%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD006-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 09:48:57 AM UTC 2026
% Result : Unsatisfiable 0.21s 1.20s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 9 unt; 2 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 17 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 9 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( equalish(add(additive_identity,X0),X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f3,axiom,
! [X0] :
( equalish(add(X0,additive_inverse(X0)),additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
fof(f11,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
fof(f12,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f22,axiom,
! [X0,X1] :
( equalish(X0,X1)
| ~ equalish(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_equality) ).
fof(f23,axiom,
! [X2,X0,X1] :
( equalish(X0,X1)
| ~ equalish(X0,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_equality) ).
fof(f28,negated_conjecture,
~ equalish(additive_inverse(additive_identity),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_not_equal_to_additive_identity_1) ).
fof(f29,plain,
~ equalish(additive_identity,additive_inverse(additive_identity)),
inference(resolution,[],[f22,f28]) ).
fof(f35,plain,
! [X0] :
( ~ equalish(X0,additive_inverse(additive_identity))
| ~ equalish(additive_identity,X0) ),
inference(resolution,[],[f23,f29]) ).
fof(f44,plain,
( ~ equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity)))
| ~ defined(additive_inverse(additive_identity)) ),
inference(resolution,[],[f35,f2]) ).
fof(f46,definition,
( spl0_1
<=> defined(additive_inverse(additive_identity)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f47,plain,
( ~ defined(additive_inverse(additive_identity))
| spl0_1 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f49,definition,
( spl0_2
<=> equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f50,plain,
( ~ equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity)))
| spl0_2 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f51,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f44,f49,f46]) ).
fof(f55,plain,
( ~ defined(additive_identity)
| spl0_1 ),
inference(resolution,[],[f47,f12]) ).
fof(f56,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f55,f11]) ).
fof(f57,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f56]) ).
fof(f59,plain,
( ~ equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity)
| spl0_2 ),
inference(resolution,[],[f50,f22]) ).
fof(f60,plain,
( ~ defined(additive_identity)
| spl0_2 ),
inference(resolution,[],[f59,f3]) ).
fof(f63,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f60,f11]) ).
fof(f64,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f63]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f51]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f57]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f64]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f65,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD006-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n019.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 00:22:18 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 0.21/1.20 % (420155)Input is clausal, will run a generic CNF schedule.
% 0.21/1.20 % (420160)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=1104519672:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.21/1.20 % (420165)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2393379632:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.21/1.20 % (420164)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4159177132:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.21/1.20 % (420162)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3753868787:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.21/1.20 % (420166)dis-21_1_sil=8000:lcm=predicate:random_seed=1848669297: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)
% 0.21/1.20 % (420161)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=385649622:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.21/1.20 % (420163)lrs+10_1_sil=8000:sp=occurrence:random_seed=3688911549:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.21/1.20 % (420164)First to succeed.
% 0.21/1.20 % (420165)Also succeeded, but the first one will report.
% 0.21/1.20 % (420164)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-420155"
% 0.21/1.20 % (420163)Also succeeded, but the first one will report.
% 0.21/1.20 % (420166)Also succeeded, but the first one will report.
% 0.21/1.20 % (420164)Refutation found. Thanks to Tanya!
% 0.21/1.20 % SZS status Unsatisfiable for theBenchmark
% 0.21/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.20 % (420164)------------------------------
% 0.21/1.20 % (420164)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.20 % (420164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.20 % (420164)CaDiCaL version: 2.1.3
% 0.21/1.20 % (420164)Termination reason: Refutation
% 0.21/1.20 % (420164)Time elapsed: 0.003 s
% 0.21/1.20 % (420164)Peak memory usage: 88 MB
% 0.21/1.20 % (420164)Instructions burned: 2 (million)
% 0.21/1.20 % (420164)------------------------------
% 0.21/1.20 % (420164)------------------------------
% 0.21/1.20 % (420155)Success in time 0.438 s
% 0.21/1.20 % Vampire exiting
%------------------------------------------------------------------------------