%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD023-1 : 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 : n013.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 09:49:03 AM UTC 2026
% Result : Unsatisfiable 3.67s 1.28s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 29 ( 10 unt; 2 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 33 ~; 23 |; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(f24,axiom,
! [X2,X0,X1] :
( equalish(add(X0,X1),add(X2,X1))
| ~ defined(X1)
| ~ equalish(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_equality_and_addition) ).
fof(f28,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f30,negated_conjecture,
equalish(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_b_3) ).
fof(f31,negated_conjecture,
~ equalish(additive_identity,add(b,additive_inverse(a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity_not_equal_to_add_4) ).
fof(f32,plain,
~ equalish(add(b,additive_inverse(a)),additive_identity),
inference(resolution,[],[f22,f31]) ).
fof(f39,plain,
! [X0] :
( ~ equalish(add(b,additive_inverse(a)),X0)
| ~ equalish(X0,additive_identity) ),
inference(resolution,[],[f23,f32]) ).
fof(f54,definition,
( spl0_2
<=> defined(additive_inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f56,plain,
( ~ defined(additive_inverse(a))
| spl0_2 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f75,plain,
! [X0] :
( ~ defined(additive_inverse(a))
| ~ equalish(b,X0)
| ~ equalish(add(X0,additive_inverse(a)),additive_identity) ),
inference(resolution,[],[f24,f39]) ).
fof(f77,definition,
( spl0_3
<=> ! [X0] :
( ~ equalish(b,X0)
| ~ equalish(add(X0,additive_inverse(a)),additive_identity) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f78,plain,
( ! [X0] :
( ~ equalish(add(X0,additive_inverse(a)),additive_identity)
| ~ equalish(b,X0) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f79,plain,
( spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f75,f54,f77]) ).
fof(f80,plain,
( ~ defined(a)
| spl0_2 ),
inference(resolution,[],[f56,f12]) ).
fof(f81,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f80,f28]) ).
fof(f82,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f81]) ).
fof(f90,plain,
( ~ equalish(b,a)
| ~ defined(a)
| ~ spl0_3 ),
inference(resolution,[],[f78,f3]) ).
fof(f93,plain,
( ~ equalish(b,a)
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f90,f28]) ).
fof(f95,plain,
( ~ equalish(a,b)
| ~ spl0_3 ),
inference(resolution,[],[f93,f22]) ).
fof(f96,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f95,f30]) ).
fof(f97,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f96]) ).
cnf(s2,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f79]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f82]) ).
cnf(s4,plain,
~ spl0_3,
inference(sat_conversion,[],[f97]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s4,s3]) ).
fof(f98,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD023-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n013.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 00:24:26 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running first-order theorem proving
% 0.06/0.22 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
% 3.67/1.28 % (1740791)Input is clausal, will run a generic CNF schedule.
% 3.67/1.28 % (1740798)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1269949048:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.67/1.28 % (1740796)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=386318162:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.67/1.28 % (1740802)dis-21_1_sil=8000:lcm=predicate:random_seed=963480628: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)
% 3.67/1.28 % (1740797)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2022175135:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.67/1.28 % (1740801)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=264452221:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.67/1.28 % (1740799)lrs+10_1_sil=8000:sp=occurrence:random_seed=3048968951:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.67/1.28 % (1740800)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3553271683:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.67/1.28 % (1740801)First to succeed.
% 3.67/1.28 % (1740801)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1740791"
% 3.67/1.28 % (1740800)Also succeeded, but the first one will report.
% 3.67/1.28 % (1740799)Also succeeded, but the first one will report.
% 3.67/1.28 % (1740802)Also succeeded, but the first one will report.
% 3.67/1.28 % (1740801)Refutation found. Thanks to Tanya!
% 3.67/1.28 % SZS status Unsatisfiable for theBenchmark
% 3.67/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.28 % (1740801)------------------------------
% 3.67/1.28 % (1740801)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.28 % (1740801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.28 % (1740801)CaDiCaL version: 2.1.3
% 3.67/1.28 % (1740801)Termination reason: Refutation
% 3.67/1.28 % (1740801)Time elapsed: 0.004 s
% 3.67/1.28 % (1740801)Peak memory usage: 89 MB
% 3.67/1.28 % (1740801)Instructions burned: 3 (million)
% 3.67/1.28 % (1740801)------------------------------
% 3.67/1.28 % (1740801)------------------------------
% 3.67/1.28 % (1740791)Success in time 0.44 s
% 3.67/1.28 % Vampire exiting
%------------------------------------------------------------------------------