%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD007-3 : 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 : n008.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 09:48:58 AM UTC 2026
% Result : Unsatisfiable 2.59s 1.12s
% Output : Refutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 9 unt; 2 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 32 ~; 23 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 18 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X0,X1,X2)
| ~ sum(X0,X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_addition_1) ).
fof(f3,axiom,
! [X0] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f4,axiom,
! [X0] :
( sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
fof(f5,axiom,
! [X2,X0,X1] :
( sum(X0,X1,X2)
| ~ sum(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f15,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,negated_conjecture,
~ sum(additive_identity,additive_inverse(additive_inverse(a)),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_2) ).
fof(f29,plain,
~ sum(additive_inverse(additive_inverse(a)),additive_identity,a),
inference(resolution,[],[f5,f28]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ sum(additive_inverse(additive_inverse(a)),X0,X1)
| ~ sum(X0,X2,additive_identity)
| ~ sum(X1,X2,a) ),
inference(resolution,[],[f29,f1]) ).
fof(f62,plain,
! [X0] :
( ~ sum(additive_inverse(a),X0,additive_identity)
| ~ sum(additive_identity,X0,a)
| ~ defined(additive_inverse(a)) ),
inference(resolution,[],[f31,f4]) ).
fof(f68,definition,
( spl0_5
<=> defined(additive_inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f69,plain,
( ~ defined(additive_inverse(a))
| spl0_5 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,definition,
( spl0_6
<=> ! [X0] :
( ~ sum(additive_inverse(a),X0,additive_identity)
| ~ sum(additive_identity,X0,a) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f72,plain,
( ! [X0] :
( ~ sum(additive_inverse(a),X0,additive_identity)
| ~ sum(additive_identity,X0,a) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f73,plain,
( ~ spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f62,f71,f68]) ).
fof(f80,plain,
( ~ defined(a)
| spl0_5 ),
inference(resolution,[],[f69,f15]) ).
fof(f81,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f80,f27]) ).
fof(f82,plain,
spl0_5,
inference(avatar_contradiction_clause,[],[f81]) ).
fof(f90,plain,
( ~ sum(additive_identity,a,a)
| ~ defined(a)
| ~ spl0_6 ),
inference(resolution,[],[f72,f4]) ).
fof(f94,plain,
( ~ defined(a)
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f90,f3]) ).
fof(f95,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f94,f27]) ).
fof(f96,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f95]) ).
cnf(s4,plain,
( ~ spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f73]) ).
cnf(s6,plain,
spl0_5,
inference(sat_conversion,[],[f82]) ).
cnf(s8,plain,
~ spl0_6,
inference(sat_conversion,[],[f96]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s4,s8,s6]) ).
fof(f97,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD007-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n008.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 00:23:09 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running first-order theorem proving
% 0.09/0.20 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
% 2.59/1.12 % (2809579)Input is clausal, will run a generic CNF schedule.
% 2.59/1.12 % (2809588)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2120880381:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.59/1.12 % (2809588)First to succeed.
% 2.59/1.12 % (2809588)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2809579"
% 2.59/1.12 % (2809590)dis-21_1_sil=8000:lcm=predicate:random_seed=2419757806: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)
% 2.59/1.12 % (2809587)lrs+10_1_sil=8000:sp=occurrence:random_seed=2376290811:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.59/1.12 % (2809585)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1444603810:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.59/1.12 % (2809584)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=2744710304:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.59/1.12 % (2809586)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=688991464:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.59/1.12 % (2809589)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3747117014:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.59/1.12 % (2809587)Also succeeded, but the first one will report.
% 2.59/1.12 % (2809589)Also succeeded, but the first one will report.
% 2.59/1.12 % (2809590)Instruction limit reached!
% 2.59/1.12 % (2809590)------------------------------
% 2.59/1.12 % (2809590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.12 % (2809590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.12 % (2809590)CaDiCaL version: 2.1.3
% 2.59/1.12 % (2809590)Termination reason: Instruction limit
% 2.59/1.12 % (2809590)Termination phase: Saturation
% 2.59/1.12 % (2809590)Time elapsed: 0.077 s
% 2.59/1.12 % (2809590)Peak memory usage: 89 MB
% 2.59/1.12 % (2809590)Instructions burned: 118 (million)
% 2.59/1.12 % (2809588)Refutation found. Thanks to Tanya!
% 2.59/1.12 % SZS status Unsatisfiable for theBenchmark
% 2.59/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 2.59/1.12 % (2809588)------------------------------
% 2.59/1.12 % (2809588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.12 % (2809588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.12 % (2809588)CaDiCaL version: 2.1.3
% 2.59/1.12 % (2809588)Termination reason: Refutation
% 2.59/1.12 % (2809588)Time elapsed: 0.002 s
% 2.59/1.12 % (2809588)Peak memory usage: 89 MB
% 2.59/1.12 % (2809588)Instructions burned: 2 (million)
% 2.59/1.12 % (2809588)------------------------------
% 2.59/1.12 % (2809588)------------------------------
% 2.59/1.12 % (2809579)Success in time 0.291 s
% 2.59/1.12 % Vampire exiting
%------------------------------------------------------------------------------