%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP172-2 : 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 : n011.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 2.58s 1.28s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 42 ( 42 unt; 5 def)
% Number of atoms : 42 ( 41 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 : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [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(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
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(f11,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lub_absorbtion) ).
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(f17,axiom,
greatest_lower_bound(identity,a) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p04d_1) ).
fof(f18,plain,
identity = greatest_lower_bound(identity,a),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
greatest_lower_bound(identity,b) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p04d_2) ).
fof(f20,plain,
identity = greatest_lower_bound(identity,b),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p04d) ).
fof(f22,plain,
multiply(a,b) != least_upper_bound(identity,multiply(a,b)),
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(f29,definition,
sF2 = greatest_lower_bound(identity,a),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f30,plain,
greatest_lower_bound(identity,a) = sF2,
inference(reorient_equations,[],[f29]) ).
fof(f31,plain,
identity = sF2,
inference(definition_folding,[],[f18,f30]) ).
fof(f32,definition,
sF3 = greatest_lower_bound(identity,b),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f33,plain,
greatest_lower_bound(identity,b) = sF3,
inference(reorient_equations,[],[f32]) ).
fof(f34,plain,
identity = sF3,
inference(definition_folding,[],[f20,f33]) ).
fof(f35,definition,
sF4 = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f36,plain,
multiply(a,b) = sF4,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF5 = least_upper_bound(identity,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f38,plain,
least_upper_bound(identity,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(f49,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,X1),X0) = greatest_lower_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f16,f40]) ).
fof(f219,plain,
multiply(greatest_lower_bound(identity,a),b) = greatest_lower_bound(b,sF4),
inference(superposition,[],[f49,f36]) ).
fof(f251,plain,
multiply(greatest_lower_bound(identity,a),b) = greatest_lower_bound(sF4,b),
inference(forward_demodulation,[],[f219,f5]) ).
fof(f266,plain,
greatest_lower_bound(sF4,b) = multiply(sF2,b),
inference(forward_demodulation,[],[f251,f30]) ).
fof(f276,plain,
greatest_lower_bound(sF4,b) = multiply(identity,b),
inference(forward_demodulation,[],[f266,f31]) ).
fof(f278,plain,
b = greatest_lower_bound(sF4,b),
inference(forward_demodulation,[],[f276,f40]) ).
fof(f281,plain,
! [X0] : greatest_lower_bound(b,X0) = greatest_lower_bound(sF4,greatest_lower_bound(b,X0)),
inference(superposition,[],[f7,f278]) ).
fof(f378,plain,
! [X0] : sF4 = least_upper_bound(sF4,greatest_lower_bound(b,X0)),
inference(superposition,[],[f11,f281]) ).
fof(f382,plain,
! [X0] : sF4 = least_upper_bound(sF4,greatest_lower_bound(X0,b)),
inference(superposition,[],[f378,f5]) ).
fof(f403,plain,
sF4 = least_upper_bound(sF4,sF3),
inference(superposition,[],[f382,f33]) ).
fof(f409,plain,
sF4 = least_upper_bound(sF4,identity),
inference(forward_demodulation,[],[f403,f34]) ).
fof(f411,plain,
sF4 = least_upper_bound(identity,sF4),
inference(forward_demodulation,[],[f409,f6]) ).
fof(f412,plain,
sF4 = sF5,
inference(forward_demodulation,[],[f411,f38]) ).
fof(f415,plain,
sF4 != sF4,
inference(superposition,[],[f39,f412]) ).
fof(f416,plain,
$false,
inference(trivial_inequality_removal,[],[f415]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP172-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n011.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 09:35:30 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 2.58/1.28 % (2152043)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.58/1.28 % (2152054)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2563106885:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.58/1.28 % (2152054)First to succeed.
% 2.58/1.28 % (2152054)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2152043"
% 2.58/1.28 % (2152053)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1592187596:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.58/1.28 % (2152052)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3932031913:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.58/1.28 % (2152050)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=2723570830:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.58/1.28 % (2152051)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=1664745685:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.58/1.28 % (2152056)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3884771098:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.58/1.28 % (2152055)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1493013472:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.58/1.28 % (2152053)Instruction limit reached!
% 2.58/1.28 % (2152053)------------------------------
% 2.58/1.28 % (2152053)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.28 % (2152053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.28 % (2152053)CaDiCaL version: 2.1.3
% 2.58/1.28 % (2152053)Termination reason: Instruction limit
% 2.58/1.28 % (2152053)Termination phase: Saturation
% 2.58/1.28 % (2152053)Time elapsed: 0.083 s
% 2.58/1.28 % (2152053)Peak memory usage: 89 MB
% 2.58/1.28 % (2152053)Instructions burned: 137 (million)
% 2.58/1.28 % (2152056)Also succeeded, but the first one will report.
% 2.58/1.28 % (2152054)Refutation found. Thanks to Tanya!
% 2.58/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.58/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 2.58/1.28 % (2152054)------------------------------
% 2.58/1.28 % (2152054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.28 % (2152054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.28 % (2152054)CaDiCaL version: 2.1.3
% 2.58/1.28 % (2152054)Termination reason: Refutation
% 2.58/1.28 % (2152054)Time elapsed: 0.006 s
% 2.58/1.28 % (2152054)Peak memory usage: 88 MB
% 2.58/1.28 % (2152054)Instructions burned: 15 (million)
% 2.58/1.28 % (2152054)------------------------------
% 2.58/1.28 % (2152054)------------------------------
% 2.58/1.28 % (2152043)Success in time 0.294 s
% 2.58/1.28 % Vampire exiting
%------------------------------------------------------------------------------