%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP166-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 2.59s 1.33s
% Output : Refutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 27 unt; 4 def)
% Number of atoms : 27 ( 26 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 : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 16 ( 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
fof(f15,axiom,
! [X2,X0,X1] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).
fof(f19,axiom,
least_upper_bound(b,identity) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat3a_2) ).
fof(f20,plain,
b = least_upper_bound(b,identity),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
least_upper_bound(a,multiply(b,a)) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lat3a) ).
fof(f22,plain,
multiply(b,a) != least_upper_bound(a,multiply(b,a)),
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
! [X0] : sF0(X0) = multiply(identity,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f24,plain,
! [X0] : multiply(identity,X0) = sF0(X0),
inference(reorient_equations,[],[f23]) ).
fof(f25,plain,
! [X0] : sF0(X0) = X0,
inference(definition_folding,[],[f1,f24]) ).
fof(f32,definition,
sF3 = least_upper_bound(b,identity),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f33,plain,
least_upper_bound(b,identity) = sF3,
inference(reorient_equations,[],[f32]) ).
fof(f34,plain,
b = sF3,
inference(definition_folding,[],[f20,f33]) ).
fof(f35,definition,
sF4 = multiply(b,a),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f36,plain,
multiply(b,a) = sF4,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF5 = least_upper_bound(a,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f38,plain,
least_upper_bound(a,sF4) = sF5,
inference(reorient_equations,[],[f37]) ).
fof(f39,plain,
sF4 != sF5,
inference(definition_folding,[],[f22,f38,f36,f36]) ).
fof(f40,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[],[f25,f24]) ).
fof(f46,plain,
! [X0,X1] : multiply(least_upper_bound(X1,identity),X0) = least_upper_bound(multiply(X1,X0),X0),
inference(superposition,[],[f15,f40]) ).
fof(f51,plain,
! [X0,X1] : multiply(least_upper_bound(X1,identity),X0) = least_upper_bound(X0,multiply(X1,X0)),
inference(forward_demodulation,[],[f46,f6]) ).
fof(f648,plain,
! [X0] : multiply(sF3,X0) = least_upper_bound(X0,multiply(b,X0)),
inference(superposition,[],[f51,f33]) ).
fof(f712,plain,
! [X0] : multiply(b,X0) = least_upper_bound(X0,multiply(b,X0)),
inference(forward_demodulation,[],[f648,f34]) ).
fof(f736,plain,
sF4 = least_upper_bound(a,sF4),
inference(superposition,[],[f712,f36]) ).
fof(f757,plain,
sF4 = sF5,
inference(forward_demodulation,[],[f736,f38]) ).
fof(f761,plain,
sF4 != sF4,
inference(superposition,[],[f39,f757]) ).
fof(f771,plain,
$false,
inference(trivial_inequality_removal,[],[f761]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP166-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n026.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 09:37:11 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.59/1.33 % (2576679)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.59/1.33 % (2576688)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3029825582:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.59/1.33 % (2576688)First to succeed.
% 2.59/1.33 % (2576688)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2576679"
% 2.59/1.33 % (2576686)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2351478440:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.59/1.33 % (2576687)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2955554969:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.59/1.33 % (2576684)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=3320785748:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.59/1.33 % (2576685)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=2137711115:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.59/1.33 % (2576690)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=587578417:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.59/1.33 % (2576689)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2328594260:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.59/1.33 % (2576687)Also succeeded, but the first one will report.
% 2.59/1.33 % (2576689)Also succeeded, but the first one will report.
% 2.59/1.33 % (2576690)Also succeeded, but the first one will report.
% 2.59/1.33 % (2576688)Refutation found. Thanks to Tanya!
% 2.59/1.33 % SZS status Unsatisfiable for theBenchmark
% 2.59/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.59/1.33 % (2576688)------------------------------
% 2.59/1.33 % (2576688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.33 % (2576688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.33 % (2576688)CaDiCaL version: 2.1.3
% 2.59/1.33 % (2576688)Termination reason: Refutation
% 2.59/1.33 % (2576688)Time elapsed: 0.010 s
% 2.59/1.33 % (2576688)Peak memory usage: 88 MB
% 2.59/1.33 % (2576688)Instructions burned: 27 (million)
% 2.59/1.33 % (2576688)------------------------------
% 2.59/1.33 % (2576688)------------------------------
% 2.59/1.33 % (2576679)Success in time 0.277 s
% 2.59/1.33 % Vampire exiting
%------------------------------------------------------------------------------