%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP556-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 2.62s 1.32s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 46 ( 46 unt; 8 def)
% Number of atoms : 46 ( 45 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 : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 67 ( 67 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : divide(divide(X0,inverse(divide(X1,divide(X0,X2)))),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_4) ).
fof(f4,plain,
divide(a,inverse(b)) != divide(b,inverse(a)),
inference(definition_unfolding,[],[f3,f2,f2]) ).
fof(f5,definition,
! [X2,X0,X1] : sF0(X1,X0,X2) = divide(X1,divide(X0,X2)),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f6,plain,
! [X2,X0,X1] : divide(X1,divide(X0,X2)) = sF0(X1,X0,X2),
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
! [X2,X0,X1] : sF1(X1,X0,X2) = inverse(sF0(X1,X0,X2)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f8,plain,
! [X2,X0,X1] : inverse(sF0(X1,X0,X2)) = sF1(X1,X0,X2),
inference(reorient_equations,[],[f7]) ).
fof(f9,definition,
! [X2,X0,X1] : sF2(X0,X1,X2) = divide(X0,sF1(X1,X0,X2)),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f10,plain,
! [X2,X0,X1] : divide(X0,sF1(X1,X0,X2)) = sF2(X0,X1,X2),
inference(reorient_equations,[],[f9]) ).
fof(f11,definition,
! [X2,X0,X1] : sF3(X0,X1,X2) = divide(sF2(X0,X1,X2),X2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f12,plain,
! [X2,X0,X1] : divide(sF2(X0,X1,X2),X2) = sF3(X0,X1,X2),
inference(reorient_equations,[],[f11]) ).
fof(f13,plain,
! [X2,X0,X1] : sF3(X0,X1,X2) = X1,
inference(definition_folding,[],[f1,f12,f10,f8,f6]) ).
fof(f14,definition,
sF4 = inverse(b),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f15,plain,
inverse(b) = sF4,
inference(reorient_equations,[],[f14]) ).
fof(f16,definition,
sF5 = divide(a,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f17,plain,
divide(a,sF4) = sF5,
inference(reorient_equations,[],[f16]) ).
fof(f18,definition,
sF6 = inverse(a),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f19,plain,
inverse(a) = sF6,
inference(reorient_equations,[],[f18]) ).
fof(f20,definition,
sF7 = divide(b,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f21,plain,
divide(b,sF6) = sF7,
inference(reorient_equations,[],[f20]) ).
fof(f22,plain,
sF5 != sF7,
inference(definition_folding,[],[f4,f21,f19,f17,f15]) ).
fof(f23,plain,
! [X2,X0,X1] : divide(sF2(X0,X1,X2),X2) = X1,
inference(forward_demodulation,[],[f13,f12]) ).
fof(f24,plain,
! [X2,X0,X1] : divide(divide(X0,sF1(X1,X0,X2)),X2) = X1,
inference(forward_demodulation,[],[f23,f10]) ).
fof(f25,plain,
! [X2,X0,X1] : divide(divide(X0,inverse(sF0(X1,X0,X2))),X2) = X1,
inference(forward_demodulation,[],[f24,f8]) ).
fof(f26,plain,
! [X2,X0,X1] : divide(divide(X0,inverse(divide(X1,divide(X0,X2)))),X2) = X1,
inference(forward_demodulation,[],[f25,f6]) ).
fof(f27,plain,
! [X0] : divide(divide(b,inverse(divide(X0,sF7))),sF6) = X0,
inference(superposition,[],[f26,f21]) ).
fof(f29,plain,
! [X2,X3,X0,X1] : divide(divide(divide(X1,inverse(divide(X0,divide(X1,X2)))),inverse(divide(X3,X0))),X2) = X3,
inference(superposition,[],[f26,f26]) ).
fof(f30,plain,
! [X2,X3,X0,X1] : divide(X2,inverse(divide(X0,divide(X2,divide(X1,X3))))) = divide(divide(X1,inverse(X0)),X3),
inference(superposition,[],[f26,f26]) ).
fof(f31,plain,
! [X0,X1] : divide(X1,inverse(divide(X0,divide(X1,sF7)))) = divide(divide(b,inverse(X0)),sF6),
inference(superposition,[],[f27,f26]) ).
fof(f37,plain,
! [X0] : divide(divide(divide(b,inverse(X0)),sF6),sF7) = X0,
inference(superposition,[],[f26,f31]) ).
fof(f142,plain,
! [X2,X0] : divide(X0,inverse(divide(X2,X0))) = X2,
inference(superposition,[],[f29,f26]) ).
fof(f187,plain,
! [X0] : divide(X0,b) = divide(divide(X0,sF6),sF7),
inference(superposition,[],[f37,f142]) ).
fof(f307,plain,
! [X2,X0,X1] : divide(divide(divide(X0,inverse(X1)),X2),divide(X0,X2)) = X1,
inference(superposition,[],[f26,f30]) ).
fof(f417,plain,
! [X0] : divide(divide(b,inverse(X0)),b) = X0,
inference(superposition,[],[f187,f37]) ).
fof(f488,plain,
! [X0] : divide(X0,divide(b,b)) = X0,
inference(superposition,[],[f417,f26]) ).
fof(f508,plain,
! [X0] : divide(divide(b,b),inverse(X0)) = X0,
inference(superposition,[],[f142,f488]) ).
fof(f751,plain,
b = divide(divide(b,b),sF4),
inference(superposition,[],[f508,f15]) ).
fof(f782,plain,
! [X0] : divide(divide(divide(divide(b,b),inverse(X0)),sF4),b) = X0,
inference(superposition,[],[f307,f751]) ).
fof(f783,plain,
! [X0] : divide(divide(X0,sF4),b) = X0,
inference(forward_demodulation,[],[f782,f508]) ).
fof(f797,plain,
a = divide(sF5,b),
inference(superposition,[],[f783,f17]) ).
fof(f815,plain,
divide(b,inverse(a)) = sF5,
inference(superposition,[],[f142,f797]) ).
fof(f819,plain,
sF5 = divide(b,sF6),
inference(forward_demodulation,[],[f815,f19]) ).
fof(f824,plain,
sF5 = sF7,
inference(forward_demodulation,[],[f819,f21]) ).
fof(f828,plain,
sF5 != sF5,
inference(superposition,[],[f22,f824]) ).
fof(f849,plain,
$false,
inference(trivial_inequality_removal,[],[f828]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP556-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:07:16 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.62/1.32 % (2176468)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.62/1.32 % (2176481)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=834422450:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.62/1.32 % (2176481)First to succeed.
% 2.62/1.32 % (2176481)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2176468"
% 2.62/1.32 % (2176483)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=902196160:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.62/1.32 % (2176480)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=113323502:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.62/1.32 % (2176482)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3022520334:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.62/1.32 % (2176479)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=630147309:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.62/1.32 % (2176477)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=1095202992:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.62/1.32 % (2176478)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=128964290:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.62/1.32 % (2176483)Also succeeded, but the first one will report.
% 2.62/1.32 % (2176480)Also succeeded, but the first one will report.
% 2.62/1.32 % (2176482)Also succeeded, but the first one will report.
% 2.62/1.32 % (2176481)Refutation found. Thanks to Tanya!
% 2.62/1.32 % SZS status Unsatisfiable for theBenchmark
% 2.62/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/1.32 % (2176481)------------------------------
% 2.62/1.32 % (2176481)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.32 % (2176481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.32 % (2176481)CaDiCaL version: 2.1.3
% 2.62/1.32 % (2176481)Termination reason: Refutation
% 2.62/1.32 % (2176481)Time elapsed: 0.014 s
% 2.62/1.32 % (2176481)Peak memory usage: 88 MB
% 2.62/1.32 % (2176481)Instructions burned: 42 (million)
% 2.62/1.32 % (2176481)------------------------------
% 2.62/1.32 % (2176481)------------------------------
% 2.62/1.32 % (2176468)Success in time 0.284 s
% 2.62/1.32 % Vampire exiting
%------------------------------------------------------------------------------