%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD034-3 : 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 : 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 09:49:07 AM UTC 2026
% Result : Unsatisfiable 3.49s 1.26s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 6 unt; 0 def)
% Number of atoms : 22 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 26 ( 16 ~; 10 |; 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 : 19 ( 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ product(X3,X5,X1)
| ~ product(X4,X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_multiplication_1) ).
fof(f8,axiom,
! [X0] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
fof(f10,axiom,
! [X2,X0,X1] :
( product(X0,X1,X2)
| ~ product(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_multiplication) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f29,negated_conjecture,
product(multiplicative_identity,m,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_3) ).
fof(f30,negated_conjecture,
~ product(m,a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_4) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ product(m,X0,X1)
| ~ product(X0,X2,a)
| ~ product(X1,X2,a) ),
inference(resolution,[],[f6,f30]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,a)
| ~ product(X2,X1,a)
| ~ product(X0,m,X2) ),
inference(resolution,[],[f34,f10]) ).
fof(f80,plain,
! [X0,X1] :
( ~ product(X0,m,X0)
| ~ product(X0,X1,a) ),
inference(factoring,[],[f37]) ).
fof(f84,plain,
! [X0] : ~ product(multiplicative_identity,X0,a),
inference(resolution,[],[f80,f29]) ).
fof(f92,plain,
~ defined(a),
inference(resolution,[],[f84,f8]) ).
fof(f96,plain,
$false,
inference(forward_subsumption_resolution,[],[f92,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD034-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n010.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 00:32:33 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.49/1.26 % (2516901)Input is clausal, will run a generic CNF schedule.
% 3.49/1.26 % (2516908)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1055193006:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.49/1.26 % (2516907)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3231749394:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.49/1.26 % (2516912)dis-21_1_sil=8000:lcm=predicate:random_seed=203639882: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)
% 3.49/1.26 % (2516906)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=3835115019:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.49/1.26 % (2516911)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1583960713:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.49/1.26 % (2516911)First to succeed.
% 3.49/1.26 % (2516909)lrs+10_1_sil=8000:sp=occurrence:random_seed=441736432:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.49/1.26 % (2516910)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=254557221:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.49/1.26 % (2516911)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2516901"
% 3.49/1.26 % (2516910)Also succeeded, but the first one will report.
% 3.49/1.26 % (2516909)Also succeeded, but the first one will report.
% 3.49/1.26 % (2516912)Instruction limit reached!
% 3.49/1.26 % (2516912)------------------------------
% 3.49/1.26 % (2516912)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.26 % (2516912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.26 % (2516912)CaDiCaL version: 2.1.3
% 3.49/1.26 % (2516912)Termination reason: Instruction limit
% 3.49/1.26 % (2516912)Termination phase: Saturation
% 3.49/1.26 % (2516912)Time elapsed: 0.054 s
% 3.49/1.26 % (2516912)Peak memory usage: 88 MB
% 3.49/1.26 % (2516912)Instructions burned: 117 (million)
% 3.49/1.26 % (2516920)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=913085762:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.49/1.26 % (2516911)Refutation found. Thanks to Tanya!
% 3.49/1.26 % SZS status Unsatisfiable for theBenchmark
% 3.49/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.26 % (2516911)------------------------------
% 3.49/1.26 % (2516911)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.26 % (2516911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.26 % (2516911)CaDiCaL version: 2.1.3
% 3.49/1.26 % (2516911)Termination reason: Refutation
% 3.49/1.26 % (2516911)Time elapsed: 0.004 s
% 3.49/1.26 % (2516911)Peak memory usage: 88 MB
% 3.49/1.26 % (2516911)Instructions burned: 4 (million)
% 3.49/1.26 % (2516911)------------------------------
% 3.49/1.26 % (2516911)------------------------------
% 3.49/1.26 % (2516901)Success in time 0.407 s
% 3.49/1.26 % Vampire exiting
%------------------------------------------------------------------------------