%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD020-3 : 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 : 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 09:49:02 AM UTC 2026
% Result : Unsatisfiable 0.20s 1.20s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 6 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 15 ~; 9 |; 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 : 18 ( 18 !; 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(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(f29,negated_conjecture,
sum(m,a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_3) ).
fof(f30,negated_conjecture,
~ sum(additive_identity,m,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_4) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| ~ sum(X1,m,X2)
| ~ sum(X0,X2,additive_identity) ),
inference(resolution,[],[f2,f30]) ).
fof(f73,plain,
! [X0,X1] :
( ~ sum(X1,m,X1)
| ~ sum(X0,X1,additive_identity) ),
inference(factoring,[],[f45]) ).
fof(f77,plain,
! [X0,X1] :
( ~ sum(m,X1,X1)
| ~ sum(X0,X1,additive_identity) ),
inference(resolution,[],[f73,f5]) ).
fof(f91,plain,
! [X0] : ~ sum(X0,a,additive_identity),
inference(resolution,[],[f77,f29]) ).
fof(f104,plain,
~ defined(a),
inference(resolution,[],[f91,f4]) ).
fof(f105,plain,
$false,
inference(forward_subsumption_resolution,[],[f104,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD020-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n013.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 00:22:36 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running first-order theorem proving
% 0.10/0.22 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
% 0.20/1.20 % (1740180)Input is clausal, will run a generic CNF schedule.
% 0.20/1.20 % (1740187)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1774172500:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.20/1.20 % (1740188)lrs+10_1_sil=8000:sp=occurrence:random_seed=4202306512:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.20/1.20 % (1740186)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4030383434:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.20/1.20 % (1740185)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=374830460:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.20/1.20 % (1740188)Refutation not found, incomplete strategy
% 0.20/1.20 % (1740188)------------------------------
% 0.20/1.20 % (1740188)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.20 % (1740188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.20 % (1740188)CaDiCaL version: 2.1.3
% 0.20/1.20 % (1740188)Termination reason: Refutation not found, incomplete strategy
% 0.20/1.20 % (1740188)Time elapsed: 0.003 s
% 0.20/1.20 % (1740188)Peak memory usage: 87 MB
% 0.20/1.20 % (1740188)Instructions burned: 3 (million)
% 0.20/1.20 % (1740189)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3105794697:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.20/1.20 % (1740190)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1855468686:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.20/1.20 % (1740191)dis-21_1_sil=8000:lcm=predicate:random_seed=2820631371: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)
% 0.20/1.20 % (1740190)First to succeed.
% 0.20/1.20 % (1740190)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1740180"
% 0.20/1.20 % (1740189)Instruction limit reached!
% 0.20/1.20 % (1740189)------------------------------
% 0.20/1.20 % (1740189)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.20 % (1740189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.20 % (1740189)CaDiCaL version: 2.1.3
% 0.20/1.20 % (1740189)Termination reason: Instruction limit
% 0.20/1.20 % (1740189)Termination phase: Saturation
% 0.20/1.20 % (1740189)Time elapsed: 0.062 s
% 0.20/1.20 % (1740189)Peak memory usage: 87 MB
% 0.20/1.20 % (1740189)Instructions burned: 114 (million)
% 0.20/1.20 % (1740191)Instruction limit reached!
% 0.20/1.20 % (1740191)------------------------------
% 0.20/1.20 % (1740191)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.20 % (1740191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.20 % (1740191)CaDiCaL version: 2.1.3
% 0.20/1.20 % (1740191)Termination reason: Instruction limit
% 0.20/1.20 % (1740191)Termination phase: Saturation
% 0.20/1.20 % (1740191)Time elapsed: 0.073 s
% 0.20/1.20 % (1740191)Peak memory usage: 89 MB
% 0.20/1.20 % (1740191)Instructions burned: 118 (million)
% 0.20/1.20 % (1740188)------------------------------
% 0.20/1.20 % (1740188)------------------------------
% 0.20/1.20 % (1740199)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=1741356995:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.20/1.20 % (1740200)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=315256683:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 0.20/1.20 % (1740199)Also succeeded, but the first one will report.
% 0.20/1.20 % (1740190)Refutation found. Thanks to Tanya!
% 0.20/1.20 % SZS status Unsatisfiable for theBenchmark
% 0.20/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.20 % (1740190)------------------------------
% 0.20/1.20 % (1740190)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.20 % (1740190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.20 % (1740190)CaDiCaL version: 2.1.3
% 0.20/1.20 % (1740190)Termination reason: Refutation
% 0.20/1.20 % (1740190)Time elapsed: 0.004 s
% 0.20/1.20 % (1740190)Peak memory usage: 88 MB
% 0.20/1.20 % (1740190)Instructions burned: 4 (million)
% 0.20/1.20 % (1740190)------------------------------
% 0.20/1.20 % (1740190)------------------------------
% 0.20/1.20 % (1740180)Success in time 0.44 s
% 0.20/1.20 % Vampire exiting
%------------------------------------------------------------------------------