%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG011-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 09:07:32 AM UTC 2026
% Result : Unsatisfiable 6.06s 2.04s
% Output : Refutation 6.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 7 unt; 3 def)
% Number of atoms : 106 ( 1 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 138 ( 72 ~; 63 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 49 ( 0 sgn 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : f(X0,f(X1,X2)) = f(f(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_is_associative) ).
fof(f2,axiom,
! [X0] :
( d(X0)
| c(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partitions_union) ).
fof(f3,axiom,
! [X0] :
( ~ d(X0)
| ~ c(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partitions_exclusive) ).
fof(f6,negated_conjecture,
! [X0,X1] :
( d(f(X0,X1))
| ~ c(X0)
| ~ c(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_1) ).
fof(f7,negated_conjecture,
! [X0,X1] :
( c(f(X0,X1))
| ~ d(X0)
| ~ d(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_2) ).
fof(f8,plain,
! [X0,X1] :
( ~ c(f(X0,X1))
| ~ c(X0)
| ~ c(X1) ),
inference(resolution,[],[f3,f6]) ).
fof(f14,plain,
! [X2,X0,X1] :
( c(f(X0,f(X1,X2)))
| ~ d(f(X0,X1))
| ~ d(X2) ),
inference(superposition,[],[f7,f1]) ).
fof(f18,plain,
! [X2,X0,X1] :
( ~ d(f(X0,X1))
| ~ d(X2)
| ~ c(X0)
| ~ c(f(X1,X2)) ),
inference(resolution,[],[f14,f8]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ d(X0)
| ~ c(X1)
| ~ c(f(X2,X0))
| ~ c(X1)
| ~ c(X2) ),
inference(resolution,[],[f18,f6]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ c(f(X2,X0))
| ~ c(X1)
| ~ d(X0)
| c(f(X1,X2)) ),
inference(resolution,[],[f18,f2]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ d(X0)
| ~ c(X1)
| ~ c(f(X2,X0))
| ~ c(X2) ),
inference(duplicate_literal_removal,[],[f31]) ).
fof(f38,definition,
( spl0_1
<=> ! [X1] : ~ c(X1) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f39,plain,
( ! [X1] : ~ c(X1)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f41,definition,
( spl0_2
<=> ! [X2,X0] :
( ~ d(X0)
| ~ c(X2)
| ~ c(f(X2,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f42,plain,
( ! [X2,X0] :
( ~ c(f(X2,X0))
| ~ c(X2)
| ~ d(X0) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f43,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f35,f41,f38]) ).
fof(f75,plain,
( ! [X0,X1] :
( ~ d(X0)
| ~ d(X1) )
| ~ spl0_1 ),
inference(resolution,[],[f39,f7]) ).
fof(f81,definition,
( spl0_4
<=> ! [X3] : ~ d(X3) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f82,plain,
( ! [X3] : ~ d(X3)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f91,plain,
( spl0_4
| spl0_4
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f75,f38,f81,f81]) ).
fof(f97,plain,
! [X2,X0,X1] :
( ~ c(X0)
| ~ d(X1)
| c(f(X0,X2))
| ~ d(X2)
| ~ d(X1) ),
inference(resolution,[],[f33,f7]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ c(X0)
| ~ d(X1)
| c(f(X0,X2))
| ~ d(X2) ),
inference(duplicate_literal_removal,[],[f97]) ).
fof(f102,plain,
( ! [X2,X0,X1] :
( ~ c(X0)
| ~ d(X1)
| ~ d(X2) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f101,f42]) ).
fof(f103,plain,
( spl0_4
| spl0_4
| spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f102,f41,f38,f81,f81]) ).
fof(f104,plain,
( ! [X0,X1] :
( ~ c(X0)
| ~ c(X1) )
| ~ spl0_4 ),
inference(resolution,[],[f82,f6]) ).
fof(f108,plain,
( ! [X0] : c(X0)
| ~ spl0_4 ),
inference(resolution,[],[f82,f2]) ).
fof(f112,plain,
( ! [X1] : ~ c(X1)
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f104,f108]) ).
fof(f117,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f112,f108]) ).
fof(f118,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f117]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f43]) ).
cnf(s6,plain,
( spl0_4
| ~ spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f91]) ).
cnf(s7,plain,
( ~ spl0_1
| spl0_4 ),
inference(rat,[],[s6]) ).
cnf(s8,plain,
( spl0_4
| ~ spl0_2
| spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f103]) ).
cnf(s9,plain,
( spl0_1
| ~ spl0_2
| spl0_4 ),
inference(rat,[],[s8]) ).
cnf(s13,plain,
~ spl0_4,
inference(sat_conversion,[],[f118]) ).
cnf(s14,plain,
( spl0_1
| ~ spl0_2 ),
inference(rat,[],[s9,s13]) ).
cnf(s15,plain,
~ spl0_1,
inference(rat,[],[s7,s13]) ).
cnf(s16,plain,
~ spl0_2,
inference(rat,[],[s14,s15]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s1,s16,s15]) ).
fof(f119,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG011-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.30 % Computer : n020.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8046.5625MB
% 0.12/0.30 % OS : Linux 6.8.0-71-generic
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Mon Sep 28 19:18:05 UTC 2026
% 0.27/0.31 % CPUTime :
% 0.27/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.35 Running first-order theorem proving
% 0.27/0.35 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
% 6.06/2.04 % (444647)Input is clausal, will run a generic CNF schedule.
% 6.06/2.04 % (444654)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=287894394:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.06/2.04 % (444652)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=4105784730:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.06/2.04 % (444655)lrs+10_1_sil=8000:sp=occurrence:random_seed=3076332019:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.06/2.04 % (444658)dis-21_1_sil=8000:lcm=predicate:random_seed=2155125497: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)
% 6.06/2.04 % (444653)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4003027721:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.06/2.04 % (444656)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=80204730:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.06/2.04 % (444657)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3301084232:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.06/2.04 % (444658)Refutation not found, incomplete strategy
% 6.06/2.04 % (444658)------------------------------
% 6.06/2.04 % (444658)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.06/2.04 % (444658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.06/2.04 % (444656)Refutation not found, incomplete strategy
% 6.06/2.04 % (444656)------------------------------
% 6.06/2.04 % (444656)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.06/2.04 % (444658)CaDiCaL version: 2.1.3
% 6.06/2.04 % (444656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.06/2.04 % (444658)Termination reason: Refutation not found, incomplete strategy
% 6.06/2.04 % (444658)Time elapsed: 0.002 s
% 6.06/2.04 % (444658)Peak memory usage: 87 MB
% 6.06/2.04 % (444656)CaDiCaL version: 2.1.3
% 6.06/2.04 % (444656)Termination reason: Refutation not found, incomplete strategy
% 6.06/2.04 % (444656)Time elapsed: 0.001 s
% 6.06/2.04 % (444656)Peak memory usage: 87 MB
% 6.06/2.04 % (444655)First to succeed.
% 6.06/2.04 % (444655)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-444647"
% 6.06/2.04 % (444657)Also succeeded, but the first one will report.
% 6.06/2.04 % (444658)------------------------------
% 6.06/2.04 % (444658)------------------------------
% 6.06/2.04 % (444656)------------------------------
% 6.06/2.04 % (444656)------------------------------
% 6.06/2.04 % (444655)Refutation found. Thanks to Tanya!
% 6.06/2.04 % SZS status Unsatisfiable for theBenchmark
% 6.06/2.04 % SZS output start Proof for theBenchmark
% See solution above
% 6.06/2.04 % (444655)------------------------------
% 6.06/2.04 % (444655)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.06/2.04 % (444655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.06/2.04 % (444655)CaDiCaL version: 2.1.3
% 6.06/2.04 % (444655)Termination reason: Refutation
% 6.06/2.04 % (444655)Time elapsed: 0.008 s
% 6.06/2.04 % (444655)Peak memory usage: 89 MB
% 6.06/2.04 % (444655)Instructions burned: 4 (million)
% 6.06/2.04 % (444655)------------------------------
% 6.06/2.04 % (444655)------------------------------
% 6.06/2.04 % (444647)Success in time 0.72 s
% 6.06/2.04 % Vampire exiting
%------------------------------------------------------------------------------