%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP167-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 10:13:09 AM UTC 2026
% Result : Unsatisfiable 6.63s 2.08s
% Output : Refutation 6.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 34 unt; 0 def)
% Number of atoms : 34 ( 33 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
fof(f16,axiom,
! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb2) ).
fof(f17,axiom,
! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X0),inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
fof(f18,axiom,
! [X0] : positive_part(X0) = least_upper_bound(X0,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat4_1) ).
fof(f19,axiom,
! [X0] : negative_part(X0) = greatest_lower_bound(X0,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat4_2) ).
fof(f22,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lat4) ).
fof(f27,plain,
! [X0] : negative_part(X0) = greatest_lower_bound(identity,X0),
inference(superposition,[],[f5,f19]) ).
fof(f37,plain,
! [X0] : positive_part(X0) = least_upper_bound(identity,X0),
inference(superposition,[],[f6,f18]) ).
fof(f171,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f174,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f171,f1]) ).
fof(f176,plain,
! [X0] : multiply(inverse(identity),X0) = X0,
inference(superposition,[],[f174,f1]) ).
fof(f177,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f174,f3]) ).
fof(f184,plain,
! [X0] : multiply(inverse(inverse(identity)),X0) = X0,
inference(superposition,[],[f174,f176]) ).
fof(f186,plain,
! [X0] : identity = multiply(inverse(inverse(inverse(X0))),X0),
inference(superposition,[],[f174,f177]) ).
fof(f189,plain,
identity = inverse(identity),
inference(superposition,[],[f184,f3]) ).
fof(f200,plain,
! [X0] : inverse(least_upper_bound(identity,X0)) = greatest_lower_bound(identity,inverse(X0)),
inference(superposition,[],[f17,f189]) ).
fof(f202,plain,
! [X0] : inverse(least_upper_bound(identity,X0)) = negative_part(inverse(X0)),
inference(forward_demodulation,[],[f200,f27]) ).
fof(f205,plain,
! [X0] : negative_part(inverse(X0)) = inverse(positive_part(X0)),
inference(forward_demodulation,[],[f202,f37]) ).
fof(f268,plain,
! [X0] : multiply(inverse(inverse(inverse(inverse(X0)))),identity) = X0,
inference(superposition,[],[f174,f186]) ).
fof(f271,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f268,f177]) ).
fof(f952,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,X1),X0) = greatest_lower_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f16,f1]) ).
fof(f1009,plain,
! [X0,X1] : greatest_lower_bound(X0,multiply(X1,X0)) = multiply(negative_part(X1),X0),
inference(forward_demodulation,[],[f952,f27]) ).
fof(f3939,plain,
! [X0] : greatest_lower_bound(X0,identity) = multiply(negative_part(inverse(X0)),X0),
inference(superposition,[],[f1009,f3]) ).
fof(f3998,plain,
! [X0] : greatest_lower_bound(X0,identity) = multiply(inverse(positive_part(X0)),X0),
inference(forward_demodulation,[],[f3939,f205]) ).
fof(f4010,plain,
! [X0] : negative_part(X0) = multiply(inverse(positive_part(X0)),X0),
inference(forward_demodulation,[],[f3998,f19]) ).
fof(f4045,plain,
! [X0] : multiply(inverse(inverse(positive_part(X0))),negative_part(X0)) = X0,
inference(superposition,[],[f174,f4010]) ).
fof(f4052,plain,
! [X0] : multiply(positive_part(X0),negative_part(X0)) = X0,
inference(forward_demodulation,[],[f4045,f271]) ).
fof(f4106,plain,
a != a,
inference(superposition,[],[f22,f4052]) ).
fof(f4120,plain,
$false,
inference(trivial_inequality_removal,[],[f4106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP167-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.44 % Computer : n009.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 27 09:35:00 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.49 Running first-order theorem proving
% 0.23/0.49 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
% 6.63/2.08 % (1773394)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.63/2.08 % (1773400)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=2078015967:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.63/2.08 % (1773401)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3545239805:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.63/2.08 % (1773402)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=649303804:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.63/2.08 % (1773403)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=784293814:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.63/2.08 % (1773405)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=372867714:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.63/2.08 % (1773406)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1035910773:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.63/2.08 % (1773404)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4073030771:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.63/2.08 % (1773406)First to succeed.
% 6.63/2.08 % (1773406)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1773394"
% 6.63/2.08 % (1773403)Instruction limit reached!
% 6.63/2.08 % (1773403)------------------------------
% 6.63/2.08 % (1773403)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/2.08 % (1773403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/2.08 % (1773403)CaDiCaL version: 2.1.3
% 6.63/2.08 % (1773403)Termination reason: Instruction limit
% 6.63/2.08 % (1773403)Termination phase: Saturation
% 6.63/2.08 % (1773403)Time elapsed: 0.137 s
% 6.63/2.08 % (1773403)Peak memory usage: 89 MB
% 6.63/2.08 % (1773403)Instructions burned: 136 (million)
% 6.63/2.08 % (1773404)Instruction limit reached!
% 6.63/2.08 % (1773404)------------------------------
% 6.63/2.08 % (1773404)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/2.08 % (1773404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/2.08 % (1773404)CaDiCaL version: 2.1.3
% 6.63/2.08 % (1773404)Termination reason: Instruction limit
% 6.63/2.08 % (1773404)Termination phase: Saturation
% 6.63/2.08 % (1773404)Time elapsed: 0.174 s
% 6.63/2.08 % (1773404)Peak memory usage: 89 MB
% 6.63/2.08 % (1773404)Instructions burned: 181 (million)
% 6.63/2.08 % (1773405)Also succeeded, but the first one will report.
% 6.63/2.08 % (1773414)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1374366107:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 6.63/2.08 % (1773415)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2224240293:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 6.63/2.08 % (1773406)Refutation found. Thanks to Tanya!
% 6.63/2.08 % SZS status Unsatisfiable for theBenchmark
% 6.63/2.08 % SZS output start Proof for theBenchmark
% See solution above
% 6.63/2.08 % (1773406)------------------------------
% 6.63/2.08 % (1773406)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/2.08 % (1773406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/2.08 % (1773406)CaDiCaL version: 2.1.3
% 6.63/2.08 % (1773406)Termination reason: Refutation
% 6.63/2.08 % (1773406)Time elapsed: 0.110 s
% 6.63/2.08 % (1773406)Peak memory usage: 89 MB
% 6.63/2.08 % (1773406)Instructions burned: 112 (million)
% 6.63/2.08 % (1773406)------------------------------
% 6.63/2.08 % (1773406)------------------------------
% 6.63/2.08 % (1773394)Success in time 0.826 s
% 6.63/2.08 % Vampire exiting
%------------------------------------------------------------------------------