%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD018-3 : 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 : n010.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 2.48s 1.12s
% Output : Refutation 2.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 35 ( 19 ~; 16 |; 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 : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 19 ( 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2)
| ~ sum(X3,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition_2) ).
fof(f3,axiom,
! [X0] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f4,axiom,
! [X0] :
( sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f15,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,negated_conjecture,
sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_2) ).
fof(f29,negated_conjecture,
~ sum(additive_identity,additive_inverse(a),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).
fof(f30,plain,
sum(a,additive_identity,additive_identity),
inference(resolution,[],[f5,f28]) ).
fof(f32,plain,
! [X0] :
( sum(X0,additive_inverse(X0),additive_identity)
| ~ defined(X0) ),
inference(resolution,[],[f5,f4]) ).
fof(f44,plain,
! [X2,X3,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| sum(X1,X2,X3)
| ~ sum(X0,X2,X3)
| ~ defined(X2) ),
inference(resolution,[],[f2,f3]) ).
fof(f104,plain,
! [X0,X1] :
( ~ sum(a,X0,X1)
| sum(additive_identity,X0,X1)
| ~ defined(X0) ),
inference(resolution,[],[f44,f30]) ).
fof(f174,plain,
( sum(additive_identity,additive_inverse(a),additive_identity)
| ~ defined(additive_inverse(a))
| ~ defined(a) ),
inference(resolution,[],[f104,f32]) ).
fof(f175,plain,
( ~ defined(additive_inverse(a))
| ~ defined(a) ),
inference(forward_subsumption_resolution,[],[f174,f29]) ).
fof(f177,plain,
~ defined(a),
inference(forward_subsumption_resolution,[],[f175,f15]) ).
fof(f178,plain,
$false,
inference(forward_subsumption_resolution,[],[f177,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD018-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n010.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 00:28:03 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running first-order theorem proving
% 0.06/0.21 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
% 2.48/1.12 % (2514315)Input is clausal, will run a generic CNF schedule.
% 2.48/1.12 % (2514323)lrs+10_1_sil=8000:sp=occurrence:random_seed=113753450:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.48/1.12 % (2514323)First to succeed.
% 2.48/1.12 % (2514323)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2514315"
% 2.48/1.12 % (2514326)dis-21_1_sil=8000:lcm=predicate:random_seed=972522239: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)
% 2.48/1.12 % (2514320)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=2872192080:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.48/1.12 % (2514321)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1604722513:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.48/1.12 % (2514324)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3485173109:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.48/1.12 % (2514325)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2856824579:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.48/1.12 % (2514322)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1396097122:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.48/1.12 % (2514324)Also succeeded, but the first one will report.
% 2.48/1.12 % (2514325)Also succeeded, but the first one will report.
% 2.48/1.12 % (2514326)Instruction limit reached!
% 2.48/1.12 % (2514326)------------------------------
% 2.48/1.12 % (2514326)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.48/1.12 % (2514326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/1.12 % (2514326)CaDiCaL version: 2.1.3
% 2.48/1.12 % (2514326)Termination reason: Instruction limit
% 2.48/1.12 % (2514326)Termination phase: Saturation
% 2.48/1.12 % (2514326)Time elapsed: 0.071 s
% 2.48/1.12 % (2514326)Peak memory usage: 89 MB
% 2.48/1.12 % (2514326)Instructions burned: 117 (million)
% 2.48/1.12 % (2514323)Refutation found. Thanks to Tanya!
% 2.48/1.12 % SZS status Unsatisfiable for theBenchmark
% 2.48/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 2.48/1.12 % (2514323)------------------------------
% 2.48/1.12 % (2514323)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.48/1.12 % (2514323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/1.12 % (2514323)CaDiCaL version: 2.1.3
% 2.48/1.12 % (2514323)Termination reason: Refutation
% 2.48/1.12 % (2514323)Time elapsed: 0.002 s
% 2.48/1.12 % (2514323)Peak memory usage: 88 MB
% 2.48/1.12 % (2514323)Instructions burned: 4 (million)
% 2.48/1.12 % (2514323)------------------------------
% 2.48/1.12 % (2514323)------------------------------
% 2.48/1.12 % (2514315)Success in time 0.268 s
% 2.48/1.12 % Vampire exiting
%------------------------------------------------------------------------------