%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP166-2 : 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 : 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 10:13:08 AM UTC 2026
% Result : Unsatisfiable 0.17s 1.91s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 22 ( 22 unt; 1 def)
% Number of atoms : 22 ( 18 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 : 4 ( 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 : 21 ( 21 !; 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(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(f19,axiom,
greatest_lower_bound(b,identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat2b_2) ).
fof(f20,plain,
identity = greatest_lower_bound(b,identity),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
greatest_lower_bound(a,multiply(a,b)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lat2b) ).
fof(f22,plain,
a != greatest_lower_bound(a,multiply(a,b)),
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
~ sP0(greatest_lower_bound(a,multiply(a,b))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f24,plain,
sP0(a),
inference(inequality_splitting,[],[f22,f23]) ).
fof(f32,plain,
identity = greatest_lower_bound(identity,b),
inference(superposition,[],[f20,f5]) ).
fof(f51,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f54,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f51,f1]) ).
fof(f160,plain,
! [X0] : multiply(X0,identity) = greatest_lower_bound(multiply(X0,identity),multiply(X0,b)),
inference(superposition,[],[f14,f32]) ).
fof(f253,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f54,f3]) ).
fof(f256,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f54,f54]) ).
fof(f264,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f253,f256]) ).
fof(f274,plain,
! [X0] : greatest_lower_bound(X0,multiply(X0,b)) = X0,
inference(backward_demodulation,[],[f160,f264]) ).
fof(f275,plain,
~ sP0(a),
inference(backward_demodulation,[],[f23,f274]) ).
fof(f276,plain,
$false,
inference(forward_subsumption_resolution,[],[f275,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP166-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n008.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 09:35:25 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 0.17/1.91 % (974026)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.17/1.91 % (974058)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=803965208:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.17/1.91 % (974052)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=149570271:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.17/1.91 % (974053)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=2857268649:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.17/1.91 % (974054)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3900211154:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.17/1.91 % (974056)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2419866470:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.17/1.91 % (974055)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2352205505:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.17/1.91 % (974055)First to succeed.
% 0.17/1.91 % (974055)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-974026"
% 0.17/1.91 % (974057)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4186345768:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.17/1.91 % (974057)Also succeeded, but the first one will report.
% 0.17/1.91 % (974056)Instruction limit reached!
% 0.17/1.91 % (974056)------------------------------
% 0.17/1.91 % (974056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.91 % (974056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.91 % (974056)CaDiCaL version: 2.1.3
% 0.17/1.91 % (974056)Termination reason: Instruction limit
% 0.17/1.91 % (974056)Termination phase: Saturation
% 0.17/1.91 % (974056)Time elapsed: 0.177 s
% 0.17/1.91 % (974056)Peak memory usage: 89 MB
% 0.17/1.91 % (974056)Instructions burned: 182 (million)
% 0.17/1.91 % (974067)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2104982220:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 0.17/1.91 % (974055)Refutation found. Thanks to Tanya!
% 0.17/1.91 % SZS status Unsatisfiable for theBenchmark
% 0.17/1.91 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.91 % (974055)------------------------------
% 0.17/1.91 % (974055)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.91 % (974055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.91 % (974055)CaDiCaL version: 2.1.3
% 0.17/1.91 % (974055)Termination reason: Refutation
% 0.17/1.91 % (974055)Time elapsed: 0.014 s
% 0.17/1.91 % (974055)Peak memory usage: 88 MB
% 0.17/1.91 % (974055)Instructions burned: 12 (million)
% 0.17/1.91 % (974055)------------------------------
% 0.17/1.91 % (974055)------------------------------
% 0.17/1.91 % (974026)Success in time 0.616 s
% 0.17/1.91 % Vampire exiting
%------------------------------------------------------------------------------