%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD021-3 : 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 : n003.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 09:49:03 AM UTC 2026
% Result : Unsatisfiable 3.48s 1.04s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 13 ( 8 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 23 ( 15 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 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(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(additive_identity,m,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_3) ).
fof(f30,negated_conjecture,
~ sum(m,a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_4) ).
fof(f31,plain,
~ sum(a,m,a),
inference(resolution,[],[f5,f30]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ sum(X1,m,X2)
| ~ sum(X0,X1,a)
| ~ sum(X0,X2,a) ),
inference(resolution,[],[f2,f31]) ).
fof(f66,plain,
! [X0] :
( ~ sum(X0,additive_identity,a)
| ~ sum(X0,additive_identity,a) ),
inference(resolution,[],[f36,f29]) ).
fof(f72,plain,
! [X0] : ~ sum(X0,additive_identity,a),
inference(duplicate_literal_removal,[],[f66]) ).
fof(f76,plain,
! [X0] : ~ sum(additive_identity,X0,a),
inference(resolution,[],[f72,f5]) ).
fof(f85,plain,
~ defined(a),
inference(resolution,[],[f76,f3]) ).
fof(f89,plain,
$false,
inference(forward_subsumption_resolution,[],[f85,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD021-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n003.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 00:24:58 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.48/1.04 % (2179445)Input is clausal, will run a generic CNF schedule.
% 3.48/1.04 % (2179456)dis-21_1_sil=8000:lcm=predicate:random_seed=25680111: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)
% 3.48/1.04 % (2179456)Instruction limit reached!
% 3.48/1.04 % (2179456)------------------------------
% 3.48/1.04 % (2179456)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.04 % (2179456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.04 % (2179456)CaDiCaL version: 2.1.3
% 3.48/1.04 % (2179456)Termination reason: Instruction limit
% 3.48/1.04 % (2179456)Termination phase: Saturation
% 3.48/1.04 % (2179456)Time elapsed: 0.029 s
% 3.48/1.04 % (2179456)Peak memory usage: 88 MB
% 3.48/1.04 % (2179456)Instructions burned: 119 (million)
% 3.48/1.04 % (2179451)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=531301678:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.48/1.04 % (2179452)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4226593457:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.48/1.04 % (2179454)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=750510959:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.48/1.04 % (2179450)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=2289296633:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.48/1.04 % (2179453)lrs+10_1_sil=8000:sp=occurrence:random_seed=3311623330:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.48/1.04 % (2179455)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1764377689:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.48/1.04 % (2179454)First to succeed.
% 3.48/1.04 % (2179454)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2179445"
% 3.48/1.04 % (2179453)Also succeeded, but the first one will report.
% 3.48/1.04 % (2179455)Also succeeded, but the first one will report.
% 3.48/1.04 % (2179458)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=12919619:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.48/1.04 % (2179458)Instruction limit reached!
% 3.48/1.04 % (2179458)------------------------------
% 3.48/1.04 % (2179458)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.04 % (2179458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.04 % (2179458)CaDiCaL version: 2.1.3
% 3.48/1.04 % (2179458)Termination reason: Instruction limit
% 3.48/1.04 % (2179458)Termination phase: Saturation
% 3.48/1.04 % (2179458)Time elapsed: 0.032 s
% 3.48/1.04 % (2179458)Peak memory usage: 88 MB
% 3.48/1.04 % (2179458)Instructions burned: 144 (million)
% 3.48/1.04 % (2179454)Refutation found. Thanks to Tanya!
% 3.48/1.04 % SZS status Unsatisfiable for theBenchmark
% 3.48/1.04 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.04 % (2179454)------------------------------
% 3.48/1.04 % (2179454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.04 % (2179454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.04 % (2179454)CaDiCaL version: 2.1.3
% 3.48/1.04 % (2179454)Termination reason: Refutation
% 3.48/1.04 % (2179454)Time elapsed: 0.003 s
% 3.48/1.04 % (2179454)Peak memory usage: 88 MB
% 3.48/1.04 % (2179454)Instructions burned: 2 (million)
% 3.48/1.04 % (2179454)------------------------------
% 3.48/1.04 % (2179454)------------------------------
% 3.48/1.04 % (2179445)Success in time 0.427 s
% 3.48/1.04 % Vampire exiting
%------------------------------------------------------------------------------