%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD018-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 09:49:02 AM UTC 2026
% Result : Unsatisfiable 0.21s 1.14s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 11 unt; 3 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 83 ( 45 ~; 35 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( equalish(add(additive_identity,X0),X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f3,axiom,
! [X0] :
( equalish(add(X0,additive_inverse(X0)),additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
fof(f12,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f22,axiom,
! [X0,X1] :
( equalish(X0,X1)
| ~ equalish(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_equality) ).
fof(f23,axiom,
! [X2,X0,X1] :
( equalish(X0,X1)
| ~ equalish(X0,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_equality) ).
fof(f24,axiom,
! [X2,X0,X1] :
( equalish(add(X0,X1),add(X2,X1))
| ~ defined(X1)
| ~ equalish(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_equality_and_addition) ).
fof(f28,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f29,negated_conjecture,
equalish(a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_additive_identity_2) ).
fof(f30,negated_conjecture,
~ equalish(additive_inverse(a),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_not_equal_to_additive_identity_3) ).
fof(f31,plain,
~ equalish(additive_identity,additive_inverse(a)),
inference(resolution,[],[f22,f30]) ).
fof(f37,plain,
! [X0] :
( ~ equalish(X0,additive_inverse(a))
| ~ equalish(additive_identity,X0) ),
inference(resolution,[],[f23,f31]) ).
fof(f46,plain,
( ~ equalish(additive_identity,add(additive_identity,additive_inverse(a)))
| ~ defined(additive_inverse(a)) ),
inference(resolution,[],[f37,f2]) ).
fof(f48,definition,
( spl0_1
<=> defined(additive_inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f49,plain,
( ~ defined(additive_inverse(a))
| spl0_1 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,definition,
( spl0_2
<=> equalish(additive_identity,add(additive_identity,additive_inverse(a))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f52,plain,
( ~ equalish(additive_identity,add(additive_identity,additive_inverse(a)))
| spl0_2 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f53,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f46,f51,f48]) ).
fof(f57,plain,
( ~ defined(a)
| spl0_1 ),
inference(resolution,[],[f49,f12]) ).
fof(f58,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f57,f28]) ).
fof(f59,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f58]) ).
fof(f61,plain,
( ~ equalish(add(additive_identity,additive_inverse(a)),additive_identity)
| spl0_2 ),
inference(resolution,[],[f52,f22]) ).
fof(f62,plain,
( ! [X0] :
( ~ equalish(add(additive_identity,additive_inverse(a)),X0)
| ~ equalish(X0,additive_identity) )
| spl0_2 ),
inference(resolution,[],[f61,f23]) ).
fof(f124,plain,
( ! [X0] :
( ~ equalish(add(X0,additive_inverse(a)),additive_identity)
| ~ defined(additive_inverse(a))
| ~ equalish(additive_identity,X0) )
| spl0_2 ),
inference(resolution,[],[f62,f24]) ).
fof(f129,definition,
( spl0_7
<=> ! [X0] :
( ~ equalish(add(X0,additive_inverse(a)),additive_identity)
| ~ equalish(additive_identity,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f130,plain,
( ! [X0] :
( ~ equalish(add(X0,additive_inverse(a)),additive_identity)
| ~ equalish(additive_identity,X0) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f131,plain,
( ~ spl0_1
| spl0_7
| spl0_2 ),
inference(avatar_split_clause,[],[f124,f51,f129,f48]) ).
fof(f221,plain,
( ~ equalish(additive_identity,a)
| ~ defined(a)
| ~ spl0_7 ),
inference(resolution,[],[f130,f3]) ).
fof(f225,plain,
( ~ equalish(additive_identity,a)
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f221,f28]) ).
fof(f234,plain,
( ~ equalish(a,additive_identity)
| ~ spl0_7 ),
inference(resolution,[],[f225,f22]) ).
fof(f235,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f234,f29]) ).
fof(f236,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f235]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f53]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f59]) ).
cnf(s7,plain,
( ~ spl0_1
| spl0_2
| spl0_7 ),
inference(sat_conversion,[],[f131]) ).
cnf(s13,plain,
~ spl0_7,
inference(sat_conversion,[],[f236]) ).
cnf(s14,plain,
( ~ spl0_1
| spl0_2 ),
inference(rat,[],[s7,s13]) ).
cnf(s16,plain,
spl0_2,
inference(rat,[],[s14,s2]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s1,s16,s2]) ).
fof(f237,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD018-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n003.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 00:29:28 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
% 0.21/1.14 % (2181644)Input is clausal, will run a generic CNF schedule.
% 0.21/1.14 % (2181653)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2888725041:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.21/1.14 % (2181653)First to succeed.
% 0.21/1.14 % (2181653)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2181644"
% 0.21/1.14 % (2181655)dis-21_1_sil=8000:lcm=predicate:random_seed=3488460468: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)
% 0.21/1.14 % (2181654)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=134013188:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.21/1.14 % (2181652)lrs+10_1_sil=8000:sp=occurrence:random_seed=1922003587:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.21/1.14 % (2181650)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3565869302:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.21/1.14 % (2181649)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=378222553:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.21/1.14 % (2181651)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1441994256:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.21/1.14 % (2181654)Also succeeded, but the first one will report.
% 0.21/1.14 % (2181652)Instruction limit reached!
% 0.21/1.14 % (2181652)------------------------------
% 0.21/1.14 % (2181652)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.14 % (2181652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.14 % (2181652)CaDiCaL version: 2.1.3
% 0.21/1.14 % (2181652)Termination reason: Instruction limit
% 0.21/1.14 % (2181652)Termination phase: Saturation
% 0.21/1.14 % (2181652)Time elapsed: 0.067 s
% 0.21/1.14 % (2181652)Peak memory usage: 89 MB
% 0.21/1.14 % (2181652)Instructions burned: 108 (million)
% 0.21/1.14 % (2181655)Instruction limit reached!
% 0.21/1.14 % (2181655)------------------------------
% 0.21/1.14 % (2181655)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.14 % (2181655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.14 % (2181655)CaDiCaL version: 2.1.3
% 0.21/1.14 % (2181655)Termination reason: Instruction limit
% 0.21/1.14 % (2181655)Termination phase: Saturation
% 0.21/1.14 % (2181655)Time elapsed: 0.073 s
% 0.21/1.14 % (2181655)Peak memory usage: 89 MB
% 0.21/1.14 % (2181655)Instructions burned: 117 (million)
% 0.21/1.14 % (2181653)Refutation found. Thanks to Tanya!
% 0.21/1.14 % SZS status Unsatisfiable for theBenchmark
% 0.21/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.14 % (2181653)------------------------------
% 0.21/1.14 % (2181653)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.14 % (2181653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.14 % (2181653)CaDiCaL version: 2.1.3
% 0.21/1.14 % (2181653)Termination reason: Refutation
% 0.21/1.14 % (2181653)Time elapsed: 0.004 s
% 0.21/1.14 % (2181653)Peak memory usage: 89 MB
% 0.21/1.14 % (2181653)Instructions burned: 6 (million)
% 0.21/1.14 % (2181653)------------------------------
% 0.21/1.14 % (2181653)------------------------------
% 0.21/1.14 % (2181644)Success in time 0.287 s
% 0.21/1.14 % Vampire exiting
%------------------------------------------------------------------------------