%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP193-2 : 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 : n010.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 10:13:18 AM UTC 2026
% Result : Unsatisfiable 3.83s 1.43s
% Output : Refutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 31 ( 31 unt; 1 def)
% Number of atoms : 31 ( 27 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
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(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(f19,axiom,
greatest_lower_bound(identity,b) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_9b_2) ).
fof(f20,plain,
identity = greatest_lower_bound(identity,b),
inference(reorient_equations,[],[f19]) ).
fof(f23,axiom,
greatest_lower_bound(a,b) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_9b_4) ).
fof(f24,plain,
identity = greatest_lower_bound(a,b),
inference(reorient_equations,[],[f23]) ).
fof(f25,axiom,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_9b_5) ).
fof(f26,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p8_9b) ).
fof(f28,definition,
~ sP0(greatest_lower_bound(a,multiply(b,c))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f29,plain,
sP0(greatest_lower_bound(a,c)),
inference(inequality_splitting,[],[f27,f28]) ).
fof(f30,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(identity,greatest_lower_bound(a,c))),
inference(backward_demodulation,[],[f26,f24]) ).
fof(f31,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(identity,greatest_lower_bound(a,c)))),
inference(forward_demodulation,[],[f30,f7]) ).
fof(f32,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))),
inference(forward_demodulation,[],[f31,f1]) ).
fof(f68,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X0,X1)),
inference(superposition,[],[f7,f10]) ).
fof(f70,plain,
! [X2,X0,X1] : greatest_lower_bound(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(X1,greatest_lower_bound(X0,X2)),
inference(superposition,[],[f7,f5]) ).
fof(f85,plain,
! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X2,greatest_lower_bound(X0,X1)),
inference(superposition,[],[f5,f7]) ).
fof(f239,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,X1),X0) = greatest_lower_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f16,f1]) ).
fof(f530,plain,
! [X2,X0,X1] : greatest_lower_bound(greatest_lower_bound(X1,X0),X2) = greatest_lower_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(greatest_lower_bound(X1,X0),X2))),
inference(superposition,[],[f68,f70]) ).
fof(f533,plain,
! [X2,X0,X1] : greatest_lower_bound(X1,greatest_lower_bound(X0,X2)) = greatest_lower_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X1,greatest_lower_bound(X0,X2)))),
inference(forward_demodulation,[],[f530,f7]) ).
fof(f547,plain,
! [X2,X0,X1] : greatest_lower_bound(X1,greatest_lower_bound(X0,X2)) = greatest_lower_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X0,X2))),
inference(forward_demodulation,[],[f533,f68]) ).
fof(f560,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c)),
inference(backward_demodulation,[],[f32,f547]) ).
fof(f777,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))),
inference(superposition,[],[f560,f85]) ).
fof(f1231,plain,
! [X0] : multiply(identity,X0) = greatest_lower_bound(X0,multiply(b,X0)),
inference(superposition,[],[f239,f20]) ).
fof(f1293,plain,
! [X0] : greatest_lower_bound(X0,multiply(b,X0)) = X0,
inference(forward_demodulation,[],[f1231,f1]) ).
fof(f1310,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c),
inference(backward_demodulation,[],[f777,f1293]) ).
fof(f1319,plain,
~ sP0(greatest_lower_bound(a,c)),
inference(backward_demodulation,[],[f28,f1310]) ).
fof(f1327,plain,
$false,
inference(forward_subsumption_resolution,[],[f1319,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP193-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:37:32 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 3.83/1.43 % (701335)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.83/1.43 % (701435)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1750235728:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.83/1.43 % (701433)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=439413163:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.83/1.43 % (701439)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1386373197:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.83/1.43 % (701436)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=631658258:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.83/1.43 % (701437)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=241182218:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.83/1.43 % (701434)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=2328933415:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.83/1.43 % (701438)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1660383387:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.83/1.43 % (701436)First to succeed.
% 3.83/1.43 % (701436)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-701335"
% 3.83/1.43 % (701438)Also succeeded, but the first one will report.
% 3.83/1.43 % (701439)Also succeeded, but the first one will report.
% 3.83/1.43 % (701437)Instruction limit reached!
% 3.83/1.43 % (701437)------------------------------
% 3.83/1.43 % (701437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.83/1.43 % (701437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.83/1.43 % (701437)CaDiCaL version: 2.1.3
% 3.83/1.43 % (701437)Termination reason: Instruction limit
% 3.83/1.43 % (701437)Termination phase: Saturation
% 3.83/1.43 % (701437)Time elapsed: 0.104 s
% 3.83/1.43 % (701437)Peak memory usage: 89 MB
% 3.83/1.43 % (701437)Instructions burned: 182 (million)
% 3.83/1.43 % (701477)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3894740232:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.83/1.43 % (701436)Refutation found. Thanks to Tanya!
% 3.83/1.43 % SZS status Unsatisfiable for theBenchmark
% 3.83/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 3.83/1.43 % (701436)------------------------------
% 3.83/1.43 % (701436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.83/1.43 % (701436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.83/1.43 % (701436)CaDiCaL version: 2.1.3
% 3.83/1.43 % (701436)Termination reason: Refutation
% 3.83/1.43 % (701436)Time elapsed: 0.041 s
% 3.83/1.43 % (701436)Peak memory usage: 88 MB
% 3.83/1.43 % (701436)Instructions burned: 60 (million)
% 3.83/1.43 % (701436)------------------------------
% 3.83/1.43 % (701436)------------------------------
% 3.83/1.43 % (701335)Success in time 0.472 s
% 3.83/1.43 % Vampire exiting
%------------------------------------------------------------------------------