%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD002-3 : 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 : n009.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 09:48:56 AM UTC 2026
% Result : Unsatisfiable 0.20s 1.40s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of formulae : 18 ( 13 unt; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f8,axiom,
! [X0] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
fof(f10,axiom,
! [X2,X0,X1] :
( product(X0,X1,X2)
| ~ product(X1,X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_multiplication) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( sum(X0,X1,X2)
| ~ sum(X3,X4,X5)
| ~ product(X5,X6,X2)
| ~ product(X3,X6,X0)
| ~ product(X4,X6,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_1) ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f29,axiom,
product(multiplicative_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_3) ).
fof(f30,negated_conjecture,
~ sum(additive_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_4) ).
fof(f31,plain,
~ sum(a,additive_identity,b),
inference(unit_resulting_resolution,[],[f5,f30]) ).
fof(f32,plain,
sum(additive_identity,a,a),
inference(unit_resulting_resolution,[],[f3,f27]) ).
fof(f34,plain,
product(multiplicative_identity,a,a),
inference(unit_resulting_resolution,[],[f8,f27]) ).
fof(f141,plain,
product(a,multiplicative_identity,b),
inference(unit_resulting_resolution,[],[f10,f29]) ).
fof(f194,plain,
sum(a,additive_identity,a),
inference(unit_resulting_resolution,[],[f5,f32]) ).
fof(f195,plain,
product(a,multiplicative_identity,a),
inference(unit_resulting_resolution,[],[f10,f34]) ).
fof(f219,plain,
~ product(additive_identity,multiplicative_identity,additive_identity),
inference(unit_resulting_resolution,[],[f11,f31,f141,f194,f195]) ).
fof(f221,plain,
~ product(multiplicative_identity,additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f10,f219]) ).
fof(f255,plain,
$false,
inference(unit_resulting_resolution,[],[f8,f14,f221]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD002-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n009.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 00:22:15 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.22 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
% 0.20/1.40 % (3650446)Input is clausal, will run a generic CNF schedule.
% 0.20/1.40 % (3650451)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=1003093912:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.20/1.40 % (3650452)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3358258961:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.20/1.40 % (3650454)lrs+10_1_sil=8000:sp=occurrence:random_seed=3001044312:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.20/1.40 % (3650457)dis-21_1_sil=8000:lcm=predicate:random_seed=3103598302: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)
% 0.20/1.40 % (3650455)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3270047485:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.20/1.40 % (3650453)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3876829066:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.20/1.40 % (3650456)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1317075368:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.20/1.40 % (3650455)Instruction limit reached!
% 0.20/1.40 % (3650455)------------------------------
% 0.20/1.40 % (3650455)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.40 % (3650455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.40 % (3650455)CaDiCaL version: 2.1.3
% 0.20/1.40 % (3650455)Termination reason: Instruction limit
% 0.20/1.40 % (3650455)Termination phase: Saturation
% 0.20/1.40 % (3650455)Time elapsed: 0.060 s
% 0.20/1.40 % (3650455)Peak memory usage: 88 MB
% 0.20/1.40 % (3650455)Instructions burned: 114 (million)
% 0.20/1.40 % (3650454)Instruction limit reached!
% 0.20/1.40 % (3650454)------------------------------
% 0.20/1.40 % (3650454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.40 % (3650454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.40 % (3650454)CaDiCaL version: 2.1.3
% 0.20/1.40 % (3650454)Termination reason: Instruction limit
% 0.20/1.40 % (3650454)Termination phase: Saturation
% 0.20/1.40 % (3650454)Time elapsed: 0.069 s
% 0.20/1.40 % (3650454)Peak memory usage: 88 MB
% 0.20/1.40 % (3650454)Instructions burned: 108 (million)
% 0.20/1.40 % (3650457)Instruction limit reached!
% 0.20/1.40 % (3650457)------------------------------
% 0.20/1.40 % (3650457)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.40 % (3650457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.40 % (3650457)CaDiCaL version: 2.1.3
% 0.20/1.40 % (3650457)Termination reason: Instruction limit
% 0.20/1.40 % (3650457)Termination phase: Saturation
% 0.20/1.40 % (3650457)Time elapsed: 0.074 s
% 0.20/1.40 % (3650457)Peak memory usage: 89 MB
% 0.20/1.40 % (3650457)Instructions burned: 118 (million)
% 0.20/1.40 % (3650456)Instruction limit reached!
% 0.20/1.40 % (3650456)------------------------------
% 0.20/1.40 % (3650456)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.40 % (3650456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.40 % (3650456)CaDiCaL version: 2.1.3
% 0.20/1.40 % (3650456)Termination reason: Instruction limit
% 0.20/1.40 % (3650456)Termination phase: Saturation
% 0.20/1.40 % (3650456)Time elapsed: 0.111 s
% 0.20/1.40 % (3650456)Peak memory usage: 88 MB
% 0.20/1.40 % (3650456)Instructions burned: 181 (million)
% 0.20/1.40 % (3650465)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=1158004939:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.20/1.40 % (3650466)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1818537004: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)
% 0.20/1.40 % (3650466)First to succeed.
% 0.20/1.40 % (3650466)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3650446"
% 0.20/1.40 % (3650467)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2244891707:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 0.20/1.40 % (3650465)Instruction limit reached!
% 0.20/1.40 % (3650465)------------------------------
% 0.20/1.40 % (3650465)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.40 % (3650465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.40 % (3650465)CaDiCaL version: 2.1.3
% 0.20/1.40 % (3650465)Termination reason: Instruction limit
% 0.20/1.40 % (3650465)Termination phase: Saturation
% 0.20/1.40 % (3650465)Time elapsed: 0.060 s
% 0.20/1.40 % (3650465)Peak memory usage: 88 MB
% 0.20/1.40 % (3650465)Instructions burned: 144 (million)
% 0.20/1.40 % (3650468)lrs+10_64_to=lpo:sil=8000:random_seed=2647187511:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 0.20/1.40 % (3650451)Also succeeded, but the first one will report.
% 0.20/1.40 % (3650468)Instruction limit reached!
% 0.20/1.40 % (3650468)------------------------------
% 0.20/1.40 % (3650468)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.40 % (3650468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.40 % (3650468)CaDiCaL version: 2.1.3
% 0.20/1.40 % (3650468)Termination reason: Instruction limit
% 0.20/1.40 % (3650468)Termination phase: Saturation
% 0.20/1.40 % (3650468)Time elapsed: 0.076 s
% 0.20/1.40 % (3650468)Peak memory usage: 90 MB
% 0.20/1.40 % (3650468)Instructions burned: 126 (million)
% 0.20/1.40 % (3650467)Instruction limit reached!
% 0.20/1.40 % (3650467)------------------------------
% 0.20/1.40 % (3650467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.40 % (3650467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.40 % (3650467)CaDiCaL version: 2.1.3
% 0.20/1.40 % (3650467)Termination reason: Instruction limit
% 0.20/1.40 % (3650467)Termination phase: Saturation
% 0.20/1.40 % (3650467)Time elapsed: 0.123 s
% 0.20/1.40 % (3650467)Peak memory usage: 88 MB
% 0.20/1.40 % (3650467)Instructions burned: 219 (million)
% 0.20/1.40 % (3650472)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2865983961:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 0.20/1.40 % (3650466)Refutation found. Thanks to Tanya!
% 0.20/1.40 % SZS status Unsatisfiable for theBenchmark
% 0.20/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.40 % (3650466)------------------------------
% 0.20/1.40 % (3650466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.40 % (3650466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.40 % (3650466)CaDiCaL version: 2.1.3
% 0.20/1.40 % (3650466)Termination reason: Refutation
% 0.20/1.40 % (3650466)Time elapsed: 0.007 s
% 0.20/1.40 % (3650466)Peak memory usage: 88 MB
% 0.20/1.40 % (3650466)Instructions burned: 11 (million)
% 0.20/1.40 % (3650466)------------------------------
% 0.20/1.40 % (3650466)------------------------------
% 0.20/1.40 % (3650446)Success in time 0.65 s
% 0.20/1.40 % Vampire exiting
%------------------------------------------------------------------------------