%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD019-3 : 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 : n004.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 0.21s 1.13s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 14 ( 6 unt; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 19 ~; 12 |; 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 : 16 ( 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X0,X1,X2)
| ~ sum(X3,X4,X0)
| ~ sum(X4,X1,X5)
| ~ 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(X0,X1,X2)
| ~ sum(X1,X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,negated_conjecture,
sum(additive_identity,additive_inverse(a),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_2) ).
fof(f29,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ sum(X1,a,X2)
| ~ sum(X0,X1,additive_identity)
| ~ sum(X0,X2,additive_identity) ),
inference(resolution,[],[f2,f29]) ).
fof(f49,plain,
! [X0] :
( ~ sum(X0,additive_identity,additive_identity)
| ~ sum(X0,a,additive_identity)
| ~ defined(a) ),
inference(resolution,[],[f40,f3]) ).
fof(f56,plain,
! [X0] :
( ~ sum(X0,a,additive_identity)
| ~ sum(X0,additive_identity,additive_identity) ),
inference(forward_subsumption_resolution,[],[f49,f27]) ).
fof(f60,plain,
( ~ sum(additive_inverse(a),additive_identity,additive_identity)
| ~ defined(a) ),
inference(resolution,[],[f56,f4]) ).
fof(f64,plain,
~ sum(additive_inverse(a),additive_identity,additive_identity),
inference(forward_subsumption_resolution,[],[f60,f27]) ).
fof(f67,plain,
~ sum(additive_identity,additive_inverse(a),additive_identity),
inference(resolution,[],[f64,f5]) ).
fof(f68,plain,
$false,
inference(forward_subsumption_resolution,[],[f67,f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD019-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n004.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 00:27:53 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 0.21/1.13 % (946979)Input is clausal, will run a generic CNF schedule.
% 0.21/1.13 % (946988)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=435370063:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.21/1.13 % (946988)First to succeed.
% 0.21/1.13 % (946988)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-946979"
% 0.21/1.13 % (946985)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3451975609:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.21/1.13 % (946987)lrs+10_1_sil=8000:sp=occurrence:random_seed=2072932150:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.21/1.13 % (946984)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=2229037255:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.21/1.13 % (946986)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3192856488:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.21/1.13 % (946987)Also succeeded, but the first one will report.
% 0.21/1.13 % (946989)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2680686594:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.21/1.13 % (946990)dis-21_1_sil=8000:lcm=predicate:random_seed=1271893742: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)
% 0.21/1.13 % (946989)Also succeeded, but the first one will report.
% 0.21/1.13 % (946990)Instruction limit reached!
% 0.21/1.13 % (946990)------------------------------
% 0.21/1.13 % (946990)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.13 % (946990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.13 % (946990)CaDiCaL version: 2.1.3
% 0.21/1.13 % (946990)Termination reason: Instruction limit
% 0.21/1.13 % (946990)Termination phase: Saturation
% 0.21/1.13 % (946990)Time elapsed: 0.074 s
% 0.21/1.13 % (946990)Peak memory usage: 89 MB
% 0.21/1.13 % (946990)Instructions burned: 118 (million)
% 0.21/1.13 % (946988)Refutation found. Thanks to Tanya!
% 0.21/1.13 % SZS status Unsatisfiable for theBenchmark
% 0.21/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.13 % (946988)------------------------------
% 0.21/1.13 % (946988)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.13 % (946988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.13 % (946988)CaDiCaL version: 2.1.3
% 0.21/1.13 % (946988)Termination reason: Refutation
% 0.21/1.13 % (946988)Time elapsed: 0.001 s
% 0.21/1.13 % (946988)Peak memory usage: 88 MB
% 0.21/1.13 % (946988)Instructions burned: 1 (million)
% 0.21/1.13 % (946988)------------------------------
% 0.21/1.13 % (946988)------------------------------
% 0.21/1.13 % (946979)Success in time 0.267 s
% 0.21/1.13 % Vampire exiting
%------------------------------------------------------------------------------