s12,plain,
spl2_6,
inference(rat,[],[s5,s11]) ).
cnf(s13,plain,
spl2_5,
inference(rat,[],[s4,s11]) ).
cnf(s14,plain,
~ spl2_2,
inference(rat,[],[s6,s12,s13]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s1,s14,s11]) ).
fof(f73,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN070+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n017.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 15:24:21 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 0.19/1.30 % (3635205)Detected formulas, will run a generic FOF schedule.
% 0.19/1.30 % (3635213)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=150149088:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.19/1.30 % (3635213)Refutation not found, incomplete strategy
% 0.19/1.30 % (3635213)------------------------------
% 0.19/1.30 % (3635213)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.30 % (3635213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.30 % (3635213)CaDiCaL version: 2.1.3
% 0.19/1.30 % (3635213)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.30 % (3635213)Time elapsed: 0.0000 s
% 0.19/1.30 % (3635213)Peak memory usage: 86 MB
% 0.19/1.30 % (3635212)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=3417065871:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.19/1.30 % (3635210)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=1818878820:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.19/1.30 % (3635214)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2637191525:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.19/1.30 % (3635211)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=1769423390:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.19/1.30 % (3635215)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=836156509:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.19/1.30 % (3635216)dis-21_1_sil=8000:lcm=predicate:random_seed=1284993881: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)
% 0.19/1.30 % (3635214)Refutation not found, incomplete strategy
% 0.19/1.30 % (3635214)------------------------------
% 0.19/1.30 % (3635214)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.30 % (3635214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.30 % (3635214)CaDiCaL version: 2.1.3
% 0.19/1.30 % (3635214)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.30 % (3635214)Time elapsed: 0.0000 s
% 0.19/1.30 % (3635214)Peak memory usage: 86 MB
% 0.19/1.30 % (3635215)First to succeed.
% 0.19/1.30 % (3635216)Also succeeded, but the first one will report.
% 0.19/1.30 % (3635215)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3635205"
% 0.19/1.30 % (3635213)------------------------------
% 0.19/1.30 % (3635213)------------------------------
% 0.19/1.30 % (3635224)lrs+10_1_sil=8000:sp=occurrence:random_seed=2202338342:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.19/1.30 % (3635224)Also succeeded, but the first one will report.
% 0.19/1.30 % (3635214)------------------------------
% 0.19/1.30 % (3635214)------------------------------
% 0.19/1.30 % (3635215)Refutation found. Thanks to Tanya!
% 0.19/1.30 % SZS status Theorem for theBenchmark
% 0.19/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.31 % (3635215)------------------------------
% 0.19/1.31 % (3635215)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (3635215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (3635215)CaDiCaL version: 2.1.3
% 0.19/1.31 % (3635215)Termination reason: Refutation
% 0.19/1.31 % (3635215)Time elapsed: 0.003 s
% 0.19/1.31 % (3635215)Peak memory usage: 89 MB
% 0.19/1.31 % (3635215)Instructions burned: 2 (million)
% 0.19/1.31 % (3635215)------------------------------
% 0.19/1.31 % (3635215)------------------------------
% 0.19/1.31 % (3635205)Success in time 0.44 s
% 0.19/1.31 % Vampire exiting
%------------------------------------------------------------------------------