%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n008.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 10:17:01 AM UTC 2026
% Result : Unsatisfiable 1.45s 0.69s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 42 unt; 0 def)
% Number of atoms : 42 ( 41 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 53 ( 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',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/Axioms/GRP004-0.ax',associativity) ).
fof(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
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(f23,plain,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
inference(definition_unfolding,[],[f22,f18,f19]) ).
fof(f29,plain,
a != multiply(least_upper_bound(identity,a),greatest_lower_bound(a,identity)),
inference(superposition,[],[f23,f6]) ).
fof(f30,plain,
a != multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a)),
inference(forward_demodulation,[],[f29,f5]) ).
fof(f97,plain,
! [X0,X1] : greatest_lower_bound(inverse(X0),inverse(X1)) = inverse(least_upper_bound(X1,X0)),
inference(superposition,[],[f17,f5]) ).
fof(f108,plain,
! [X0,X1] : inverse(least_upper_bound(X0,X1)) = inverse(least_upper_bound(X1,X0)),
inference(superposition,[],[f97,f17]) ).
fof(f185,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f188,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f185,f1]) ).
fof(f192,plain,
! [X0] : multiply(inverse(identity),X0) = X0,
inference(superposition,[],[f188,f1]) ).
fof(f193,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f188,f3]) ).
fof(f200,plain,
! [X0] : multiply(inverse(inverse(identity)),X0) = X0,
inference(superposition,[],[f188,f192]) ).
fof(f204,plain,
! [X0] : identity = multiply(inverse(inverse(inverse(X0))),X0),
inference(superposition,[],[f188,f193]) ).
fof(f209,plain,
identity = inverse(identity),
inference(superposition,[],[f200,f3]) ).
fof(f234,plain,
! [X0] : multiply(inverse(inverse(inverse(inverse(X0)))),identity) = X0,
inference(superposition,[],[f188,f204]) ).
fof(f237,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f234,f193]) ).
fof(f242,plain,
! [X0] : multiply(X0,identity) = X0,
inference(superposition,[],[f193,f237]) ).
fof(f245,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(superposition,[],[f3,f237]) ).
fof(f247,plain,
! [X0,X1] : inverse(least_upper_bound(X1,inverse(X0))) = greatest_lower_bound(inverse(X1),X0),
inference(superposition,[],[f17,f237]) ).
fof(f252,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[],[f188,f237]) ).
fof(f280,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(superposition,[],[f245,f4]) ).
fof(f1398,plain,
! [X0,X1] : multiply(X0,identity) = multiply(X1,inverse(multiply(inverse(X0),X1))),
inference(superposition,[],[f252,f280]) ).
fof(f1403,plain,
! [X0,X1] : multiply(X1,inverse(multiply(inverse(X0),X1))) = X0,
inference(forward_demodulation,[],[f1398,f242]) ).
fof(f21086,plain,
! [X0,X1] : multiply(inverse(inverse(X0)),least_upper_bound(identity,X1)) = least_upper_bound(X0,multiply(inverse(inverse(X0)),X1)),
inference(superposition,[],[f13,f193]) ).
fof(f21278,plain,
! [X0,X1] : multiply(X0,least_upper_bound(identity,X1)) = least_upper_bound(X0,multiply(X0,X1)),
inference(forward_demodulation,[],[f21086,f237]) ).
fof(f21355,plain,
! [X0] : least_upper_bound(X0,identity) = multiply(X0,least_upper_bound(identity,inverse(X0))),
inference(superposition,[],[f21278,f245]) ).
fof(f22513,plain,
! [X0] : multiply(least_upper_bound(identity,inverse(inverse(X0))),inverse(least_upper_bound(inverse(X0),identity))) = X0,
inference(superposition,[],[f1403,f21355]) ).
fof(f22520,plain,
! [X0] : multiply(least_upper_bound(identity,inverse(inverse(X0))),inverse(least_upper_bound(identity,inverse(X0)))) = X0,
inference(forward_demodulation,[],[f22513,f108]) ).
fof(f22564,plain,
! [X0] : multiply(least_upper_bound(identity,inverse(inverse(X0))),greatest_lower_bound(inverse(identity),X0)) = X0,
inference(forward_demodulation,[],[f22520,f247]) ).
fof(f22590,plain,
! [X0] : multiply(least_upper_bound(identity,inverse(inverse(X0))),greatest_lower_bound(identity,X0)) = X0,
inference(forward_demodulation,[],[f22564,f209]) ).
fof(f22604,plain,
! [X0] : multiply(least_upper_bound(identity,X0),greatest_lower_bound(identity,X0)) = X0,
inference(forward_demodulation,[],[f22590,f237]) ).
fof(f22695,plain,
a != a,
inference(superposition,[],[f30,f22604]) ).
fof(f22707,plain,
$false,
inference(trivial_inequality_removal,[],[f22695]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP167-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:35:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.45/0.69 % (974970)Will run a generic schedule for satisfiability detection.
% 1.45/0.69 % (974982)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1297715574:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.45/0.69 % (974981)% WARNING: option uhcvi not known.
% 1.45/0.69 % (974981)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3219359910:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.45/0.69 % (974980)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1192868732_2999 on theBenchmark for (2999ds/0Mi)
% 1.45/0.69 % (974984)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3715905095:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.45/0.69 % (974983)dis+10_1_sil=32000:sp=arity:random_seed=1755640148:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.45/0.69 % (974985)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1997573809:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.45/0.69 % (974986)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3548891017:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.45/0.69 % TRYING [1]
% 1.45/0.69 % TRYING [2]
% 1.45/0.69 % TRYING [3]
% 1.45/0.69 % TRYING [4]
% 1.45/0.69 % TRYING [5]
% 1.45/0.69 % (974983)Instruction limit reached!
% 1.45/0.69 % (974983)------------------------------
% 1.45/0.69 % (974983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.69 % (974983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.69 % (974983)CaDiCaL version: 2.1.3
% 1.45/0.69 % (974983)Termination reason: Instruction limit
% 1.45/0.69 % (974983)Termination phase: Saturation
% 1.45/0.69 % (974983)Time elapsed: 0.059 s
% 1.45/0.69 % (974983)Peak memory usage: 12 MB
% 1.45/0.69 % (974983)Instructions burned: 104 (million)
% 1.45/0.69 % (974984)Instruction limit reached!
% 1.45/0.69 % (974984)------------------------------
% 1.45/0.69 % (974984)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.69 % (974984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.69 % (974984)CaDiCaL version: 2.1.3
% 1.45/0.69 % (974984)Termination reason: Instruction limit
% 1.45/0.69 % (974984)Termination phase: Saturation
% 1.45/0.69 % (974984)Time elapsed: 0.070 s
% 1.45/0.69 % (974984)Peak memory usage: 12 MB
% 1.45/0.69 % (974984)Instructions burned: 116 (million)
% 1.45/0.69 % (974985)Instruction limit reached!
% 1.45/0.69 % (974985)------------------------------
% 1.45/0.69 % (974985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.69 % (974985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.69 % (974985)CaDiCaL version: 2.1.3
% 1.45/0.69 % (974985)Termination reason: Instruction limit
% 1.45/0.69 % (974985)Termination phase: Saturation
% 1.45/0.69 % (974985)Time elapsed: 0.073 s
% 1.45/0.69 % (974985)Peak memory usage: 12 MB
% 1.45/0.69 % (974985)Instructions burned: 132 (million)
% 1.45/0.69 % (975014)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2170755289:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.45/0.69 % TRYING [1]
% 1.45/0.69 % TRYING [2]
% 1.45/0.69 % TRYING [3]
% 1.45/0.69 % (975015)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2227262490:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.45/0.69 % (975016)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1407292377:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.45/0.69 % TRYING [4]
% 1.45/0.69 % (974986)Instruction limit reached!
% 1.45/0.69 % (974986)------------------------------
% 1.45/0.69 % (974986)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.69 % (974986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.69 % (974986)CaDiCaL version: 2.1.3
% 1.45/0.69 % (974986)Termination reason: Instruction limit
% 1.45/0.69 % (974986)Termination phase: Saturation
% 1.45/0.69 % (974986)Time elapsed: 0.098 s
% 1.45/0.69 % (974986)Peak memory usage: 13 MB
% 1.45/0.69 % (974986)Instructions burned: 160 (million)
% 1.45/0.69 % (975020)ott-21_1_sil=16000:fs=off:random_seed=342684551:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.45/0.69 % TRYING [5]
% 1.45/0.69 % (975015)Instruction limit reached!
% 1.45/0.69 % (975015)------------------------------
% 1.45/0.69 % (975015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.69 % (975015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.69 % (975015)CaDiCaL version: 2.1.3
% 1.45/0.69 % (975015)Termination reason: Instruction limit
% 1.45/0.69 % (975015)Termination phase: Saturation
% 1.45/0.69 % (975015)Time elapsed: 0.084 s
% 1.45/0.69 % (975015)Peak memory usage: 13 MB
% 1.45/0.69 % (975015)Instructions burned: 132 (million)
% 1.45/0.69 % TRYING [6]
% 1.45/0.69 % (975029)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=818876188:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.45/0.69 % (975020)Instruction limit reached!
% 1.45/0.69 % (975020)------------------------------
% 1.45/0.69 % (975020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.69 % (975020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.69 % (975020)CaDiCaL version: 2.1.3
% 1.45/0.69 % (975020)Termination reason: Instruction limit
% 1.45/0.69 % (975020)Termination phase: Saturation
% 1.45/0.69 % (975020)Time elapsed: 0.081 s
% 1.45/0.69 % (975020)Peak memory usage: 12 MB
% 1.45/0.69 % (975020)Instructions burned: 182 (million)
% 1.45/0.69 % (975044)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4004622925:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.45/0.69 % TRYING [1]
% 1.45/0.69 % TRYING [2]
% 1.45/0.69 % TRYING [3]
% 1.45/0.69 % (974982) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-974970-974982"...
% 1.45/0.69 % (974982)...printing done.
% 1.45/0.69 % (974982)Refutation found. Thanks to Tanya!
% 1.45/0.69 % SZS status Unsatisfiable for theBenchmark
% 1.45/0.69 % SZS output start Proof for theBenchmark
% See solution above
% 1.45/0.69 % (974982)------------------------------
% 1.45/0.69 % (974982)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.69 % (974982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.69 % (974982)CaDiCaL version: 2.1.3
% 1.45/0.69 % (974982)Termination reason: Refutation
% 1.45/0.69 % (974982)Time elapsed: 0.243 s
% 1.45/0.69 % (974982)Peak memory usage: 19 MB
% 1.45/0.69 % (974982)Instructions burned: 917 (million)
% 1.45/0.69 % (974970)Success in time 0.262 s
% 1.45/0.69 % Vampire exiting
%------------------------------------------------------------------------------