%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP553-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 10:14:51 AM UTC 2026
% Result : Unsatisfiable 0.17s 1.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 21 unt; 1 def)
% Number of atoms : 21 ( 16 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 : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(divide(X0,inverse(divide(X1,divide(X0,X2)))),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
fof(f4,plain,
divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1)),
inference(definition_unfolding,[],[f3,f2,f2]) ).
fof(f5,definition,
~ sP0(divide(inverse(a1),inverse(a1))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f6,plain,
sP0(divide(inverse(b1),inverse(b1))),
inference(inequality_splitting,[],[f4,f5]) ).
fof(f7,plain,
! [X2,X3,X0,X1] : divide(divide(divide(X1,inverse(divide(X0,divide(X1,X2)))),inverse(divide(X3,X0))),X2) = X3,
inference(superposition,[],[f1,f1]) ).
fof(f8,plain,
! [X2,X3,X0,X1] : divide(X2,inverse(divide(X0,divide(X2,divide(X1,X3))))) = divide(divide(X1,inverse(X0)),X3),
inference(superposition,[],[f1,f1]) ).
fof(f15,plain,
! [X2,X0] : divide(X0,inverse(divide(X2,X0))) = X2,
inference(superposition,[],[f7,f1]) ).
fof(f19,plain,
! [X2,X3,X0,X1] : divide(X1,inverse(X0)) = divide(divide(X2,inverse(divide(X3,divide(X2,X1)))),inverse(divide(X0,X3))),
inference(superposition,[],[f15,f7]) ).
fof(f27,plain,
! [X2,X3] : divide(divide(X2,inverse(X3)),X2) = X3,
inference(backward_demodulation,[],[f7,f19]) ).
fof(f34,plain,
! [X0,X1] : divide(X0,divide(X1,X1)) = X0,
inference(superposition,[],[f1,f27]) ).
fof(f44,plain,
! [X0,X1] : divide(divide(X0,X0),inverse(X1)) = X1,
inference(superposition,[],[f27,f34]) ).
fof(f104,plain,
! [X2,X3,X0,X1] : divide(X1,inverse(divide(X2,divide(X1,X0)))) = divide(divide(divide(X3,X3),inverse(X2)),inverse(X0)),
inference(superposition,[],[f8,f44]) ).
fof(f108,plain,
! [X2,X0,X1] : divide(X2,inverse(X0)) = divide(X1,inverse(divide(X2,divide(X1,X0)))),
inference(forward_demodulation,[],[f104,f44]) ).
fof(f119,plain,
! [X3,X0,X1] : divide(divide(X1,inverse(X0)),X3) = divide(X0,inverse(divide(X1,X3))),
inference(backward_demodulation,[],[f8,f108]) ).
fof(f142,plain,
! [X2,X3] : divide(X3,inverse(divide(X2,X2))) = X3,
inference(backward_demodulation,[],[f27,f119]) ).
fof(f214,plain,
! [X0,X1] : divide(X1,X1) = divide(X0,X0),
inference(superposition,[],[f44,f142]) ).
fof(f231,plain,
! [X0] : ~ sP0(divide(X0,X0)),
inference(superposition,[],[f5,f214]) ).
fof(f232,plain,
! [X0] : sP0(divide(X0,X0)),
inference(superposition,[],[f6,f214]) ).
fof(f239,plain,
$false,
inference(forward_subsumption_resolution,[],[f231,f232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP553-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n013.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 10:06:21 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 0.17/1.50 % (4177969)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.17/1.50 % (4178068)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=576219395:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.17/1.50 % (4178070)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3705346121:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.17/1.50 % (4178072)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1047225974:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.17/1.50 % (4178067)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=863083733:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.17/1.50 % (4178069)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2585114988:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.17/1.50 % (4178066)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=3016845711:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.17/1.50 % (4178069)First to succeed.
% 0.17/1.50 % (4178070)Also succeeded, but the first one will report.
% 0.17/1.50 % (4178069)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4177969"
% 0.17/1.50 % (4178072)Also succeeded, but the first one will report.
% 0.17/1.50 % (4178071)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1033859312:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.17/1.50 % (4178071)Also succeeded, but the first one will report.
% 0.17/1.50 % (4178069)Refutation found. Thanks to Tanya!
% 0.17/1.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (4178069)------------------------------
% 0.17/1.50 % (4178069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (4178069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (4178069)CaDiCaL version: 2.1.3
% 0.17/1.50 % (4178069)Termination reason: Refutation
% 0.17/1.50 % (4178069)Time elapsed: 0.015 s
% 0.17/1.50 % (4178069)Peak memory usage: 88 MB
% 0.17/1.50 % (4178069)Instructions burned: 21 (million)
% 0.17/1.50 % (4178069)------------------------------
% 0.17/1.50 % (4178069)------------------------------
% 0.17/1.50 % (4177969)Success in time 0.458 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------