%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP115-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 10:12:37 AM UTC 2026
% Result : Unsatisfiable 0.25s 1.71s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 40 ( 40 unt; 1 def)
% Number of atoms : 40 ( 36 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 90 ( 90 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X1),X2)),multiply(identity,multiply(X2,X2)))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(a,multiply(a,a)) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_order3) ).
fof(f3,plain,
identity != multiply(a,multiply(a,a)),
inference(reorient_equations,[],[f2]) ).
fof(f4,definition,
~ sP0(multiply(a,multiply(a,a))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f5,plain,
sP0(identity),
inference(inequality_splitting,[],[f3,f4]) ).
fof(f9,plain,
! [X2,X0,X1] : multiply(X1,multiply(multiply(X1,multiply(multiply(X1,X2),multiply(identity,multiply(multiply(identity,X0),multiply(identity,X0))))),X0)) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f13,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(multiply(X1,multiply(multiply(X1,X2),multiply(identity,multiply(X0,X0)))),multiply(multiply(identity,multiply(multiply(identity,X0),multiply(identity,multiply(multiply(identity,X3),multiply(identity,X3))))),X3))) = X2,
inference(superposition,[],[f9,f9]) ).
fof(f15,plain,
! [X2,X0,X1] : multiply(multiply(X1,X0),multiply(identity,X2)) = multiply(X1,multiply(X0,X2)),
inference(superposition,[],[f9,f1]) ).
fof(f17,plain,
! [X2,X0,X1] : multiply(multiply(X1,X0),multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2)))) = multiply(X1,multiply(X0,multiply(identity,multiply(X2,X2)))),
inference(superposition,[],[f1,f9]) ).
fof(f18,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(multiply(X1,multiply(X0,X3)),multiply(identity,multiply(X3,X3)))) = multiply(multiply(X1,multiply(multiply(X1,X0),multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))))),X2),
inference(superposition,[],[f1,f9]) ).
fof(f20,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(multiply(X1,multiply(X0,X3)),multiply(identity,multiply(X3,X3)))) = multiply(multiply(X1,multiply(X1,multiply(X0,multiply(identity,multiply(X2,X2))))),X2),
inference(backward_demodulation,[],[f18,f17]) ).
fof(f25,plain,
! [X2,X0,X1] : multiply(X0,multiply(X0,multiply(multiply(multiply(X0,X1),X2),multiply(X2,X2)))) = X1,
inference(backward_demodulation,[],[f1,f15]) ).
fof(f30,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(multiply(X1,multiply(multiply(X1,X2),multiply(identity,multiply(X0,X0)))),multiply(multiply(identity,multiply(identity,multiply(X0,multiply(multiply(identity,X3),multiply(identity,X3))))),X3))) = X2,
inference(forward_demodulation,[],[f13,f15]) ).
fof(f35,plain,
! [X2,X3,X0,X1] : multiply(multiply(X1,multiply(X1,multiply(X0,multiply(identity,multiply(X2,X2))))),X2) = multiply(X1,multiply(X1,multiply(multiply(X0,X3),multiply(X3,X3)))),
inference(forward_demodulation,[],[f20,f15]) ).
fof(f40,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(multiply(X1,multiply(multiply(X1,X2),multiply(identity,multiply(X0,X0)))),multiply(multiply(identity,multiply(identity,multiply(X0,multiply(identity,multiply(X3,X3))))),X3))) = X2,
inference(forward_demodulation,[],[f30,f15]) ).
fof(f44,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(multiply(X1,multiply(X1,multiply(X2,multiply(X0,X0)))),multiply(multiply(identity,multiply(identity,multiply(X0,multiply(identity,multiply(X3,X3))))),X3))) = X2,
inference(forward_demodulation,[],[f40,f15]) ).
fof(f54,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(multiply(X0,X1),multiply(identity,identity)))) = X1,
inference(superposition,[],[f25,f15]) ).
fof(f57,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(X0,multiply(X1,identity)))) = X1,
inference(forward_demodulation,[],[f54,f15]) ).
fof(f62,plain,
! [X2,X0,X1] : multiply(X1,multiply(X1,multiply(X0,identity))) = multiply(X1,multiply(X1,multiply(multiply(X0,X2),multiply(X2,X2)))),
inference(superposition,[],[f25,f57]) ).
fof(f63,plain,
! [X2,X0,X1] : multiply(X1,multiply(multiply(X1,multiply(X1,multiply(X0,identity))),X2)) = multiply(X0,multiply(identity,X2)),
inference(superposition,[],[f15,f57]) ).
fof(f66,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(multiply(X0,X1),identity))) = X1,
inference(backward_demodulation,[],[f25,f62]) ).
fof(f69,plain,
! [X2,X0,X1] : multiply(multiply(X1,multiply(X1,multiply(X0,multiply(identity,multiply(X2,X2))))),X2) = multiply(X1,multiply(X1,multiply(X0,identity))),
inference(backward_demodulation,[],[f35,f62]) ).
fof(f75,plain,
! [X2,X0,X1] : multiply(X1,multiply(multiply(X1,multiply(X1,multiply(X2,multiply(X0,X0)))),multiply(identity,multiply(identity,multiply(X0,identity))))) = X2,
inference(backward_demodulation,[],[f44,f69]) ).
fof(f80,plain,
! [X2,X0,X1] : multiply(X1,multiply(X1,multiply(multiply(X1,multiply(X2,multiply(X0,X0))),multiply(identity,multiply(X0,identity))))) = X2,
inference(forward_demodulation,[],[f75,f15]) ).
fof(f81,plain,
! [X2,X0,X1] : multiply(X1,multiply(X1,multiply(X1,multiply(multiply(X2,multiply(X0,X0)),multiply(X0,identity))))) = X2,
inference(forward_demodulation,[],[f80,f15]) ).
fof(f83,plain,
! [X0,X1] : multiply(X1,multiply(X1,multiply(X0,identity))) = multiply(X1,multiply(multiply(X1,X0),identity)),
inference(superposition,[],[f66,f66]) ).
fof(f91,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(multiply(multiply(X0,X1),identity),identity))) = multiply(X0,multiply(multiply(X0,multiply(X0,multiply(X1,identity))),identity)),
inference(superposition,[],[f83,f83]) ).
fof(f93,plain,
! [X2,X0,X1] : multiply(X0,multiply(multiply(multiply(X0,X1),identity),X2)) = multiply(multiply(X0,multiply(X0,multiply(X1,identity))),multiply(identity,X2)),
inference(superposition,[],[f15,f83]) ).
fof(f96,plain,
! [X2,X0,X1] : multiply(X0,multiply(multiply(multiply(X0,X1),identity),X2)) = multiply(X0,multiply(multiply(X0,multiply(X1,identity)),X2)),
inference(forward_demodulation,[],[f93,f15]) ).
fof(f97,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(multiply(multiply(X0,X1),identity),identity))) = multiply(X1,multiply(identity,identity)),
inference(forward_demodulation,[],[f91,f63]) ).
fof(f100,plain,
! [X0,X1] : multiply(X1,multiply(identity,identity)) = multiply(X0,multiply(X0,multiply(multiply(X0,multiply(X1,identity)),identity))),
inference(forward_demodulation,[],[f97,f96]) ).
fof(f102,plain,
! [X0,X1] : multiply(X1,multiply(identity,identity)) = multiply(X0,multiply(X0,multiply(X0,multiply(multiply(X1,identity),identity)))),
inference(forward_demodulation,[],[f100,f83]) ).
fof(f104,plain,
! [X1] : multiply(X1,identity) = multiply(X1,multiply(identity,identity)),
inference(forward_demodulation,[],[f102,f57]) ).
fof(f147,plain,
! [X0] : identity = multiply(X0,multiply(X0,multiply(X0,identity))),
inference(superposition,[],[f57,f104]) ).
fof(f164,plain,
! [X0,X1] : multiply(X1,multiply(X1,multiply(X1,multiply(multiply(X0,multiply(identity,identity)),identity)))) = X0,
inference(superposition,[],[f81,f104]) ).
fof(f168,plain,
! [X0] : multiply(X0,multiply(identity,identity)) = X0,
inference(forward_demodulation,[],[f164,f57]) ).
fof(f174,plain,
! [X1] : multiply(X1,identity) = X1,
inference(backward_demodulation,[],[f104,f168]) ).
fof(f190,plain,
! [X0] : identity = multiply(X0,multiply(X0,X0)),
inference(backward_demodulation,[],[f147,f174]) ).
fof(f202,plain,
~ sP0(identity),
inference(backward_demodulation,[],[f4,f190]) ).
fof(f219,plain,
$false,
inference(forward_subsumption_resolution,[],[f202,f5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP115-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n007.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 27 09:17:24 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 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
% 0.25/1.71 % (1150162)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.25/1.71 % (1150170)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3181621173:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.25/1.71 % (1150169)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2865581761:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.25/1.71 % (1150173)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4253039552:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.25/1.71 % (1150170)First to succeed.
% 0.25/1.71 % (1150170)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1150162"
% 0.25/1.71 % (1150173)Also succeeded, but the first one will report.
% 0.25/1.71 % (1150167)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=2262240735:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.25/1.71 % (1150171)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1383174240:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.25/1.71 % (1150168)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=1256905433:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.25/1.71 % (1150172)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=848137365:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.25/1.71 % (1150171)Also succeeded, but the first one will report.
% 0.25/1.71 % (1150172)Also succeeded, but the first one will report.
% 0.25/1.71 % (1150170)Refutation found. Thanks to Tanya!
% 0.25/1.71 % SZS status Unsatisfiable for theBenchmark
% 0.25/1.71 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/1.71 % (1150170)------------------------------
% 0.25/1.71 % (1150170)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.25/1.71 % (1150170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/1.71 % (1150170)CaDiCaL version: 2.1.3
% 0.25/1.71 % (1150170)Termination reason: Refutation
% 0.25/1.71 % (1150170)Time elapsed: 0.013 s
% 0.25/1.71 % (1150170)Peak memory usage: 88 MB
% 0.25/1.71 % (1150170)Instructions burned: 22 (million)
% 0.25/1.71 % (1150170)------------------------------
% 0.25/1.71 % (1150170)------------------------------
% 0.25/1.71 % (1150162)Success in time 0.455 s
% 0.25/1.71 % Vampire exiting
%------------------------------------------------------------------------------