%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP169-2 : 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 : n001.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 2.34s 1.40s
% Output : Refutation 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 37 ( 37 unt; 1 def)
% Number of atoms : 37 ( 33 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 39 !; 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(f7,axiom,
! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_glb) ).
fof(f10,axiom,
! [X0] : greatest_lower_bound(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_gld) ).
fof(f14,axiom,
! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb1) ).
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,
greatest_lower_bound(inverse(a),inverse(b)) = inverse(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p02b_1) ).
fof(f18,plain,
inverse(a) = greatest_lower_bound(inverse(a),inverse(b)),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
greatest_lower_bound(a,b) != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p02b) ).
fof(f20,plain,
b != greatest_lower_bound(a,b),
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
~ sP0(greatest_lower_bound(a,b)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f22,plain,
sP0(b),
inference(inequality_splitting,[],[f20,f21]) ).
fof(f50,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f53,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f50,f1]) ).
fof(f56,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f53,f3]) ).
fof(f58,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f53,f53]) ).
fof(f61,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f56,f58]) ).
fof(f62,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X0,X1)),
inference(superposition,[],[f7,f10]) ).
fof(f233,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,greatest_lower_bound(X0,X1)),
inference(superposition,[],[f62,f5]) ).
fof(f251,plain,
! [X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),X0) = greatest_lower_bound(identity,multiply(X1,X0)),
inference(superposition,[],[f16,f3]) ).
fof(f607,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[],[f61,f58]) ).
fof(f608,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[],[f53,f58]) ).
fof(f611,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f607,f61]) ).
fof(f925,plain,
! [X2,X0,X1] : multiply(X1,greatest_lower_bound(X2,multiply(inverse(X1),X0))) = greatest_lower_bound(multiply(X1,X2),X0),
inference(superposition,[],[f14,f608]) ).
fof(f1491,plain,
greatest_lower_bound(identity,multiply(inverse(b),a)) = multiply(inverse(a),a),
inference(superposition,[],[f251,f18]) ).
fof(f1535,plain,
identity = greatest_lower_bound(identity,multiply(inverse(b),a)),
inference(forward_demodulation,[],[f1491,f3]) ).
fof(f1689,plain,
identity = greatest_lower_bound(multiply(inverse(b),a),identity),
inference(superposition,[],[f233,f1535]) ).
fof(f1692,plain,
identity = multiply(inverse(b),greatest_lower_bound(a,multiply(inverse(inverse(b)),identity))),
inference(forward_demodulation,[],[f1689,f925]) ).
fof(f1699,plain,
identity = multiply(inverse(b),greatest_lower_bound(a,inverse(inverse(b)))),
inference(forward_demodulation,[],[f1692,f61]) ).
fof(f1706,plain,
identity = multiply(inverse(b),greatest_lower_bound(a,b)),
inference(forward_demodulation,[],[f1699,f611]) ).
fof(f1937,plain,
greatest_lower_bound(a,b) = multiply(b,identity),
inference(superposition,[],[f608,f1706]) ).
fof(f1946,plain,
b = greatest_lower_bound(a,b),
inference(forward_demodulation,[],[f1937,f61]) ).
fof(f1952,plain,
~ sP0(b),
inference(backward_demodulation,[],[f21,f1946]) ).
fof(f1954,plain,
$false,
inference(forward_subsumption_resolution,[],[f1952,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP169-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 09:41:00 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 2.34/1.40 % (3299689)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.34/1.40 % (3299694)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=2509147788:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.34/1.40 % (3299700)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=117231400:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.34/1.40 % (3299695)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=2196285315:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.34/1.40 % (3299697)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=738089698:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.34/1.40 % (3299698)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4084499535:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.34/1.40 % (3299696)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2296062656:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.34/1.40 % (3299699)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2463287656:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.34/1.40 % (3299697)First to succeed.
% 2.34/1.40 % (3299697)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3299689"
% 2.34/1.40 % (3299698)Also succeeded, but the first one will report.
% 2.34/1.40 % (3299700)Also succeeded, but the first one will report.
% 2.34/1.40 % (3299699)Instruction limit reached!
% 2.34/1.40 % (3299699)------------------------------
% 2.34/1.40 % (3299699)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.34/1.40 % (3299699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/1.40 % (3299699)CaDiCaL version: 2.1.3
% 2.34/1.40 % (3299699)Termination reason: Instruction limit
% 2.34/1.40 % (3299699)Termination phase: Saturation
% 2.34/1.40 % (3299699)Time elapsed: 0.167 s
% 2.34/1.40 % (3299699)Peak memory usage: 91 MB
% 2.34/1.40 % (3299699)Instructions burned: 258 (million)
% 2.34/1.40 % (3299708)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2957047564:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 2.34/1.40 % (3299697)Refutation found. Thanks to Tanya!
% 2.34/1.40 % SZS status Unsatisfiable for theBenchmark
% 2.34/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 2.34/1.40 % (3299697)------------------------------
% 2.34/1.40 % (3299697)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.34/1.40 % (3299697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/1.40 % (3299697)CaDiCaL version: 2.1.3
% 2.34/1.40 % (3299697)Termination reason: Refutation
% 2.34/1.40 % (3299697)Time elapsed: 0.054 s
% 2.34/1.40 % (3299697)Peak memory usage: 89 MB
% 2.34/1.40 % (3299697)Instructions burned: 86 (million)
% 2.34/1.40 % (3299697)------------------------------
% 2.34/1.40 % (3299697)------------------------------
% 2.34/1.40 % (3299689)Success in time 0.458 s
% 2.34/1.40 % Vampire exiting
%------------------------------------------------------------------------------