%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n014.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 09:20:04 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 38 ( 8 unt; 3 def)
% Number of atoms : 100 ( 1 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 128 ( 66 ~; 59 |; 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 : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 45 !; 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(f5,axiom,
d(a2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition_d_not_empty) ).
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(f65,plain,
( ! [X0,X1] :
( ~ d(X0)
| ~ d(X1) )
| ~ spl0_1 ),
inference(resolution,[],[f39,f7]) ).
fof(f71,definition,
( spl0_4
<=> ! [X3] : ~ d(X3) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f72,plain,
( ! [X3] : ~ d(X3)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f81,plain,
( spl0_4
| spl0_4
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f65,f38,f71,f71]) ).
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,f71,f71]) ).
fof(f115,plain,
( $false
| ~ spl0_4 ),
inference(resolution,[],[f72,f5]) ).
fof(f117,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f115]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f43]) ).
cnf(s6,plain,
( spl0_4
| ~ spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f81]) ).
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(s10,plain,
~ spl0_4,
inference(sat_conversion,[],[f117]) ).
cnf(s15,plain,
( spl0_1
| ~ spl0_2 ),
inference(rat,[],[s9,s10]) ).
cnf(s16,plain,
~ spl0_1,
inference(rat,[],[s7,s10]) ).
cnf(s17,plain,
~ spl0_2,
inference(rat,[],[s15,s16]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s1,s17,s16]) ).
fof(f127,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG011-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n014.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 19:17:16 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.25 % (2085882)Will run a generic schedule for satisfiability detection.
% 0.08/0.25 % (2085896)dis+10_1_sil=32000:sp=arity:random_seed=1643330868:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.25 % (2085896) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2085882-2085896"...
% 0.08/0.25 % (2085896)...printing done.
% 0.08/0.25 % (2085894)% WARNING: option uhcvi not known.
% 0.08/0.25 % (2085896)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (2085896)------------------------------
% 0.08/0.26 % (2085896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (2085896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (2085896)CaDiCaL version: 2.1.3
% 0.08/0.26 % (2085896)Termination reason: Refutation
% 0.08/0.26 % (2085896)Time elapsed: 0.002 s
% 0.08/0.26 % (2085896)Peak memory usage: 12 MB
% 0.08/0.26 % (2085896)Instructions burned: 5 (million)
% 0.08/0.26 % (2085882)Success in time 0.029 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------