%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP173-1 : 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 : n016.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 10:13:11 AM UTC 2026
% Result : Unsatisfiable 0.19s 1.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 37 ( 37 unt; 5 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 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 : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 18 ( 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
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(f17,axiom,
least_upper_bound(identity,a) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p05a_1) ).
fof(f18,plain,
identity = least_upper_bound(identity,a),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
least_upper_bound(identity,inverse(a)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p05a_2) ).
fof(f20,plain,
identity = least_upper_bound(identity,inverse(a)),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
identity != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p05a) ).
fof(f22,definition,
! [X0] : sF0(X0) = multiply(identity,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f23,plain,
! [X0] : multiply(identity,X0) = sF0(X0),
inference(reorient_equations,[],[f22]) ).
fof(f24,plain,
! [X0] : sF0(X0) = X0,
inference(definition_folding,[],[f1,f23]) ).
fof(f25,definition,
! [X0] : sF1(X0) = multiply(inverse(X0),X0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f26,plain,
! [X0] : multiply(inverse(X0),X0) = sF1(X0),
inference(reorient_equations,[],[f25]) ).
fof(f27,plain,
! [X0] : identity = sF1(X0),
inference(definition_folding,[],[f3,f26]) ).
fof(f28,definition,
sF2 = least_upper_bound(identity,a),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f29,plain,
least_upper_bound(identity,a) = sF2,
inference(reorient_equations,[],[f28]) ).
fof(f30,plain,
identity = sF2,
inference(definition_folding,[],[f18,f29]) ).
fof(f31,definition,
sF3 = inverse(a),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f32,plain,
inverse(a) = sF3,
inference(reorient_equations,[],[f31]) ).
fof(f33,definition,
sF4 = least_upper_bound(identity,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f34,plain,
least_upper_bound(identity,sF3) = sF4,
inference(reorient_equations,[],[f33]) ).
fof(f35,plain,
identity = sF4,
inference(definition_folding,[],[f20,f34,f32]) ).
fof(f36,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(forward_demodulation,[],[f27,f26]) ).
fof(f37,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[],[f24,f23]) ).
fof(f44,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f15,f37]) ).
fof(f53,plain,
identity = multiply(sF3,a),
inference(superposition,[],[f36,f32]) ).
fof(f225,plain,
least_upper_bound(a,identity) = multiply(least_upper_bound(identity,sF3),a),
inference(superposition,[],[f44,f53]) ).
fof(f246,plain,
least_upper_bound(a,identity) = multiply(sF4,a),
inference(forward_demodulation,[],[f225,f34]) ).
fof(f260,plain,
least_upper_bound(a,identity) = multiply(identity,a),
inference(forward_demodulation,[],[f246,f35]) ).
fof(f271,plain,
a = least_upper_bound(a,identity),
inference(forward_demodulation,[],[f260,f37]) ).
fof(f278,plain,
a = least_upper_bound(identity,a),
inference(forward_demodulation,[],[f271,f6]) ).
fof(f282,plain,
a = sF2,
inference(forward_demodulation,[],[f278,f29]) ).
fof(f284,plain,
identity = a,
inference(forward_demodulation,[],[f282,f30]) ).
fof(f288,plain,
identity != identity,
inference(superposition,[],[f21,f284]) ).
fof(f294,plain,
$false,
inference(trivial_inequality_removal,[],[f288]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP173-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 09:40:17 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 Running first-order theorem proving
% 0.16/0.43 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
% 0.19/1.50 % (2368802)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.19/1.50 % (2368819)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2627489965:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.19/1.50 % (2368819)First to succeed.
% 0.19/1.50 % (2368819)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2368802"
% 0.19/1.50 % (2368814)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=3449426559:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.19/1.50 % (2368815)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=1762506927:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.19/1.50 % (2368817)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2952039005:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.19/1.50 % (2368821)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4220728977:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.19/1.50 % (2368820)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3044059000:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.19/1.50 % (2368820)Also succeeded, but the first one will report.
% 0.19/1.50 % (2368818)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=846526058:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.19/1.50 % (2368818)Also succeeded, but the first one will report.
% 0.19/1.50 % (2368821)Also succeeded, but the first one will report.
% 0.19/1.50 % (2368819)Refutation found. Thanks to Tanya!
% 0.19/1.50 % SZS status Unsatisfiable for theBenchmark
% 0.19/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.50 % (2368819)------------------------------
% 0.19/1.50 % (2368819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (2368819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (2368819)CaDiCaL version: 2.1.3
% 0.19/1.50 % (2368819)Termination reason: Refutation
% 0.19/1.50 % (2368819)Time elapsed: 0.007 s
% 0.19/1.50 % (2368819)Peak memory usage: 88 MB
% 0.19/1.50 % (2368819)Instructions burned: 10 (million)
% 0.19/1.50 % (2368819)------------------------------
% 0.19/1.50 % (2368819)------------------------------
% 0.19/1.50 % (2368802)Success in time 0.407 s
% 0.19/1.50 % Vampire exiting
%------------------------------------------------------------------------------