%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP178-2 : 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 : n014.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 10:13:12 AM UTC 2026
% Result : Unsatisfiable 5.42s 1.74s
% Output : Refutation 5.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 24 ( 24 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1 ( 1 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 35 !; 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(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(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(f21,axiom,
greatest_lower_bound(identity,c) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p09b_3) ).
fof(f22,plain,
identity = greatest_lower_bound(identity,c),
inference(reorient_equations,[],[f21]) ).
fof(f23,axiom,
greatest_lower_bound(a,b) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p09b_4) ).
fof(f24,plain,
identity = greatest_lower_bound(a,b),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p09b) ).
fof(f53,plain,
! [X2,X3,X0,X1] : greatest_lower_bound(multiply(X0,X1),greatest_lower_bound(multiply(X0,X2),X3)) = greatest_lower_bound(multiply(X0,greatest_lower_bound(X1,X2)),X3),
inference(superposition,[],[f7,f14]) ).
fof(f62,plain,
! [X2,X3,X0,X1] : greatest_lower_bound(multiply(X0,greatest_lower_bound(X3,X2)),multiply(X1,X2)) = greatest_lower_bound(multiply(X0,X3),multiply(greatest_lower_bound(X0,X1),X2)),
inference(superposition,[],[f53,f16]) ).
fof(f89,plain,
! [X0,X1] : greatest_lower_bound(multiply(X0,identity),multiply(greatest_lower_bound(X0,X1),c)) = greatest_lower_bound(multiply(X0,identity),multiply(X1,c)),
inference(superposition,[],[f62,f22]) ).
fof(f642,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f3]) ).
fof(f666,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f642,f1]) ).
fof(f677,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f666,f3]) ).
fof(f679,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f666,f666]) ).
fof(f695,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f677,f679]) ).
fof(f701,plain,
! [X0,X1] : greatest_lower_bound(X0,multiply(greatest_lower_bound(X0,X1),c)) = greatest_lower_bound(X0,multiply(X1,c)),
inference(superposition,[],[f89,f695]) ).
fof(f827,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,multiply(identity,c)),
inference(superposition,[],[f701,f24]) ).
fof(f865,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c),
inference(forward_demodulation,[],[f827,f1]) ).
fof(f888,plain,
$false,
inference(forward_subsumption_resolution,[],[f865,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP178-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n014.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 09:35:47 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 5.42/1.74 % (548629)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.42/1.74 % (548635)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=174499154:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 5.42/1.74 % (548640)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=777999115:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 5.42/1.74 % (548636)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1297331040:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 5.42/1.74 % (548637)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2050560504:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 5.42/1.74 % (548638)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=862688079:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 5.42/1.74 % (548634)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=1475883573:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 5.42/1.74 % (548638)Refutation not found, incomplete strategy
% 5.42/1.74 % (548638)------------------------------
% 5.42/1.74 % (548638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.74 % (548638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.74 % (548638)CaDiCaL version: 2.1.3
% 5.42/1.74 % (548638)Termination reason: Refutation not found, incomplete strategy
% 5.42/1.74 % (548638)Time elapsed: 0.002 s
% 5.42/1.74 % (548638)Peak memory usage: 87 MB
% 5.42/1.74 % (548638)Instructions burned: 1 (million)
% 5.42/1.74 % (548639)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=653907166:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 5.42/1.74 % (548637)Instruction limit reached!
% 5.42/1.74 % (548637)------------------------------
% 5.42/1.74 % (548637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.74 % (548637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.74 % (548637)CaDiCaL version: 2.1.3
% 5.42/1.74 % (548637)Termination reason: Instruction limit
% 5.42/1.74 % (548637)Termination phase: Saturation
% 5.42/1.74 % (548637)Time elapsed: 0.084 s
% 5.42/1.74 % (548637)Peak memory usage: 89 MB
% 5.42/1.74 % (548637)Instructions burned: 137 (million)
% 5.42/1.74 % (548639)Instruction limit reached!
% 5.42/1.74 % (548639)------------------------------
% 5.42/1.74 % (548639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.74 % (548639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.74 % (548639)CaDiCaL version: 2.1.3
% 5.42/1.74 % (548639)Termination reason: Instruction limit
% 5.42/1.74 % (548639)Termination phase: Saturation
% 5.42/1.74 % (548639)Time elapsed: 0.168 s
% 5.42/1.74 % (548639)Peak memory usage: 91 MB
% 5.42/1.74 % (548639)Instructions burned: 259 (million)
% 5.42/1.74 % (548648)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2873748171:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 5.42/1.74 % (548638)------------------------------
% 5.42/1.74 % (548638)------------------------------
% 5.42/1.74 % (548649)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=381057802:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 5.42/1.74 % (548635)First to succeed.
% 5.42/1.74 % (548635)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-548629"
% 5.42/1.74 % (548651)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1500938737:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 5.42/1.74 % (548651)Instruction limit reached!
% 5.42/1.74 % (548651)------------------------------
% 5.42/1.74 % (548651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.74 % (548651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.74 % (548651)CaDiCaL version: 2.1.3
% 5.42/1.74 % (548651)Termination reason: Instruction limit
% 5.42/1.74 % (548651)Termination phase: Saturation
% 5.42/1.74 % (548651)Time elapsed: 0.115 s
% 5.42/1.74 % (548651)Peak memory usage: 92 MB
% 5.42/1.74 % (548651)Instructions burned: 217 (million)
% 5.42/1.74 % (548635)Refutation found. Thanks to Tanya!
% 5.42/1.74 % SZS status Unsatisfiable for theBenchmark
% 5.42/1.74 % SZS output start Proof for theBenchmark
% See solution above
% 5.42/1.74 % (548635)------------------------------
% 5.42/1.74 % (548635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.74 % (548635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.74 % (548635)CaDiCaL version: 2.1.3
% 5.42/1.74 % (548635)Termination reason: Refutation
% 5.42/1.74 % (548635)Time elapsed: 0.399 s
% 5.42/1.74 % (548635)Peak memory usage: 129 MB
% 5.42/1.74 % (548635)Instructions burned: 1065 (million)
% 5.42/1.74 % (548635)------------------------------
% 5.42/1.74 % (548635)------------------------------
% 5.42/1.74 % (548629)Success in time 0.677 s
% 5.42/1.74 % Vampire exiting
%------------------------------------------------------------------------------