%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN318+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 : 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 01:50:11 PM UTC 2026
% Result : Theorem 4.10s 1.46s
% Output : Refutation 4.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 7 unt; 3 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 83 ( 32 ~; 21 |; 8 &)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 33 ( 0 sgn 26 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0] :
( ! [X1] :
( big_f(X1)
=> ( big_f(X0)
=> big_g(X1) ) )
=> ( p
=> ! [X1] :
( big_f(X1)
=> big_g(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_2_4) ).
fof(f2,negated_conjecture,
~ ? [X0] :
( ! [X1] :
( big_f(X1)
=> ( big_f(X0)
=> big_g(X1) ) )
=> ( p
=> ! [X1] :
( big_f(X1)
=> big_g(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ? [X0] :
( ! [X1] :
( big_f(X1)
=> ( big_f(X0)
=> big_g(X1) ) )
=> ( p
=> ! [X2] :
( big_f(X2)
=> big_g(X0) ) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
~ ? [X0] :
( ! [X1] :
( big_f(X1)
=> ( big_f(X0)
=> big_g(X1) ) )
=> ! [X2] :
( big_f(X2)
=> big_g(X0) ) ),
inference(pure_predicate_removal,[],[f3]) ).
fof(f5,plain,
! [X0] :
( ? [X2] :
( ~ big_g(X0)
& big_f(X2) )
& ! [X1] :
( big_g(X1)
| ~ big_f(X0)
| ~ big_f(X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f6,plain,
! [X0] :
( ? [X2] :
( ~ big_g(X0)
& big_f(X2) )
& ! [X1] :
( big_g(X1)
| ~ big_f(X0)
| ~ big_f(X1) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X0] :
( ? [X1] :
( ~ big_g(X0)
& big_f(X1) )
& ! [X2] :
( big_g(X2)
| ~ big_f(X0)
| ~ big_f(X2) ) ),
inference(rectify,[],[f6]) ).
fof(f8,plain,
! [X0] :
( ~ big_g(X0)
& big_f(sK0(X0))
& ! [X2] :
( big_g(X2)
| ~ big_f(X0)
| ~ big_f(X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f7]) ).
fof(f9,plain,
! [X2,X0] :
( big_g(X2)
| ~ big_f(X0)
| ~ big_f(X2) ),
inference(cnf_transformation,[],[f8]) ).
fof(f10,plain,
! [X0] : big_f(sK0(X0)),
inference(cnf_transformation,[],[f8]) ).
fof(f11,plain,
! [X0] : ~ big_g(X0),
inference(cnf_transformation,[],[f8]) ).
fof(f12,plain,
! [X2] :
( big_g(X2)
| ~ big_f(X2)
| sP1 ),
inference(cnf_transformation,[],[f12_D]) ).
fof(f12_D,definition,
( ! [X2] :
( big_g(X2)
| ~ big_f(X2) )
<=> ~ sP1 ),
introduced(definition,[new_symbols(definition,[sP1])],[general_splitting_component_introduction]) ).
fof(f13,plain,
! [X0] :
( ~ big_f(X0)
| ~ sP1 ),
inference(general_splitting,[],[f9,f12_D]) ).
fof(f14,plain,
! [X2] :
( ~ big_f(X2)
| sP1 ),
inference(forward_subsumption_resolution,[],[f12,f11]) ).
fof(f16,definition,
( spl2_1
<=> sP1 ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f20,definition,
( spl2_2
<=> ! [X0] : ~ big_f(X0) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f21,plain,
( ! [X0] : ~ big_f(X0)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f22,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f13,f20,f16]) ).
fof(f23,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f14,f20,f16]) ).
fof(f24,plain,
( $false
| ~ spl2_2 ),
inference(resolution,[],[f10,f21]) ).
fof(f25,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f24]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f23]) ).
cnf(s3,plain,
~ spl2_2,
inference(sat_conversion,[],[f25]) ).
cnf(s4,plain,
spl2_1,
inference(rat,[],[s2,s3]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s4]) ).
fof(f26,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN318+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 15:37:25 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 4.10/1.46 % (3653155)Detected formulas, will run a generic FOF schedule.
% 4.10/1.46 % (3653264)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=490119373:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.10/1.46 % (3653262)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=2847037640:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.10/1.46 % (3653263)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=217648893:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.10/1.46 % (3653265)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1853756067:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.10/1.46 % (3653265)First to succeed.
% 4.10/1.46 % (3653265)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3653155"
% 4.10/1.46 % (3653267)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2374827731:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.10/1.46 % (3653266)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1567230072:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.10/1.46 % (3653268)dis-21_1_sil=8000:lcm=predicate:random_seed=802347412: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)
% 4.10/1.46 % (3653266)Also succeeded, but the first one will report.
% 4.10/1.46 % (3653267)Also succeeded, but the first one will report.
% 4.10/1.46 % (3653268)Also succeeded, but the first one will report.
% 4.10/1.46 % (3653265)Refutation found. Thanks to Tanya!
% 4.10/1.46 % SZS status Theorem for theBenchmark
% 4.10/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 4.10/1.46 % (3653265)------------------------------
% 4.10/1.46 % (3653265)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.10/1.46 % (3653265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.10/1.46 % (3653265)CaDiCaL version: 2.1.3
% 4.10/1.46 % (3653265)Termination reason: Refutation
% 4.10/1.46 % (3653265)Time elapsed: 0.002 s
% 4.10/1.46 % (3653265)Peak memory usage: 89 MB
% 4.10/1.46 % (3653265)------------------------------
% 4.10/1.46 % (3653265)------------------------------
% 4.10/1.46 % (3653155)Success in time 0.479 s
% 4.10/1.46 % Vampire exiting
%------------------------------------------------------------------------------