%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP526-1 : 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 : n009.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 10:14:47 AM UTC 2026
% Result : Unsatisfiable 4.77s 1.92s
% Output : Refutation 4.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 57 ( 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(X0,divide(divide(X0,X1),divide(X2,X1))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f4,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f5,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f4]) ).
fof(f6,plain,
! [X0,X1] : inverse(X1) = divide(inverse(divide(X0,X0)),X1),
inference(superposition,[],[f3,f3]) ).
fof(f7,plain,
! [X0,X1] : inverse(X1) = divide(inverse(inverse(divide(X0,X0))),X1),
inference(superposition,[],[f6,f3]) ).
fof(f24,plain,
! [X0,X1] : divide(X1,inverse(divide(X0,X1))) = X0,
inference(superposition,[],[f1,f3]) ).
fof(f28,plain,
! [X2,X0,X1] : inverse(divide(divide(divide(X1,X1),X2),divide(X0,X2))) = X0,
inference(superposition,[],[f3,f1]) ).
fof(f33,plain,
! [X2,X0] : inverse(divide(inverse(X2),divide(X0,X2))) = X0,
inference(forward_demodulation,[],[f28,f3]) ).
fof(f62,plain,
! [X0,X1] : inverse(X1) = divide(divide(X0,X1),X0),
inference(superposition,[],[f24,f33]) ).
fof(f69,plain,
! [X0,X1] : divide(divide(X1,X0),inverse(X0)) = X1,
inference(superposition,[],[f1,f62]) ).
fof(f74,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[],[f2,f3]) ).
fof(f76,plain,
! [X0,X1] : multiply(X1,divide(X0,X1)) = X0,
inference(superposition,[],[f74,f24]) ).
fof(f78,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(divide(X1,X1),X0),
inference(superposition,[],[f74,f3]) ).
fof(f87,plain,
! [X0,X1] : divide(inverse(X1),inverse(multiply(X0,X1))) = X0,
inference(superposition,[],[f24,f74]) ).
fof(f96,plain,
! [X0,X1] : multiply(inverse(X1),multiply(X0,X1)) = X0,
inference(forward_demodulation,[],[f87,f74]) ).
fof(f97,plain,
! [X0,X1] : divide(X1,X0) = multiply(X1,inverse(X0)),
inference(superposition,[],[f76,f62]) ).
fof(f107,plain,
! [X0,X1] : multiply(divide(X1,X0),X0) = X1,
inference(forward_demodulation,[],[f69,f74]) ).
fof(f119,plain,
! [X0,X1] : divide(divide(X0,inverse(X1)),X1) = X0,
inference(superposition,[],[f107,f97]) ).
fof(f120,plain,
! [X0,X1] : divide(multiply(X0,X1),X1) = X0,
inference(forward_demodulation,[],[f119,f74]) ).
fof(f122,plain,
! [X0,X1] : divide(X0,divide(X0,X1)) = X1,
inference(superposition,[],[f120,f76]) ).
fof(f131,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(superposition,[],[f76,f120]) ).
fof(f156,plain,
! [X0,X1] : inverse(divide(inverse(inverse(divide(X1,X1))),X0)) = X0,
inference(superposition,[],[f7,f122]) ).
fof(f157,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f156,f7]) ).
fof(f191,plain,
a2 != multiply(multiply(b2,inverse(b2)),a2),
inference(superposition,[],[f5,f131]) ).
fof(f192,plain,
a2 != multiply(a2,multiply(b2,inverse(b2))),
inference(forward_demodulation,[],[f191,f131]) ).
fof(f196,plain,
a2 != multiply(a2,divide(b2,b2)),
inference(forward_demodulation,[],[f192,f97]) ).
fof(f200,plain,
! [X0,X1] : multiply(divide(X1,X1),X0) = X0,
inference(forward_demodulation,[],[f78,f157]) ).
fof(f213,plain,
! [X0,X1] : divide(X1,X1) = multiply(inverse(X0),X0),
inference(superposition,[],[f96,f200]) ).
fof(f215,plain,
! [X0,X1] : divide(X1,X1) = multiply(X0,inverse(X0)),
inference(forward_demodulation,[],[f213,f131]) ).
fof(f219,plain,
! [X0,X1] : divide(X1,X1) = divide(X0,X0),
inference(forward_demodulation,[],[f215,f97]) ).
fof(f297,plain,
! [X0] : a2 != multiply(a2,divide(X0,X0)),
inference(superposition,[],[f196,f219]) ).
fof(f351,plain,
a2 != a2,
inference(superposition,[],[f297,f76]) ).
fof(f352,plain,
$false,
inference(trivial_inequality_removal,[],[f351]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP526-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n009.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 10:06:45 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 4.77/1.92 % (1793178)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.77/1.92 % (1793183)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=2433179080:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.77/1.92 % (1793189)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=897877416:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.77/1.92 % (1793189)First to succeed.
% 4.77/1.92 % (1793189)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1793178"
% 4.77/1.92 % (1793185)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2895825022:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.77/1.92 % (1793184)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=3951555705:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.77/1.92 % (1793186)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2987966570:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.77/1.92 % (1793186)Also succeeded, but the first one will report.
% 4.77/1.92 % (1793187)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3260436425:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.77/1.92 % (1793188)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=65773180:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.77/1.92 % (1793188)Also succeeded, but the first one will report.
% 4.77/1.92 % (1793187)Also succeeded, but the first one will report.
% 4.77/1.92 % (1793189)Refutation found. Thanks to Tanya!
% 4.77/1.92 % SZS status Unsatisfiable for theBenchmark
% 4.77/1.92 % SZS output start Proof for theBenchmark
% See solution above
% 4.77/1.92 % (1793189)------------------------------
% 4.77/1.92 % (1793189)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.92 % (1793189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.92 % (1793189)CaDiCaL version: 2.1.3
% 4.77/1.92 % (1793189)Termination reason: Refutation
% 4.77/1.92 % (1793189)Time elapsed: 0.009 s
% 4.77/1.92 % (1793189)Peak memory usage: 88 MB
% 4.77/1.92 % (1793189)Instructions burned: 12 (million)
% 4.77/1.92 % (1793189)------------------------------
% 4.77/1.92 % (1793189)------------------------------
% 4.77/1.92 % (1793178)Success in time 0.534 s
% 4.77/1.92 % Vampire exiting
%------------------------------------------------------------------------------