%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP185-4 : 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 10:13:16 AM UTC 2026
% Result : Unsatisfiable 6.10s 2.34s
% Output : Refutation 6.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 33 ( 33 unt; 1 def)
% Number of atoms : 33 ( 17 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 : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [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(f8,axiom,
! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_lub) ).
fof(f12,axiom,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).
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,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22b_1) ).
fof(f18,plain,
identity = inverse(identity),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
! [X0] : inverse(inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22b_2) ).
fof(f20,axiom,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22b_3) ).
fof(f21,negated_conjecture,
greatest_lower_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p22b) ).
fof(f22,plain,
least_upper_bound(multiply(a,b),identity) != greatest_lower_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))),
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
~ sP0(least_upper_bound(multiply(a,b),identity)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f24,plain,
sP0(greatest_lower_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))),
inference(inequality_splitting,[],[f22,f23]) ).
fof(f25,plain,
sP0(greatest_lower_bound(least_upper_bound(multiply(a,b),identity),least_upper_bound(multiply(a,least_upper_bound(b,identity)),multiply(identity,least_upper_bound(b,identity))))),
inference(backward_demodulation,[],[f24,f15]) ).
fof(f26,plain,
sP0(greatest_lower_bound(least_upper_bound(multiply(a,b),identity),least_upper_bound(multiply(a,least_upper_bound(b,identity)),least_upper_bound(multiply(identity,b),multiply(identity,identity))))),
inference(forward_demodulation,[],[f25,f13]) ).
fof(f27,plain,
sP0(greatest_lower_bound(least_upper_bound(multiply(a,b),identity),least_upper_bound(multiply(a,least_upper_bound(b,identity)),least_upper_bound(multiply(identity,b),identity)))),
inference(forward_demodulation,[],[f26,f1]) ).
fof(f28,plain,
sP0(greatest_lower_bound(least_upper_bound(multiply(a,b),identity),least_upper_bound(multiply(a,least_upper_bound(b,identity)),least_upper_bound(b,identity)))),
inference(forward_demodulation,[],[f27,f1]) ).
fof(f29,plain,
sP0(greatest_lower_bound(least_upper_bound(multiply(a,b),identity),least_upper_bound(least_upper_bound(multiply(a,b),multiply(a,identity)),least_upper_bound(b,identity)))),
inference(forward_demodulation,[],[f28,f13]) ).
fof(f30,plain,
sP0(greatest_lower_bound(least_upper_bound(multiply(a,b),identity),least_upper_bound(multiply(a,b),least_upper_bound(multiply(a,identity),least_upper_bound(b,identity))))),
inference(forward_demodulation,[],[f29,f8]) ).
fof(f41,plain,
sP0(greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(a,b),least_upper_bound(multiply(a,identity),least_upper_bound(b,identity))))),
inference(superposition,[],[f30,f6]) ).
fof(f42,plain,
~ sP0(least_upper_bound(identity,multiply(a,b))),
inference(superposition,[],[f23,f6]) ).
fof(f51,plain,
! [X0,X1] : greatest_lower_bound(X1,least_upper_bound(X0,X1)) = X1,
inference(superposition,[],[f12,f6]) ).
fof(f63,plain,
! [X0] : inverse(multiply(identity,X0)) = multiply(inverse(X0),identity),
inference(superposition,[],[f20,f18]) ).
fof(f80,plain,
! [X0] : inverse(X0) = multiply(inverse(X0),identity),
inference(forward_demodulation,[],[f63,f1]) ).
fof(f119,plain,
! [X0] : multiply(X0,identity) = X0,
inference(superposition,[],[f80,f19]) ).
fof(f129,plain,
sP0(greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(a,b),least_upper_bound(a,least_upper_bound(b,identity))))),
inference(backward_demodulation,[],[f41,f119]) ).
fof(f167,plain,
sP0(greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(a,least_upper_bound(b,identity)),multiply(a,b)))),
inference(superposition,[],[f129,f6]) ).
fof(f168,plain,
sP0(greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(a,least_upper_bound(least_upper_bound(b,identity),multiply(a,b))))),
inference(forward_demodulation,[],[f167,f8]) ).
fof(f170,plain,
sP0(greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))))),
inference(forward_demodulation,[],[f168,f8]) ).
fof(f354,plain,
! [X2,X0,X1] : greatest_lower_bound(X2,least_upper_bound(X0,least_upper_bound(X1,X2))) = X2,
inference(superposition,[],[f51,f8]) ).
fof(f365,plain,
sP0(least_upper_bound(identity,multiply(a,b))),
inference(backward_demodulation,[],[f170,f354]) ).
fof(f368,plain,
$false,
inference(forward_subsumption_resolution,[],[f365,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP185-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.48 % Computer : n016.cluster.edu
% 0.21/0.48 % Model : x86_64 x86_64
% 0.21/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.48 % Memory : 8046.5625MB
% 0.21/0.48 % OS : Linux 6.8.0-71-generic
% 0.21/0.48 % CPULimit : 300
% 0.21/0.48 % WCLimit : 300
% 0.21/0.48 % DateTime : Sun Sep 27 09:41:17 UTC 2026
% 0.21/0.48 % CPUTime :
% 0.21/0.48 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.54 Running first-order theorem proving
% 0.27/0.54 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
% 6.10/2.34 % (2371762)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.10/2.34 % (2371771)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3083041313:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.10/2.34 % (2371767)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=4247344617:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.10/2.34 % (2371770)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3482790487:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.10/2.34 % (2371772)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4272218749:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.10/2.34 % (2371769)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1059108472:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.10/2.34 % (2371768)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=2732913150:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.10/2.34 % (2371770)First to succeed.
% 6.10/2.34 % (2371770)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2371762"
% 6.10/2.34 % (2371772)Also succeeded, but the first one will report.
% 6.10/2.34 % (2371773)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1550722427:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.10/2.34 % (2371771)Instruction limit reached!
% 6.10/2.34 % (2371771)------------------------------
% 6.10/2.34 % (2371771)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/2.34 % (2371771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/2.34 % (2371771)CaDiCaL version: 2.1.3
% 6.10/2.34 % (2371771)Termination reason: Instruction limit
% 6.10/2.34 % (2371771)Termination phase: Saturation
% 6.10/2.34 % (2371771)Time elapsed: 0.100 s
% 6.10/2.34 % (2371771)Peak memory usage: 89 MB
% 6.10/2.34 % (2371771)Instructions burned: 183 (million)
% 6.10/2.34 % (2371781)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2195666234:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 6.10/2.34 % (2371770)Refutation found. Thanks to Tanya!
% 6.10/2.34 % SZS status Unsatisfiable for theBenchmark
% 6.10/2.34 % SZS output start Proof for theBenchmark
% See solution above
% 6.10/2.34 % (2371770)------------------------------
% 6.10/2.34 % (2371770)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/2.34 % (2371770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/2.34 % (2371770)CaDiCaL version: 2.1.3
% 6.10/2.34 % (2371770)Termination reason: Refutation
% 6.10/2.34 % (2371770)Time elapsed: 0.020 s
% 6.10/2.34 % (2371770)Peak memory usage: 88 MB
% 6.10/2.34 % (2371770)Instructions burned: 17 (million)
% 6.10/2.34 % (2371770)------------------------------
% 6.10/2.34 % (2371770)------------------------------
% 6.10/2.34 % (2371762)Success in time 0.706 s
% 6.10/2.34 % Vampire exiting
%------------------------------------------------------------------------------