%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN412+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 : n020.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 01:50:32 PM UTC 2026
% Result : Theorem 2.52s 1.12s
% Output : Refutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 4 unt; 3 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 60 ( 30 ~; 22 |; 2 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 15 ( 0 sgn 11 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ? [X0] :
! [X1] :
( f(X0,X1)
<=> ~ f(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kalish255) ).
fof(f2,negated_conjecture,
~ ~ ? [X0] :
! [X1] :
( f(X0,X1)
<=> ~ f(X0,X0) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0] :
! [X1] :
( f(X0,X1)
<=> ~ f(X0,X0) ),
inference(flattening,[],[f2]) ).
fof(f4,plain,
? [X0] :
! [X1] :
( ( f(X0,X1)
| f(X0,X0) )
& ( ~ f(X0,X0)
| ~ f(X0,X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f5,plain,
! [X1] :
( ( f(sK0,X1)
| f(sK0,sK0) )
& ( ~ f(sK0,sK0)
| ~ f(sK0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f4]) ).
fof(f6,plain,
! [X1] :
( ~ f(sK0,sK0)
| ~ f(sK0,X1) ),
inference(cnf_transformation,[],[f5]) ).
fof(f7,plain,
! [X1] :
( f(sK0,X1)
| f(sK0,sK0) ),
inference(cnf_transformation,[],[f5]) ).
fof(f9,definition,
( spl1_1
<=> ! [X1] : ~ f(sK0,X1) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f10,plain,
( ! [X1] : ~ f(sK0,X1)
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f9]) ).
fof(f12,definition,
( spl1_2
<=> f(sK0,sK0) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f13,plain,
( ~ f(sK0,sK0)
| spl1_2 ),
inference(avatar_component_clause,[],[f12]) ).
fof(f14,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f6,f12,f9]) ).
fof(f15,plain,
( f(sK0,sK0)
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f12]) ).
fof(f17,definition,
( spl1_3
<=> ! [X1] : f(sK0,X1) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f18,plain,
( ! [X1] : f(sK0,X1)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f19,plain,
( spl1_2
| spl1_3 ),
inference(avatar_split_clause,[],[f7,f17,f12]) ).
fof(f20,plain,
( $false
| spl1_2
| ~ spl1_3 ),
inference(resolution,[],[f18,f13]) ).
fof(f21,plain,
( spl1_2
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f20]) ).
fof(f24,plain,
( $false
| ~ spl1_1
| ~ spl1_2 ),
inference(resolution,[],[f15,f10]) ).
fof(f25,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_contradiction_clause,[],[f24]) ).
cnf(s1,plain,
( spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f14]) ).
cnf(s2,plain,
( spl1_2
| spl1_3 ),
inference(sat_conversion,[],[f19]) ).
cnf(s3,plain,
( spl1_2
| ~ spl1_3 ),
inference(sat_conversion,[],[f21]) ).
cnf(s5,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f25]) ).
cnf(s6,plain,
spl1_2,
inference(rat,[],[s2,s3]) ).
cnf(s7,plain,
~ spl1_1,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s6,s7]) ).
fof(f26,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN412+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n020.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 15:55:50 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 2.52/1.12 % (269991)Detected formulas, will run a generic FOF schedule.
% 2.52/1.12 % (270002)dis-21_1_sil=8000:lcm=predicate:random_seed=1473301445: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)
% 2.52/1.12 % (270002)First to succeed.
% 2.52/1.12 % (270002)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-269991"
% 2.52/1.12 % (269996)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=809890768:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.52/1.12 % (269998)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=2996909124:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.52/1.12 % (269999)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2182876230:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.52/1.12 % (270000)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=199799645:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.52/1.12 % (269997)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=2086689991:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.52/1.12 % (270001)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3240777546:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.52/1.12 % (270000)Also succeeded, but the first one will report.
% 2.52/1.12 % (269999)Also succeeded, but the first one will report.
% 2.52/1.12 % (270001)Also succeeded, but the first one will report.
% 2.52/1.12 % (270002)Refutation found. Thanks to Tanya!
% 2.52/1.12 % SZS status Theorem for theBenchmark
% 2.52/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 2.52/1.12 % (270002)------------------------------
% 2.52/1.12 % (270002)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.52/1.12 % (270002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/1.12 % (270002)CaDiCaL version: 2.1.3
% 2.52/1.12 % (270002)Termination reason: Refutation
% 2.52/1.12 % (270002)Time elapsed: 0.001 s
% 2.52/1.12 % (270002)Peak memory usage: 89 MB
% 2.52/1.12 % (270002)------------------------------
% 2.52/1.12 % (270002)------------------------------
% 2.52/1.12 % (269991)Success in time 0.271 s
% 2.52/1.12 % Vampire exiting
%------------------------------------------------------------------------------