%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP585-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 10:14:55 AM UTC 2026
% Result : Unsatisfiable 3.40s 1.34s
% Output : Refutation 3.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 14
% Syntax : Number of formulae : 102 ( 102 unt; 11 def)
% Number of atoms : 102 ( 101 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-3 aty)
% Number of variables : 79 ( 79 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : double_divide(X0,inverse(double_divide(inverse(double_divide(double_divide(X0,X1),inverse(X2))),X1))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
fof(f4,plain,
inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))),
inference(definition_unfolding,[],[f3,f2,f2]) ).
fof(f5,definition,
! [X2,X0,X1] : sF0(X0,X1,X2) = double_divide(double_divide(X0,X1),inverse(X2)),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f6,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,X1),inverse(X2)) = sF0(X0,X1,X2),
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
! [X2,X0,X1] : sF1(X0,X1,X2) = inverse(sF0(X0,X1,X2)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f8,plain,
! [X2,X0,X1] : inverse(sF0(X0,X1,X2)) = sF1(X0,X1,X2),
inference(reorient_equations,[],[f7]) ).
fof(f9,definition,
! [X2,X0,X1] : sF2(X0,X1,X2) = double_divide(sF1(X0,X1,X2),X1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f10,plain,
! [X2,X0,X1] : double_divide(sF1(X0,X1,X2),X1) = sF2(X0,X1,X2),
inference(reorient_equations,[],[f9]) ).
fof(f11,definition,
! [X2,X0,X1] : sF3(X0,X1,X2) = inverse(sF2(X0,X1,X2)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f12,plain,
! [X2,X0,X1] : inverse(sF2(X0,X1,X2)) = sF3(X0,X1,X2),
inference(reorient_equations,[],[f11]) ).
fof(f13,definition,
! [X2,X0,X1] : sF4(X0,X1,X2) = double_divide(X0,sF3(X0,X1,X2)),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f14,plain,
! [X2,X0,X1] : double_divide(X0,sF3(X0,X1,X2)) = sF4(X0,X1,X2),
inference(reorient_equations,[],[f13]) ).
fof(f15,plain,
! [X2,X0,X1] : sF4(X0,X1,X2) = X2,
inference(definition_folding,[],[f1,f14,f12,f10,f8,f6]) ).
fof(f16,definition,
sF5 = inverse(a1),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f17,plain,
inverse(a1) = sF5,
inference(reorient_equations,[],[f16]) ).
fof(f18,definition,
sF6 = double_divide(a1,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f19,plain,
double_divide(a1,sF5) = sF6,
inference(reorient_equations,[],[f18]) ).
fof(f20,definition,
sF7 = inverse(sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f21,plain,
inverse(sF6) = sF7,
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
sF8 = inverse(b1),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f23,plain,
inverse(b1) = sF8,
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
sF9 = double_divide(b1,sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f25,plain,
double_divide(b1,sF8) = sF9,
inference(reorient_equations,[],[f24]) ).
fof(f26,definition,
sF10 = inverse(sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f27,plain,
inverse(sF9) = sF10,
inference(reorient_equations,[],[f26]) ).
fof(f28,plain,
sF7 != sF10,
inference(definition_folding,[],[f4,f27,f25,f23,f21,f19,f17]) ).
fof(f29,plain,
! [X2,X0,X1] : double_divide(X0,sF3(X0,X1,X2)) = X2,
inference(forward_demodulation,[],[f15,f14]) ).
fof(f30,plain,
! [X2,X0,X1] : double_divide(X0,inverse(sF2(X0,X1,X2))) = X2,
inference(forward_demodulation,[],[f29,f12]) ).
fof(f31,plain,
! [X2,X0,X1] : double_divide(X0,inverse(double_divide(sF1(X0,X1,X2),X1))) = X2,
inference(forward_demodulation,[],[f30,f10]) ).
fof(f32,plain,
! [X2,X0,X1] : double_divide(X0,inverse(double_divide(inverse(sF0(X0,X1,X2)),X1))) = X2,
inference(forward_demodulation,[],[f31,f8]) ).
fof(f33,plain,
! [X2,X0,X1] : double_divide(X0,inverse(double_divide(inverse(double_divide(double_divide(X0,X1),inverse(X2))),X1))) = X2,
inference(forward_demodulation,[],[f32,f6]) ).
fof(f34,plain,
! [X0] : double_divide(b1,inverse(double_divide(inverse(double_divide(sF9,inverse(X0))),sF8))) = X0,
inference(superposition,[],[f33,f25]) ).
fof(f36,plain,
! [X2,X3,X0,X1] : double_divide(X1,inverse(double_divide(inverse(double_divide(X0,inverse(X3))),inverse(double_divide(inverse(double_divide(double_divide(X1,X2),inverse(X0))),X2))))) = X3,
inference(superposition,[],[f33,f33]) ).
fof(f37,plain,
! [X0,X1] : a1 = double_divide(X0,inverse(double_divide(inverse(double_divide(double_divide(X0,X1),sF5)),X1))),
inference(superposition,[],[f33,f17]) ).
fof(f38,plain,
! [X0,X1] : b1 = double_divide(X0,inverse(double_divide(inverse(double_divide(double_divide(X0,X1),sF8)),X1))),
inference(superposition,[],[f33,f23]) ).
fof(f40,plain,
! [X0,X1] : sF9 = double_divide(X0,inverse(double_divide(inverse(double_divide(double_divide(X0,X1),sF10)),X1))),
inference(superposition,[],[f33,f27]) ).
fof(f41,plain,
! [X2,X3,X0,X1] : double_divide(inverse(double_divide(double_divide(double_divide(X1,X2),X3),inverse(X0))),X3) = double_divide(X1,inverse(double_divide(inverse(X0),X2))),
inference(superposition,[],[f33,f33]) ).
fof(f42,plain,
a1 = double_divide(b1,inverse(double_divide(inverse(double_divide(sF9,sF5)),sF8))),
inference(superposition,[],[f34,f17]) ).
fof(f202,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,X2),inverse(double_divide(X0,inverse(double_divide(inverse(X1),X2))))) = X1,
inference(superposition,[],[f33,f41]) ).
fof(f222,plain,
! [X0] : double_divide(sF6,inverse(double_divide(a1,inverse(double_divide(inverse(X0),sF5))))) = X0,
inference(superposition,[],[f202,f19]) ).
fof(f234,plain,
! [X0,X1] : a1 = double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(double_divide(sF5,X1))))),
inference(superposition,[],[f202,f17]) ).
fof(f282,plain,
sF6 = double_divide(sF6,inverse(double_divide(a1,inverse(double_divide(sF7,sF5))))),
inference(superposition,[],[f222,f21]) ).
fof(f283,plain,
sF9 = double_divide(sF6,inverse(double_divide(a1,inverse(double_divide(sF10,sF5))))),
inference(superposition,[],[f222,f27]) ).
fof(f438,plain,
! [X0] : a1 = double_divide(double_divide(double_divide(sF5,X0),inverse(double_divide(sF5,X0))),inverse(a1)),
inference(superposition,[],[f234,f234]) ).
fof(f454,plain,
! [X0] : a1 = double_divide(double_divide(double_divide(sF5,X0),inverse(double_divide(sF5,X0))),sF5),
inference(forward_demodulation,[],[f438,f17]) ).
fof(f463,plain,
a1 = double_divide(double_divide(b1,inverse(b1)),sF5),
inference(superposition,[],[f454,f38]) ).
fof(f464,plain,
a1 = double_divide(double_divide(sF9,inverse(sF9)),sF5),
inference(superposition,[],[f454,f40]) ).
fof(f477,plain,
a1 = double_divide(double_divide(sF9,sF10),sF5),
inference(forward_demodulation,[],[f464,f27]) ).
fof(f478,plain,
a1 = double_divide(double_divide(b1,sF8),sF5),
inference(forward_demodulation,[],[f463,f23]) ).
fof(f482,plain,
a1 = double_divide(sF9,sF5),
inference(forward_demodulation,[],[f478,f25]) ).
fof(f484,plain,
a1 = double_divide(b1,inverse(double_divide(inverse(a1),sF8))),
inference(superposition,[],[f42,f482]) ).
fof(f486,plain,
a1 = double_divide(sF9,inverse(double_divide(inverse(double_divide(a1,sF5)),sF5))),
inference(superposition,[],[f37,f482]) ).
fof(f493,plain,
a1 = double_divide(sF9,inverse(double_divide(inverse(sF6),sF5))),
inference(forward_demodulation,[],[f486,f19]) ).
fof(f494,plain,
a1 = double_divide(b1,inverse(double_divide(sF5,sF8))),
inference(forward_demodulation,[],[f484,f17]) ).
fof(f495,plain,
a1 = double_divide(sF9,inverse(double_divide(sF7,sF5))),
inference(forward_demodulation,[],[f493,f21]) ).
fof(f575,plain,
! [X0,X1] : double_divide(inverse(double_divide(X0,inverse(X1))),inverse(X0)) = X1,
inference(superposition,[],[f36,f33]) ).
fof(f659,plain,
a1 = double_divide(sF9,inverse(double_divide(inverse(a1),sF10))),
inference(superposition,[],[f37,f477]) ).
fof(f671,plain,
a1 = double_divide(sF9,inverse(double_divide(sF5,sF10))),
inference(forward_demodulation,[],[f659,f17]) ).
fof(f726,plain,
double_divide(b1,inverse(double_divide(inverse(a1),sF8))) = double_divide(sF7,sF5),
inference(superposition,[],[f34,f495]) ).
fof(f739,plain,
double_divide(b1,inverse(double_divide(sF5,sF8))) = double_divide(sF7,sF5),
inference(forward_demodulation,[],[f726,f17]) ).
fof(f742,plain,
a1 = double_divide(sF7,sF5),
inference(forward_demodulation,[],[f739,f494]) ).
fof(f744,plain,
sF6 = double_divide(sF6,inverse(double_divide(a1,inverse(a1)))),
inference(superposition,[],[f282,f742]) ).
fof(f755,plain,
sF6 = double_divide(sF6,inverse(double_divide(a1,sF5))),
inference(forward_demodulation,[],[f744,f17]) ).
fof(f758,plain,
sF6 = double_divide(sF6,inverse(sF6)),
inference(forward_demodulation,[],[f755,f19]) ).
fof(f760,plain,
sF6 = double_divide(sF6,sF7),
inference(forward_demodulation,[],[f758,f21]) ).
fof(f800,plain,
double_divide(b1,inverse(double_divide(inverse(a1),sF8))) = double_divide(sF5,sF10),
inference(superposition,[],[f34,f671]) ).
fof(f815,plain,
double_divide(b1,inverse(double_divide(sF5,sF8))) = double_divide(sF5,sF10),
inference(forward_demodulation,[],[f800,f17]) ).
fof(f818,plain,
a1 = double_divide(sF5,sF10),
inference(forward_demodulation,[],[f815,f494]) ).
fof(f823,plain,
a1 = double_divide(sF5,inverse(double_divide(inverse(double_divide(a1,sF5)),sF10))),
inference(superposition,[],[f37,f818]) ).
fof(f831,plain,
a1 = double_divide(sF5,inverse(double_divide(inverse(sF6),sF10))),
inference(forward_demodulation,[],[f823,f19]) ).
fof(f834,plain,
a1 = double_divide(sF5,inverse(double_divide(sF7,sF10))),
inference(forward_demodulation,[],[f831,f21]) ).
fof(f854,plain,
! [X0] : a1 = double_divide(inverse(double_divide(X0,sF5)),inverse(X0)),
inference(superposition,[],[f575,f17]) ).
fof(f1005,plain,
double_divide(sF7,sF10) = double_divide(inverse(a1),inverse(sF5)),
inference(superposition,[],[f575,f834]) ).
fof(f1019,plain,
double_divide(sF7,sF10) = double_divide(sF5,inverse(sF5)),
inference(forward_demodulation,[],[f1005,f17]) ).
fof(f1049,plain,
a1 = double_divide(inverse(a1),inverse(sF7)),
inference(superposition,[],[f854,f742]) ).
fof(f1079,plain,
a1 = double_divide(sF5,inverse(sF7)),
inference(forward_demodulation,[],[f1049,f17]) ).
fof(f1095,plain,
sF7 = double_divide(inverse(a1),inverse(sF5)),
inference(superposition,[],[f575,f1079]) ).
fof(f1109,plain,
sF7 = double_divide(sF5,inverse(sF5)),
inference(forward_demodulation,[],[f1095,f17]) ).
fof(f1113,plain,
sF5 = double_divide(inverse(sF7),inverse(sF5)),
inference(superposition,[],[f575,f1109]) ).
fof(f1121,plain,
sF9 = double_divide(sF5,inverse(double_divide(inverse(double_divide(sF7,sF10)),inverse(sF5)))),
inference(superposition,[],[f40,f1109]) ).
fof(f1126,plain,
sF9 = double_divide(sF5,inverse(double_divide(inverse(double_divide(sF5,inverse(sF5))),inverse(sF5)))),
inference(forward_demodulation,[],[f1121,f1019]) ).
fof(f1130,plain,
sF9 = double_divide(sF5,inverse(sF5)),
inference(forward_demodulation,[],[f1126,f575]) ).
fof(f1133,plain,
sF7 = sF9,
inference(forward_demodulation,[],[f1130,f1109]) ).
fof(f1135,plain,
sF10 = inverse(sF7),
inference(superposition,[],[f27,f1133]) ).
fof(f1185,plain,
sF5 = double_divide(sF10,inverse(sF5)),
inference(forward_demodulation,[],[f1113,f1135]) ).
fof(f1192,plain,
a1 = double_divide(sF10,inverse(double_divide(inverse(double_divide(sF5,sF5)),inverse(sF5)))),
inference(superposition,[],[f37,f1185]) ).
fof(f1202,plain,
a1 = double_divide(sF10,inverse(a1)),
inference(forward_demodulation,[],[f1192,f854]) ).
fof(f1208,plain,
a1 = double_divide(sF10,sF5),
inference(forward_demodulation,[],[f1202,f17]) ).
fof(f1215,plain,
sF9 = double_divide(sF6,inverse(double_divide(a1,inverse(a1)))),
inference(superposition,[],[f283,f1208]) ).
fof(f1229,plain,
sF9 = double_divide(sF6,inverse(double_divide(a1,sF5))),
inference(forward_demodulation,[],[f1215,f17]) ).
fof(f1231,plain,
sF9 = double_divide(sF6,inverse(sF6)),
inference(forward_demodulation,[],[f1229,f19]) ).
fof(f1233,plain,
sF9 = double_divide(sF6,sF7),
inference(forward_demodulation,[],[f1231,f21]) ).
fof(f1235,plain,
sF6 = sF9,
inference(forward_demodulation,[],[f1233,f760]) ).
fof(f1236,plain,
sF6 = sF7,
inference(forward_demodulation,[],[f1235,f1133]) ).
fof(f1252,plain,
inverse(sF6) = sF10,
inference(superposition,[],[f1135,f1236]) ).
fof(f1253,plain,
sF7 = sF10,
inference(forward_demodulation,[],[f1252,f21]) ).
fof(f1260,plain,
sF6 = sF10,
inference(forward_demodulation,[],[f1253,f1236]) ).
fof(f1268,plain,
sF6 != sF7,
inference(superposition,[],[f28,f1260]) ).
fof(f1290,plain,
sF6 != sF6,
inference(forward_demodulation,[],[f1268,f1236]) ).
fof(f1291,plain,
$false,
inference(trivial_inequality_removal,[],[f1290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP585-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n018.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 10:09:53 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 3.40/1.34 % (2104639)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.40/1.34 % (2104726)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=830817705:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.40/1.34 % (2104724)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=3455018085:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.40/1.34 % (2104725)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=3123606461:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.40/1.34 % (2104728)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2990708733:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.40/1.34 % (2104727)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=768149219:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.40/1.34 % (2104729)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2257577403:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.40/1.34 % (2104730)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2368887804:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.40/1.34 % (2104728)First to succeed.
% 3.40/1.34 % (2104728)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2104639"
% 3.40/1.34 % (2104730)Also succeeded, but the first one will report.
% 3.40/1.34 % (2104729)Also succeeded, but the first one will report.
% 3.40/1.34 % (2104727)Also succeeded, but the first one will report.
% 3.40/1.34 % (2104728)Refutation found. Thanks to Tanya!
% 3.40/1.34 % SZS status Unsatisfiable for theBenchmark
% 3.40/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.87/1.54 % (2104728)------------------------------
% 3.87/1.54 % (2104728)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.87/1.54 % (2104728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.87/1.54 % (2104728)CaDiCaL version: 2.1.3
% 3.87/1.54 % (2104728)Termination reason: Refutation
% 3.87/1.54 % (2104728)Time elapsed: 0.036 s
% 3.87/1.54 % (2104728)Peak memory usage: 89 MB
% 3.87/1.54 % (2104728)Instructions burned: 65 (million)
% 3.87/1.54 % (2104728)------------------------------
% 3.87/1.54 % (2104728)------------------------------
% 3.87/1.54 % (2104639)Success in time 0.461 s
% 3.87/1.54 % Vampire exiting
%------------------------------------------------------------------------------