%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD015-3 : 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 : n001.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 09:49:01 AM UTC 2026
% Result : Unsatisfiable 3.67s 1.21s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 22 ( 10 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 21 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X4,X5,X2)
| ~ sum(X0,X3,X4)
| ~ sum(X3,X5,X1)
| sum(X0,X1,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(X1,X0,X2)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
fof(f29,negated_conjecture,
sum(additive_identity,additive_inverse(a),additive_inverse(b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_3) ).
fof(f30,negated_conjecture,
~ sum(additive_identity,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_4) ).
fof(f31,plain,
sum(additive_inverse(a),additive_identity,additive_inverse(b)),
inference(resolution,[],[f5,f29]) ).
fof(f33,plain,
! [X0] :
( sum(X0,additive_inverse(X0),additive_identity)
| ~ defined(X0) ),
inference(resolution,[],[f5,f4]) ).
fof(f35,plain,
! [X2,X3,X0,X1] :
( ~ sum(X1,X2,X3)
| ~ sum(X0,X1,additive_identity)
| sum(X0,X3,X2)
| ~ defined(X2) ),
inference(resolution,[],[f1,f3]) ).
fof(f90,plain,
! [X0,X1] :
( ~ sum(X0,additive_inverse(X1),additive_identity)
| sum(X0,additive_identity,X1)
| ~ defined(X1)
| ~ defined(X1) ),
inference(resolution,[],[f35,f4]) ).
fof(f91,plain,
! [X0] :
( ~ sum(X0,additive_inverse(a),additive_identity)
| sum(X0,additive_inverse(b),additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[],[f35,f31]) ).
fof(f94,plain,
! [X0,X1] :
( ~ sum(X0,additive_inverse(X1),additive_identity)
| sum(X0,additive_identity,X1)
| ~ defined(X1) ),
inference(duplicate_literal_removal,[],[f90]) ).
fof(f97,plain,
! [X0] :
( ~ sum(X0,additive_inverse(a),additive_identity)
| sum(X0,additive_inverse(b),additive_identity) ),
inference(forward_subsumption_resolution,[],[f91,f14]) ).
fof(f232,plain,
( sum(a,additive_inverse(b),additive_identity)
| ~ defined(a) ),
inference(resolution,[],[f97,f33]) ).
fof(f236,plain,
sum(a,additive_inverse(b),additive_identity),
inference(forward_subsumption_resolution,[],[f232,f27]) ).
fof(f383,plain,
( sum(a,additive_identity,b)
| ~ defined(b) ),
inference(resolution,[],[f94,f236]) ).
fof(f385,plain,
sum(a,additive_identity,b),
inference(forward_subsumption_resolution,[],[f383,f28]) ).
fof(f392,plain,
sum(additive_identity,a,b),
inference(resolution,[],[f385,f5]) ).
fof(f393,plain,
$false,
inference(forward_subsumption_resolution,[],[f392,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD015-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n001.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 00:32:35 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
% 3.67/1.21 % (904740)Input is clausal, will run a generic CNF schedule.
% 3.67/1.21 % (904747)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1387162142:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.67/1.21 % (904751)dis-21_1_sil=8000:lcm=predicate:random_seed=3359410813: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)
% 3.67/1.21 % (904748)lrs+10_1_sil=8000:sp=occurrence:random_seed=516627105:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.67/1.21 % (904750)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=788469782:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.67/1.21 % (904745)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=1886638647:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.67/1.21 % (904749)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1811137923:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.67/1.21 % (904746)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2263369651:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.67/1.21 % (904748)First to succeed.
% 3.67/1.21 % (904748)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-904740"
% 3.67/1.21 % (904749)Instruction limit reached!
% 3.67/1.21 % (904749)------------------------------
% 3.67/1.21 % (904749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.21 % (904749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.21 % (904749)CaDiCaL version: 2.1.3
% 3.67/1.21 % (904749)Termination reason: Instruction limit
% 3.67/1.21 % (904749)Termination phase: Saturation
% 3.67/1.21 % (904749)Time elapsed: 0.068 s
% 3.67/1.21 % (904749)Peak memory usage: 88 MB
% 3.67/1.21 % (904749)Instructions burned: 116 (million)
% 3.67/1.21 % (904751)Instruction limit reached!
% 3.67/1.21 % (904751)------------------------------
% 3.67/1.21 % (904751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.21 % (904751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.21 % (904751)CaDiCaL version: 2.1.3
% 3.67/1.21 % (904751)Termination reason: Instruction limit
% 3.67/1.21 % (904751)Termination phase: Saturation
% 3.67/1.21 % (904751)Time elapsed: 0.097 s
% 3.67/1.21 % (904751)Peak memory usage: 89 MB
% 3.67/1.21 % (904751)Instructions burned: 117 (million)
% 3.67/1.21 % (904750)Instruction limit reached!
% 3.67/1.21 % (904750)------------------------------
% 3.67/1.21 % (904750)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.21 % (904750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.21 % (904750)CaDiCaL version: 2.1.3
% 3.67/1.21 % (904750)Termination reason: Instruction limit
% 3.67/1.21 % (904750)Termination phase: Saturation
% 3.67/1.21 % (904750)Time elapsed: 0.107 s
% 3.67/1.21 % (904750)Peak memory usage: 89 MB
% 3.67/1.21 % (904750)Instructions burned: 180 (million)
% 3.67/1.21 % (904759)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=165195109:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.67/1.21 % (904748)Refutation found. Thanks to Tanya!
% 3.67/1.21 % SZS status Unsatisfiable for theBenchmark
% 3.67/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.21 % (904748)------------------------------
% 3.67/1.21 % (904748)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.21 % (904748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.21 % (904748)CaDiCaL version: 2.1.3
% 3.67/1.21 % (904748)Termination reason: Refutation
% 3.67/1.21 % (904748)Time elapsed: 0.008 s
% 3.67/1.21 % (904748)Peak memory usage: 88 MB
% 3.67/1.21 % (904748)Instructions burned: 10 (million)
% 3.67/1.21 % (904748)------------------------------
% 3.67/1.21 % (904748)------------------------------
% 3.67/1.21 % (904740)Success in time 0.433 s
% 3.67/1.21 % Vampire exiting
%------------------------------------------------------------------------------