%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD040-3 : 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 : n005.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 09:49:09 AM UTC 2026
% Result : Unsatisfiable 5.56s 1.58s
% Output : Refutation 5.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 19 ( 12 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 27 ( 13 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 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(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(f8,axiom,
! [X0] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
fof(f9,axiom,
! [X0] :
( product(multiplicative_inverse(X0),X0,multiplicative_identity)
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_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(f18,axiom,
! [X0] :
( sum(additive_identity,X0,additive_identity)
| ~ defined(X0)
| defined(multiplicative_inverse(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_2) ).
fof(f29,negated_conjecture,
sum(additive_identity,additive_identity,multiplicative_inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_3) ).
fof(f34,plain,
sum(additive_inverse(a),a,additive_identity),
inference(unit_resulting_resolution,[],[f4,f27]) ).
fof(f35,plain,
product(multiplicative_identity,a,a),
inference(unit_resulting_resolution,[],[f8,f27]) ).
fof(f36,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(unit_resulting_resolution,[],[f9,f28,f27]) ).
fof(f50,plain,
defined(multiplicative_inverse(a)),
inference(unit_resulting_resolution,[],[f18,f28,f27]) ).
fof(f63,plain,
sum(additive_identity,multiplicative_inverse(a),multiplicative_inverse(a)),
inference(unit_resulting_resolution,[],[f3,f50]) ).
fof(f157,plain,
sum(multiplicative_inverse(a),multiplicative_inverse(a),multiplicative_inverse(a)),
inference(unit_resulting_resolution,[],[f2,f29,f63,f63]) ).
fof(f345,plain,
sum(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(unit_resulting_resolution,[],[f11,f36,f36,f36,f157]) ).
fof(f358,plain,
sum(a,a,a),
inference(unit_resulting_resolution,[],[f11,f35,f35,f35,f345]) ).
fof(f7356,plain,
$false,
inference(unit_resulting_resolution,[],[f2,f28,f358,f34,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD040-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 % Computer : n005.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.21 % CPULimit : 300
% 0.07/0.21 % WCLimit : 300
% 0.07/0.21 % DateTime : Tue Sep 29 00:33:47 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running first-order theorem proving
% 0.07/0.24 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
% 5.56/1.58 % (1331389)Input is clausal, will run a generic CNF schedule.
% 5.56/1.58 % (1331398)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=114840210:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.56/1.58 % (1331395)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1491162484:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.56/1.58 % (1331398)Instruction limit reached!
% 5.56/1.58 % (1331398)------------------------------
% 5.56/1.58 % (1331398)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.58 % (1331398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.58 % (1331398)CaDiCaL version: 2.1.3
% 5.56/1.58 % (1331398)Termination reason: Instruction limit
% 5.56/1.58 % (1331398)Termination phase: Saturation
% 5.56/1.58 % (1331398)Time elapsed: 0.034 s
% 5.56/1.58 % (1331398)Peak memory usage: 88 MB
% 5.56/1.58 % (1331398)Instructions burned: 114 (million)
% 5.56/1.58 % (1331399)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=885187948:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.56/1.58 % (1331394)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=3146646779:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.56/1.58 % (1331397)lrs+10_1_sil=8000:sp=occurrence:random_seed=3045700507:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.56/1.58 % (1331400)dis-21_1_sil=8000:lcm=predicate:random_seed=571157213: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)
% 5.56/1.58 % (1331396)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=170355177:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.56/1.58 % (1331397)Instruction limit reached!
% 5.56/1.58 % (1331397)------------------------------
% 5.56/1.58 % (1331397)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.58 % (1331397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.58 % (1331397)CaDiCaL version: 2.1.3
% 5.56/1.58 % (1331397)Termination reason: Instruction limit
% 5.56/1.58 % (1331397)Termination phase: Saturation
% 5.56/1.58 % (1331397)Time elapsed: 0.068 s
% 5.56/1.58 % (1331397)Peak memory usage: 88 MB
% 5.56/1.58 % (1331397)Instructions burned: 107 (million)
% 5.56/1.58 % (1331403)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=3464388439:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 5.56/1.58 % (1331400)Instruction limit reached!
% 5.56/1.58 % (1331400)------------------------------
% 5.56/1.58 % (1331400)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.58 % (1331400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.58 % (1331400)CaDiCaL version: 2.1.3
% 5.56/1.58 % (1331400)Termination reason: Instruction limit
% 5.56/1.58 % (1331400)Termination phase: Saturation
% 5.56/1.58 % (1331400)Time elapsed: 0.073 s
% 5.56/1.58 % (1331400)Peak memory usage: 89 MB
% 5.56/1.58 % (1331400)Instructions burned: 118 (million)
% 5.56/1.58 % (1331399)Instruction limit reached!
% 5.56/1.58 % (1331399)------------------------------
% 5.56/1.58 % (1331399)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.58 % (1331399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.58 % (1331399)CaDiCaL version: 2.1.3
% 5.56/1.58 % (1331399)Termination reason: Instruction limit
% 5.56/1.58 % (1331399)Termination phase: Saturation
% 5.56/1.58 % (1331399)Time elapsed: 0.105 s
% 5.56/1.58 % (1331399)Peak memory usage: 88 MB
% 5.56/1.58 % (1331399)Instructions burned: 180 (million)
% 5.56/1.58 % (1331403)Instruction limit reached!
% 5.56/1.58 % (1331403)------------------------------
% 5.56/1.58 % (1331403)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.58 % (1331403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.58 % (1331403)CaDiCaL version: 2.1.3
% 5.56/1.58 % (1331403)Termination reason: Instruction limit
% 5.56/1.58 % (1331403)Termination phase: Saturation
% 5.56/1.58 % (1331403)Time elapsed: 0.047 s
% 5.56/1.58 % (1331403)Peak memory usage: 89 MB
% 5.56/1.58 % (1331403)Instructions burned: 146 (million)
% 5.56/1.58 % (1331413)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2793052729:avsq=on:i=194:fgj=on:bd=preordered_2997 on theBenchmark for (2997ds/194Mi)
% 5.56/1.58 % (1331411)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2974808136:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.56/1.58 % (1331410)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2862918419: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)
% 5.56/1.58 % (1331412)lrs+10_64_to=lpo:sil=8000:random_seed=3458873309:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 5.56/1.58 % (1331413)Instruction limit reached!
% 5.56/1.58 % (1331413)------------------------------
% 5.56/1.58 % (1331413)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.58 % (1331413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.58 % (1331413)CaDiCaL version: 2.1.3
% 5.56/1.58 % (1331413)Termination reason: Instruction limit
% 5.56/1.58 % (1331413)Termination phase: Saturation
% 5.56/1.58 % (1331413)Time elapsed: 0.074 s
% 5.56/1.58 % (1331413)Peak memory usage: 89 MB
% 5.56/1.58 % (1331413)Instructions burned: 196 (million)
% 5.56/1.58 % (1331412)Instruction limit reached!
% 5.56/1.58 % (1331412)------------------------------
% 5.56/1.58 % (1331412)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.58 % (1331412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.58 % (1331412)CaDiCaL version: 2.1.3
% 5.56/1.58 % (1331412)Termination reason: Instruction limit
% 5.56/1.58 % (1331412)Termination phase: Saturation
% 5.56/1.58 % (1331412)Time elapsed: 0.071 s
% 5.56/1.58 % (1331412)Peak memory usage: 90 MB
% 5.56/1.58 % (1331412)Instructions burned: 127 (million)
% 5.56/1.58 % (1331410)First to succeed.
% 5.56/1.58 % (1331410)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1331389"
% 5.56/1.58 % (1331411)Instruction limit reached!
% 5.56/1.58 % (1331411)------------------------------
% 5.56/1.58 % (1331411)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.58 % (1331411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.58 % (1331411)CaDiCaL version: 2.1.3
% 5.56/1.58 % (1331411)Termination reason: Instruction limit
% 5.56/1.58 % (1331411)Termination phase: Saturation
% 5.56/1.58 % (1331411)Time elapsed: 0.122 s
% 5.56/1.58 % (1331411)Peak memory usage: 88 MB
% 5.56/1.58 % (1331411)Instructions burned: 220 (million)
% 5.56/1.58 % (1331418)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3825826471:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 5.56/1.58 % (1331419)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=2649456932:i=3394:sd=4:ss=included:sgt=64_2995 on theBenchmark for (2995ds/3394Mi)
% 5.56/1.58 % (1331418)Instruction limit reached!
% 5.56/1.58 % (1331418)------------------------------
% 5.56/1.58 % (1331418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.58 % (1331418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.58 % (1331418)CaDiCaL version: 2.1.3
% 5.56/1.58 % (1331418)Termination reason: Instruction limit
% 5.56/1.58 % (1331418)Termination phase: Saturation
% 5.56/1.58 % (1331418)Time elapsed: 0.060 s
% 5.56/1.58 % (1331418)Peak memory usage: 90 MB
% 5.56/1.58 % (1331418)Instructions burned: 159 (million)
% 5.56/1.58 % (1331420)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=1663152768:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2995 on theBenchmark for (2995ds/106Mi)
% 5.56/1.58 % (1331423)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=494818061:i=107_2994 on theBenchmark for (2994ds/107Mi)
% 5.56/1.58 % (1331420)Instruction limit reached!
% 5.56/1.58 % (1331420)------------------------------
% 5.56/1.58 % (1331420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.58 % (1331420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.58 % (1331420)CaDiCaL version: 2.1.3
% 5.56/1.58 % (1331420)Termination reason: Instruction limit
% 5.56/1.58 % (1331420)Termination phase: Saturation
% 5.56/1.58 % (1331420)Time elapsed: 0.055 s
% 5.56/1.58 % (1331420)Peak memory usage: 89 MB
% 5.56/1.58 % (1331420)Instructions burned: 106 (million)
% 5.56/1.58 % (1331410)Refutation found. Thanks to Tanya!
% 5.56/1.58 % SZS status Unsatisfiable for theBenchmark
% 5.56/1.58 % SZS output start Proof for theBenchmark
% See solution above
% 5.56/1.58 % (1331410)------------------------------
% 5.56/1.58 % (1331410)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.58 % (1331410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.58 % (1331410)CaDiCaL version: 2.1.3
% 5.56/1.58 % (1331410)Termination reason: Refutation
% 5.56/1.58 % (1331410)Time elapsed: 0.088 s
% 5.56/1.58 % (1331410)Peak memory usage: 92 MB
% 5.56/1.58 % (1331410)Instructions burned: 170 (million)
% 5.56/1.58 % (1331410)------------------------------
% 5.56/1.58 % (1331410)------------------------------
% 5.56/1.58 % (1331389)Success in time 0.705 s
% 5.56/1.58 % Vampire exiting
%------------------------------------------------------------------------------