%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP185-2 : 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 : n002.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 10:13:15 AM UTC 2026
% Result : Unsatisfiable 2.63s 1.32s
% Output : Refutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 46 ( 46 unt; 1 def)
% Number of atoms : 46 ( 25 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 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 : 45 ( 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
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(f11,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
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',p22a_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',p22a_2) ).
fof(f20,axiom,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22a_3) ).
fof(f21,negated_conjecture,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p22a) ).
fof(f22,plain,
multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) != least_upper_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(multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f24,plain,
sP0(least_upper_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(least_upper_bound(multiply(a,least_upper_bound(b,identity)),multiply(identity,least_upper_bound(b,identity)))),
inference(backward_demodulation,[],[f23,f15]) ).
fof(f26,plain,
sP0(least_upper_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(f27,plain,
sP0(least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,least_upper_bound(b,identity)),multiply(identity,least_upper_bound(b,identity)))))),
inference(forward_demodulation,[],[f26,f8]) ).
fof(f28,plain,
~ sP0(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(f29,plain,
sP0(least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,least_upper_bound(b,identity)),least_upper_bound(multiply(identity,b),multiply(identity,identity)))))),
inference(forward_demodulation,[],[f27,f13]) ).
fof(f30,plain,
~ sP0(least_upper_bound(multiply(a,least_upper_bound(b,identity)),least_upper_bound(multiply(identity,b),identity))),
inference(forward_demodulation,[],[f28,f1]) ).
fof(f31,plain,
sP0(least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,least_upper_bound(b,identity)),least_upper_bound(multiply(identity,b),identity))))),
inference(forward_demodulation,[],[f29,f1]) ).
fof(f32,plain,
~ sP0(least_upper_bound(multiply(a,least_upper_bound(b,identity)),least_upper_bound(b,identity))),
inference(forward_demodulation,[],[f30,f1]) ).
fof(f33,plain,
sP0(least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,least_upper_bound(b,identity)),least_upper_bound(b,identity))))),
inference(forward_demodulation,[],[f31,f1]) ).
fof(f34,plain,
~ sP0(least_upper_bound(least_upper_bound(multiply(a,b),multiply(a,identity)),least_upper_bound(b,identity))),
inference(forward_demodulation,[],[f32,f13]) ).
fof(f35,plain,
sP0(least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(least_upper_bound(multiply(a,b),multiply(a,identity)),least_upper_bound(b,identity))))),
inference(forward_demodulation,[],[f33,f13]) ).
fof(f36,plain,
~ sP0(least_upper_bound(multiply(a,b),least_upper_bound(multiply(a,identity),least_upper_bound(b,identity)))),
inference(forward_demodulation,[],[f34,f8]) ).
fof(f37,plain,
sP0(least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,b),least_upper_bound(multiply(a,identity),least_upper_bound(b,identity)))))),
inference(forward_demodulation,[],[f35,f8]) ).
fof(f55,plain,
! [X0,X1] : least_upper_bound(X1,greatest_lower_bound(X0,X1)) = X1,
inference(superposition,[],[f11,f5]) ).
fof(f66,plain,
! [X0] : inverse(multiply(identity,X0)) = multiply(inverse(X0),identity),
inference(superposition,[],[f20,f18]) ).
fof(f83,plain,
! [X0] : inverse(X0) = multiply(inverse(X0),identity),
inference(forward_demodulation,[],[f66,f1]) ).
fof(f90,plain,
! [X0] : multiply(X0,identity) = X0,
inference(superposition,[],[f83,f19]) ).
fof(f99,plain,
sP0(least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,b),least_upper_bound(a,least_upper_bound(b,identity)))))),
inference(backward_demodulation,[],[f37,f90]) ).
fof(f100,plain,
~ sP0(least_upper_bound(multiply(a,b),least_upper_bound(a,least_upper_bound(b,identity)))),
inference(backward_demodulation,[],[f36,f90]) ).
fof(f170,plain,
! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X2,least_upper_bound(X0,X1)),
inference(superposition,[],[f6,f8]) ).
fof(f329,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(least_upper_bound(X0,X1),X0),
inference(superposition,[],[f55,f12]) ).
fof(f339,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X1,X0)),
inference(forward_demodulation,[],[f329,f8]) ).
fof(f849,plain,
! [X2,X0,X1] : least_upper_bound(X2,least_upper_bound(X0,X1)) = least_upper_bound(X2,least_upper_bound(X0,least_upper_bound(X1,X2))),
inference(superposition,[],[f339,f8]) ).
fof(f851,plain,
! [X2,X0,X1] : least_upper_bound(least_upper_bound(X0,X1),X2) = least_upper_bound(X0,least_upper_bound(least_upper_bound(X1,X0),X2)),
inference(superposition,[],[f8,f339]) ).
fof(f861,plain,
! [X2,X0,X1] : least_upper_bound(least_upper_bound(X0,X1),X2) = least_upper_bound(X0,least_upper_bound(X1,least_upper_bound(X0,X2))),
inference(forward_demodulation,[],[f851,f8]) ).
fof(f868,plain,
! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X0,least_upper_bound(X1,least_upper_bound(X0,X2))),
inference(forward_demodulation,[],[f861,f8]) ).
fof(f874,plain,
sP0(least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(a,least_upper_bound(b,identity))))),
inference(backward_demodulation,[],[f99,f868]) ).
fof(f879,plain,
sP0(least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(a,b)))),
inference(forward_demodulation,[],[f874,f849]) ).
fof(f1451,plain,
sP0(least_upper_bound(multiply(a,b),least_upper_bound(a,least_upper_bound(b,identity)))),
inference(superposition,[],[f879,f170]) ).
fof(f1465,plain,
$false,
inference(forward_subsumption_resolution,[],[f1451,f100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP185-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n002.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 09:39:07 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 2.63/1.32 % (3294221)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.63/1.32 % (3294233)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3961134605:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.63/1.32 % (3294233)First to succeed.
% 2.63/1.32 % (3294233)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3294221"
% 2.63/1.32 % (3294232)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4145762203:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.63/1.32 % (3294231)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=784273030:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.63/1.32 % (3294230)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=4013363040:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.63/1.32 % (3294235)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=159998247:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.63/1.32 % (3294236)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1866465015:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.63/1.32 % (3294234)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3309354312:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.63/1.32 % (3294235)Also succeeded, but the first one will report.
% 2.63/1.32 % (3294234)Instruction limit reached!
% 2.63/1.32 % (3294234)------------------------------
% 2.63/1.32 % (3294234)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.32 % (3294234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.32 % (3294234)CaDiCaL version: 2.1.3
% 2.63/1.32 % (3294234)Termination reason: Instruction limit
% 2.63/1.32 % (3294234)Termination phase: Saturation
% 2.63/1.32 % (3294234)Time elapsed: 0.110 s
% 2.63/1.32 % (3294234)Peak memory usage: 89 MB
% 2.63/1.32 % (3294234)Instructions burned: 182 (million)
% 2.63/1.32 % (3294233)Refutation found. Thanks to Tanya!
% 2.63/1.32 % SZS status Unsatisfiable for theBenchmark
% 2.63/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.63/1.32 % (3294233)------------------------------
% 2.63/1.32 % (3294233)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.32 % (3294233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.32 % (3294233)CaDiCaL version: 2.1.3
% 2.63/1.32 % (3294233)Termination reason: Refutation
% 2.63/1.32 % (3294233)Time elapsed: 0.019 s
% 2.63/1.32 % (3294233)Peak memory usage: 88 MB
% 2.63/1.32 % (3294233)Instructions burned: 56 (million)
% 2.63/1.32 % (3294233)------------------------------
% 2.63/1.32 % (3294233)------------------------------
% 2.63/1.32 % (3294221)Success in time 0.282 s
% 2.63/1.32 % Vampire exiting
%------------------------------------------------------------------------------