%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN069+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 : n016.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 3.59s 1.19s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 8 unt; 3 def)
% Number of atoms : 140 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 156 ( 64 ~; 48 |; 38 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 53 ( 0 sgn 40 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ( big_f(X0)
& ! [X1] :
( ( big_g(X1)
& big_h(X0,X1) )
=> big_j(X0,X1) ) )
=> ! [X2] :
( big_g(X2)
& big_h(X0,X2)
& big_k(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel45_1) ).
fof(f2,axiom,
~ ? [X0] :
( big_l(X0)
& big_k(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel45_2) ).
fof(f3,axiom,
? [X0] :
( big_f(X0)
& ! [X1] :
( big_h(X0,X1)
=> big_l(X1) )
& ! [X2] :
( ( big_g(X2)
& big_h(X0,X2) )
=> big_j(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel45_3) ).
fof(f4,conjecture,
? [X0] :
( big_f(X0)
& ~ ? [X1] :
( big_g(X1)
& big_h(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel45) ).
fof(f5,negated_conjecture,
~ ? [X0] :
( big_f(X0)
& ~ ? [X1] :
( big_g(X1)
& big_h(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X0] :
( ! [X2] :
( big_g(X2)
& big_h(X0,X2)
& big_k(X2) )
| ~ big_f(X0)
| ? [X1] :
( ~ big_j(X0,X1)
& big_g(X1)
& big_h(X0,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f7,plain,
! [X0] :
( ! [X2] :
( big_g(X2)
& big_h(X0,X2)
& big_k(X2) )
| ~ big_f(X0)
| ? [X1] :
( ~ big_j(X0,X1)
& big_g(X1)
& big_h(X0,X1) ) ),
inference(flattening,[],[f6]) ).
fof(f8,plain,
! [X0] :
( ~ big_l(X0)
| ~ big_k(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
? [X0] :
( big_f(X0)
& ! [X1] :
( big_l(X1)
| ~ big_h(X0,X1) )
& ! [X2] :
( big_j(X0,X2)
| ~ big_g(X2)
| ~ big_h(X0,X2) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f10,plain,
? [X0] :
( big_f(X0)
& ! [X1] :
( big_l(X1)
| ~ big_h(X0,X1) )
& ! [X2] :
( big_j(X0,X2)
| ~ big_g(X2)
| ~ big_h(X0,X2) ) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0] :
( ~ big_f(X0)
| ? [X1] :
( big_g(X1)
& big_h(X0,X1) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f12,definition,
! [X0] :
( ? [X1] :
( ~ big_j(X0,X1)
& big_g(X1)
& big_h(X0,X1) )
| ~ sP0(X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f13,plain,
! [X0] :
( ! [X2] :
( big_g(X2)
& big_h(X0,X2)
& big_k(X2) )
| ~ big_f(X0)
| sP0(X0) ),
inference(definition_folding,[],[f7,f12]) ).
fof(f14,plain,
! [X0] :
( ? [X1] :
( ~ big_j(X0,X1)
& big_g(X1)
& big_h(X0,X1) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f12]) ).
fof(f15,plain,
! [X0] :
( ( ~ big_j(X0,sK1(X0))
& big_g(sK1(X0))
& big_h(X0,sK1(X0)) )
| ~ sP0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f14]) ).
fof(f16,plain,
! [X0] :
( ! [X1] :
( big_g(X1)
& big_h(X0,X1)
& big_k(X1) )
| ~ big_f(X0)
| sP0(X0) ),
inference(rectify,[],[f13]) ).
fof(f17,plain,
( big_f(sK2)
& ! [X1] :
( big_l(X1)
| ~ big_h(sK2,X1) )
& ! [X2] :
( big_j(sK2,X2)
| ~ big_g(X2)
| ~ big_h(sK2,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f10]) ).
fof(f18,plain,
! [X0] :
( ~ big_f(X0)
| ( big_g(sK3(X0))
& big_h(X0,sK3(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f11]) ).
fof(f19,plain,
! [X0] :
( big_h(X0,sK1(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f20,plain,
! [X0] :
( big_g(sK1(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f21,plain,
! [X0] :
( ~ big_j(X0,sK1(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f22,plain,
! [X0,X1] :
( big_k(X1)
| ~ big_f(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f25,plain,
! [X0] :
( ~ big_k(X0)
| ~ big_l(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f26,plain,
! [X2] :
( big_j(sK2,X2)
| ~ big_g(X2)
| ~ big_h(sK2,X2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
! [X1] :
( big_l(X1)
| ~ big_h(sK2,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
big_f(sK2),
inference(cnf_transformation,[],[f17]) ).
fof(f29,plain,
! [X0] :
( big_h(X0,sK3(X0))
| ~ big_f(X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,definition,
( spl4_1
<=> ! [X0] :
( ~ big_f(X0)
| sP0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f33,plain,
( ! [X0] :
( sP0(X0)
| ~ big_f(X0) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f35,definition,
( spl4_2
<=> ! [X1] : big_k(X1) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f36,plain,
( ! [X1] : big_k(X1)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f37,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f22,f35,f32]) ).
fof(f42,plain,
( ! [X0] : ~ big_l(X0)
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f25,f36]) ).
fof(f43,plain,
( ! [X0] : ~ big_h(sK2,X0)
| ~ spl4_2 ),
inference(resolution,[],[f42,f27]) ).
fof(f45,plain,
( ~ big_f(sK2)
| ~ spl4_2 ),
inference(resolution,[],[f43,f29]) ).
fof(f46,plain,
( $false
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f45,f28]) ).
fof(f47,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f46]) ).
fof(f55,plain,
( ~ big_g(sK1(sK2))
| ~ big_h(sK2,sK1(sK2))
| ~ sP0(sK2) ),
inference(resolution,[],[f26,f21]) ).
fof(f56,plain,
( ~ big_h(sK2,sK1(sK2))
| ~ sP0(sK2) ),
inference(forward_subsumption_resolution,[],[f55,f20]) ).
fof(f57,plain,
~ sP0(sK2),
inference(forward_subsumption_resolution,[],[f56,f19]) ).
fof(f58,plain,
( ~ big_f(sK2)
| ~ spl4_1 ),
inference(resolution,[],[f57,f33]) ).
fof(f61,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f58,f28]) ).
fof(f62,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f61]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f37]) ).
cnf(s3,plain,
~ spl4_2,
inference(sat_conversion,[],[f47]) ).
cnf(s5,plain,
~ spl4_1,
inference(sat_conversion,[],[f62]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
fof(f63,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN069+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n016.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 15:33:33 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 3.59/1.19 % (3710872)Detected formulas, will run a generic FOF schedule.
% 3.59/1.19 % (3710877)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=1543487192:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.59/1.19 % (3710878)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=2575856801:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.59/1.19 % (3710880)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3975568514:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.59/1.19 % (3710881)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3774804461:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.59/1.19 % (3710882)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3277433928:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.59/1.19 % (3710879)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=844905773:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.59/1.19 % (3710883)dis-21_1_sil=8000:lcm=predicate:random_seed=2237549260: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)
% 3.59/1.19 % (3710881)Refutation not found, incomplete strategy
% 3.59/1.19 % (3710881)------------------------------
% 3.59/1.19 % (3710881)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.19 % (3710881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.19 % (3710880)Refutation not found, incomplete strategy
% 3.59/1.19 % (3710880)------------------------------
% 3.59/1.19 % (3710880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.19 % (3710881)CaDiCaL version: 2.1.3
% 3.59/1.19 % (3710881)Termination reason: Refutation not found, incomplete strategy
% 3.59/1.19 % (3710881)Time elapsed: 0.001 s
% 3.59/1.19 % (3710880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.19 % (3710881)Peak memory usage: 86 MB
% 3.59/1.19 % (3710880)CaDiCaL version: 2.1.3
% 3.59/1.19 % (3710880)Termination reason: Refutation not found, incomplete strategy
% 3.59/1.19 % (3710880)Time elapsed: 0.0000 s
% 3.59/1.19 % (3710880)Peak memory usage: 86 MB
% 3.59/1.19 % (3710883)Also succeeded, but the first one will report.
% 3.59/1.19 % (3710882)First to succeed.
% 3.59/1.19 % (3710882)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3710872"
% 3.59/1.19 % (3710880)------------------------------
% 3.59/1.19 % (3710880)------------------------------
% 3.59/1.19 % (3710881)------------------------------
% 3.59/1.19 % (3710881)------------------------------
% 3.59/1.19 % (3710882)Refutation found. Thanks to Tanya!
% 3.59/1.19 % SZS status Theorem for theBenchmark
% 3.59/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/1.20 % (3710882)------------------------------
% 3.59/1.20 % (3710882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.20 % (3710882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.20 % (3710882)CaDiCaL version: 2.1.3
% 3.59/1.20 % (3710882)Termination reason: Refutation
% 3.59/1.20 % (3710882)Time elapsed: 0.003 s
% 3.59/1.20 % (3710882)Peak memory usage: 89 MB
% 3.59/1.20 % (3710882)Instructions burned: 2 (million)
% 3.59/1.20 % (3710882)------------------------------
% 3.59/1.20 % (3710882)------------------------------
% 3.59/1.20 % (3710872)Success in time 0.431 s
% 3.59/1.20 % Vampire exiting
%------------------------------------------------------------------------------