%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL098-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 09:37:57 AM UTC 2026
% Result : Unsatisfiable 3.70s 1.28s
% Output : Refutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 38 ( 10 unt; 3 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 103 ( 56 ~; 44 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X2,X0,X1] :
( member(pair(X0,X1),trancl(X2))
| ~ member(pair(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r_into_trancl) ).
fof(f8,axiom,
! [X0] : trans(trancl(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_trancl) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( ~ trans(X0)
| ~ member(pair(X1,X2),X0)
| ~ member(pair(X2,X3),X0)
| member(pair(X1,X3),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transD) ).
fof(f10,axiom,
! [X2,X0,X1] :
( member(pair(X1,sk1(X0,X1,X2)),r)
| ~ member(pair(X0,X2),r)
| ~ member(pair(X0,X1),r) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD_2h1) ).
fof(f11,axiom,
! [X2,X0,X1] :
( member(pair(X2,sk1(X0,X1,X2)),r)
| ~ member(pair(X0,X2),r)
| ~ member(pair(X0,X1),r) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD_2h2) ).
fof(f13,axiom,
member(pair(y,z),r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD_2h4) ).
fof(f14,axiom,
! [X0] :
( member(pair(X0,sk2(X0)),trancl(r))
| ~ member(pair(x,X0),r) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD_2h5) ).
fof(f15,axiom,
! [X0] :
( member(pair(y,sk2(X0)),r)
| ~ member(pair(x,X0),r) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD_2h6) ).
fof(f16,negated_conjecture,
member(pair(x,sk3),r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD_2c1) ).
fof(f17,negated_conjecture,
! [X0] :
( ~ member(pair(sk3,X0),trancl(r))
| ~ member(pair(z,X0),r) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD_2c2) ).
fof(f49,definition,
( spl1_2
<=> member(pair(x,sk3),r) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f50,plain,
( ~ member(pair(x,sk3),r)
| spl1_2 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( member(pair(X0,X3),trancl(X2))
| ~ member(pair(X1,X3),trancl(X2))
| ~ member(pair(X0,X1),trancl(X2)) ),
inference(resolution,[],[f9,f8]) ).
fof(f58,plain,
! [X0,X1] :
( ~ member(pair(X0,X1),trancl(r))
| ~ member(pair(sk3,X0),trancl(r))
| ~ member(pair(z,X1),r) ),
inference(resolution,[],[f52,f17]) ).
fof(f60,plain,
! [X0,X1] :
( ~ member(pair(sk3,X0),trancl(r))
| ~ member(pair(z,X1),r)
| ~ member(pair(X0,X1),r) ),
inference(resolution,[],[f58,f7]) ).
fof(f67,plain,
! [X0] :
( ~ member(pair(z,X0),r)
| ~ member(pair(sk2(sk3),X0),r)
| ~ member(pair(x,sk3),r) ),
inference(resolution,[],[f60,f14]) ).
fof(f81,definition,
( spl1_5
<=> ! [X0] :
( ~ member(pair(z,X0),r)
| ~ member(pair(sk2(sk3),X0),r) ) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f82,plain,
( ! [X0] :
( ~ member(pair(sk2(sk3),X0),r)
| ~ member(pair(z,X0),r) )
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f83,plain,
( ~ spl1_2
| spl1_5 ),
inference(avatar_split_clause,[],[f67,f81,f49]) ).
fof(f84,plain,
( $false
| spl1_2 ),
inference(resolution,[],[f50,f16]) ).
fof(f85,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f84]) ).
fof(f90,plain,
( ! [X0,X1] :
( ~ member(pair(z,sk1(X0,sk2(sk3),X1)),r)
| ~ member(pair(X0,X1),r)
| ~ member(pair(X0,sk2(sk3)),r) )
| ~ spl1_5 ),
inference(resolution,[],[f82,f10]) ).
fof(f103,plain,
( ! [X0] :
( ~ member(pair(X0,z),r)
| ~ member(pair(X0,sk2(sk3)),r)
| ~ member(pair(X0,z),r)
| ~ member(pair(X0,sk2(sk3)),r) )
| ~ spl1_5 ),
inference(resolution,[],[f90,f11]) ).
fof(f104,plain,
( ! [X0] :
( ~ member(pair(X0,sk2(sk3)),r)
| ~ member(pair(X0,z),r) )
| ~ spl1_5 ),
inference(duplicate_literal_removal,[],[f103]) ).
fof(f109,plain,
( ~ member(pair(y,z),r)
| ~ member(pair(x,sk3),r)
| ~ spl1_5 ),
inference(resolution,[],[f104,f15]) ).
fof(f111,definition,
( spl1_7
<=> member(pair(y,z),r) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f112,plain,
( ~ member(pair(y,z),r)
| spl1_7 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f113,plain,
( ~ spl1_2
| ~ spl1_7
| ~ spl1_5 ),
inference(avatar_split_clause,[],[f109,f81,f111,f49]) ).
fof(f114,plain,
( $false
| spl1_7 ),
inference(resolution,[],[f112,f13]) ).
fof(f115,plain,
spl1_7,
inference(avatar_contradiction_clause,[],[f114]) ).
cnf(s3,plain,
( ~ spl1_2
| spl1_5 ),
inference(sat_conversion,[],[f83]) ).
cnf(s4,plain,
spl1_2,
inference(sat_conversion,[],[f85]) ).
cnf(s6,plain,
( ~ spl1_2
| ~ spl1_5
| ~ spl1_7 ),
inference(sat_conversion,[],[f113]) ).
cnf(s7,plain,
spl1_7,
inference(sat_conversion,[],[f115]) ).
cnf(s8,plain,
( ~ spl1_2
| ~ spl1_5 ),
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
~ spl1_5,
inference(rat,[],[s8,s4]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s3,s9,s4]) ).
fof(f116,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL098-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n005.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 21:34:46 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 3.70/1.28 % (1213771)Input is clausal, will run a generic CNF schedule.
% 3.70/1.28 % (1213776)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=2349872535:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.70/1.28 % (1213780)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4184681516:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.70/1.28 % (1213777)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2814377029:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.70/1.28 % (1213779)lrs+10_1_sil=8000:sp=occurrence:random_seed=2580264944:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.70/1.28 % (1213781)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2761805889:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.70/1.28 % (1213778)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4266871361:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.70/1.28 % (1213782)dis-21_1_sil=8000:lcm=predicate:random_seed=720965764:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.70/1.28 % (1213780)Refutation not found, incomplete strategy
% 3.70/1.28 % (1213780)------------------------------
% 3.70/1.28 % (1213780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.28 % (1213780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.28 % (1213780)CaDiCaL version: 2.1.3
% 3.70/1.28 % (1213780)Termination reason: Refutation not found, incomplete strategy
% 3.70/1.28 % (1213780)Time elapsed: 0.001 s
% 3.70/1.28 % (1213780)Peak memory usage: 87 MB
% 3.70/1.28 % (1213782)First to succeed.
% 3.70/1.28 % (1213781)Also succeeded, but the first one will report.
% 3.70/1.28 % (1213782)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1213771"
% 3.70/1.28 % (1213779)Also succeeded, but the first one will report.
% 3.70/1.28 % (1213780)------------------------------
% 3.70/1.28 % (1213780)------------------------------
% 3.70/1.28 % (1213782)Refutation found. Thanks to Tanya!
% 3.70/1.28 % SZS status Unsatisfiable for theBenchmark
% 3.70/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.70/1.28 % (1213782)------------------------------
% 3.70/1.28 % (1213782)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.28 % (1213782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.28 % (1213782)CaDiCaL version: 2.1.3
% 3.70/1.28 % (1213782)Termination reason: Refutation
% 3.70/1.28 % (1213782)Time elapsed: 0.004 s
% 3.70/1.28 % (1213782)Peak memory usage: 89 MB
% 3.70/1.28 % (1213782)Instructions burned: 4 (million)
% 3.70/1.28 % (1213782)------------------------------
% 3.70/1.28 % (1213782)------------------------------
% 3.70/1.28 % (1213771)Success in time 0.441 s
% 3.70/1.28 % Vampire exiting
%------------------------------------------------------------------------------