%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP670-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 10:15:33 AM UTC 2026
% Result : Unsatisfiable 72.15s 12.74s
% Output : Refutation 84.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 10
% Syntax : Number of formulae : 113 ( 113 unt; 0 def)
% Number of atoms : 113 ( 112 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 256 ( 256 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
fof(f2,axiom,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
fof(f3,axiom,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
fof(f4,axiom,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
fof(f5,axiom,
! [X0] : mult(X0,unit) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
fof(f6,axiom,
! [X0] : mult(unit,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
fof(f7,axiom,
! [X0,X1] : mult(i(X0),mult(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
fof(f8,axiom,
! [X0,X1] : mult(mult(X0,X1),i(X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c08) ).
fof(f9,axiom,
! [X2,X0,X1] : mult(mult(X0,X1),mult(X2,mult(X0,X1))) = mult(mult(mult(X0,mult(X1,X2)),X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c09) ).
fof(f10,negated_conjecture,
mult(mult(a,b),mult(mult(c,b),c)) != mult(mult(a,mult(mult(b,c),b)),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f13,plain,
! [X0,X1] : mult(mult(unit,X0),mult(X1,mult(unit,X0))) = mult(mult(mult(X0,X1),unit),X0),
inference(superposition,[],[f9,f6]) ).
fof(f15,plain,
! [X0,X1] : mult(mult(unit,X0),mult(X1,mult(unit,X0))) = mult(mult(X0,X1),X0),
inference(forward_demodulation,[],[f13,f5]) ).
fof(f17,plain,
! [X0,X1] : mult(mult(X0,X1),X0) = mult(X0,mult(X1,X0)),
inference(forward_demodulation,[],[f15,f6]) ).
fof(f23,plain,
mult(mult(a,b),mult(mult(c,b),c)) != mult(mult(a,mult(b,mult(c,b))),c),
inference(superposition,[],[f10,f17]) ).
fof(f27,plain,
mult(mult(a,mult(b,mult(c,b))),c) != mult(mult(a,b),mult(c,mult(b,c))),
inference(forward_demodulation,[],[f23,f17]) ).
fof(f30,plain,
! [X0,X1] : mult(X0,X1) = mult(X1,mult(ld(X1,X0),X1)),
inference(superposition,[],[f17,f1]) ).
fof(f32,plain,
! [X0] : ld(unit,X0) = X0,
inference(superposition,[],[f6,f1]) ).
fof(f42,plain,
! [X0,X1] : mult(mult(X1,X0),mult(unit,mult(X1,X0))) = mult(mult(mult(X1,X0),X1),X0),
inference(superposition,[],[f9,f5]) ).
fof(f49,plain,
! [X0,X1] : mult(mult(X1,X0),mult(unit,mult(X1,X0))) = mult(mult(X1,mult(X0,X1)),X0),
inference(forward_demodulation,[],[f42,f17]) ).
fof(f55,plain,
! [X0,X1] : mult(mult(X1,mult(X0,X1)),X0) = mult(mult(X1,X0),mult(X1,X0)),
inference(forward_demodulation,[],[f49,f6]) ).
fof(f86,plain,
! [X0] : unit = mult(X0,i(X0)),
inference(superposition,[],[f8,f6]) ).
fof(f97,plain,
! [X0,X1] : mult(mult(X0,i(X0)),mult(X1,mult(X0,i(X0)))) = mult(X0,mult(i(X0),X1)),
inference(superposition,[],[f9,f8]) ).
fof(f99,plain,
! [X0,X1] : i(X1) = ld(mult(X0,X1),X0),
inference(superposition,[],[f2,f8]) ).
fof(f100,plain,
! [X0,X1] : mult(X0,mult(X0,X1)) = mult(mult(X0,X1),mult(i(X1),mult(X0,X1))),
inference(superposition,[],[f17,f8]) ).
fof(f105,plain,
! [X2,X0,X1] : mult(mult(X0,mult(X1,X2)),X0) = rd(mult(mult(X0,X1),mult(X2,mult(X0,X1))),X1),
inference(superposition,[],[f4,f9]) ).
fof(f106,plain,
! [X0,X1] : mult(X0,mult(X1,X0)) = rd(mult(mult(X0,X1),mult(X0,X1)),X1),
inference(superposition,[],[f4,f55]) ).
fof(f108,plain,
! [X0,X1] : mult(X0,X1) = rd(X0,i(X1)),
inference(superposition,[],[f4,f8]) ).
fof(f111,plain,
! [X2,X0,X1] : mult(X0,mult(mult(X1,X2),X0)) = rd(mult(mult(X0,X1),mult(X2,mult(X0,X1))),X1),
inference(forward_demodulation,[],[f105,f17]) ).
fof(f113,plain,
! [X0,X1] : rd(X0,X1) = mult(X0,i(X1)),
inference(superposition,[],[f8,f3]) ).
fof(f128,plain,
! [X0,X1] : mult(mult(mult(X0,i(X0)),X1),mult(mult(X0,i(X0)),X1)) = mult(mult(X0,mult(i(X0),X1)),X1),
inference(superposition,[],[f55,f97]) ).
fof(f132,plain,
! [X0,X1] : mult(X1,mult(X0,i(X0))) = ld(mult(X0,i(X0)),mult(X0,mult(i(X0),X1))),
inference(superposition,[],[f2,f97]) ).
fof(f137,plain,
! [X0,X1] : mult(X1,unit) = ld(unit,mult(X0,mult(i(X0),X1))),
inference(forward_demodulation,[],[f132,f86]) ).
fof(f141,plain,
! [X0,X1] : mult(mult(X0,mult(i(X0),X1)),X1) = mult(mult(unit,X1),mult(unit,X1)),
inference(forward_demodulation,[],[f128,f86]) ).
fof(f151,plain,
! [X0,X1] : mult(X1,unit) = mult(X0,mult(i(X0),X1)),
inference(forward_demodulation,[],[f137,f32]) ).
fof(f155,plain,
! [X0,X1] : mult(mult(X0,mult(i(X0),X1)),X1) = mult(X1,X1),
inference(forward_demodulation,[],[f141,f6]) ).
fof(f164,plain,
! [X0,X1] : mult(X0,mult(i(X0),X1)) = X1,
inference(forward_demodulation,[],[f151,f5]) ).
fof(f182,plain,
! [X0,X1] : mult(X1,X0) = ld(i(X1),X0),
inference(superposition,[],[f164,f1]) ).
fof(f193,plain,
! [X0,X1] : ld(X1,X0) = mult(i(X1),X0),
inference(superposition,[],[f2,f164]) ).
fof(f194,plain,
! [X0,X1] : mult(X0,X1) = mult(X1,mult(mult(i(X1),X0),X1)),
inference(superposition,[],[f17,f164]) ).
fof(f345,plain,
! [X0,X1] : i(X1) = rd(X0,mult(X1,X0)),
inference(superposition,[],[f4,f7]) ).
fof(f350,plain,
! [X0,X1] : mult(i(X1),X0) = mult(X0,mult(i(mult(X1,X0)),X0)),
inference(superposition,[],[f100,f7]) ).
fof(f351,plain,
! [X0,X1] : mult(i(X1),X0) = mult(X0,ld(mult(X1,X0),X0)),
inference(forward_demodulation,[],[f350,f193]) ).
fof(f369,plain,
! [X0,X1] : ld(X1,X0) = mult(X0,ld(mult(X1,X0),X0)),
inference(forward_demodulation,[],[f351,f193]) ).
fof(f388,plain,
! [X0,X1] : i(X1) = rd(ld(X1,X0),X0),
inference(superposition,[],[f345,f1]) ).
fof(f392,plain,
! [X2,X0,X1] : i(mult(mult(X0,mult(X1,X2)),X0)) = rd(X1,mult(mult(X0,X1),mult(X2,mult(X0,X1)))),
inference(superposition,[],[f345,f9]) ).
fof(f397,plain,
! [X0,X1] : i(mult(X0,X1)) = rd(i(X1),X0),
inference(superposition,[],[f345,f8]) ).
fof(f408,plain,
! [X2,X0,X1] : rd(X1,mult(mult(X0,X1),mult(X2,mult(X0,X1)))) = rd(i(X0),mult(X0,mult(X1,X2))),
inference(forward_demodulation,[],[f392,f397]) ).
fof(f440,plain,
! [X0,X1] : ld(X0,X1) = i(ld(X1,X0)),
inference(superposition,[],[f99,f1]) ).
fof(f509,plain,
! [X2,X0,X1] : mult(mult(X2,X0),mult(i(X1),mult(X2,X0))) = mult(mult(mult(X2,rd(X0,X1)),X2),X0),
inference(superposition,[],[f9,f113]) ).
fof(f525,plain,
! [X0,X1] : i(X1) = mult(X0,rd(i(X0),X1)),
inference(superposition,[],[f164,f113]) ).
fof(f538,plain,
! [X2,X0,X1] : mult(mult(X2,X0),mult(i(X1),mult(X2,X0))) = mult(mult(X2,mult(rd(X0,X1),X2)),X0),
inference(forward_demodulation,[],[f509,f17]) ).
fof(f557,plain,
! [X2,X0,X1] : mult(mult(X2,mult(rd(X0,X1),X2)),X0) = mult(mult(X2,X0),ld(X1,mult(X2,X0))),
inference(forward_demodulation,[],[f538,f193]) ).
fof(f572,plain,
! [X0,X1] : rd(i(X1),X0) = ld(X1,i(X0)),
inference(superposition,[],[f2,f525]) ).
fof(f625,plain,
! [X0,X1] : mult(mult(X1,ld(X1,X0)),mult(X1,ld(X1,X0))) = mult(mult(X0,X1),ld(X1,X0)),
inference(superposition,[],[f55,f30]) ).
fof(f626,plain,
! [X0,X1] : mult(ld(X1,X0),X1) = ld(X1,mult(X0,X1)),
inference(superposition,[],[f2,f30]) ).
fof(f651,plain,
! [X0,X1] : mult(X0,X0) = mult(mult(X0,X1),ld(X1,X0)),
inference(forward_demodulation,[],[f625,f1]) ).
fof(f691,plain,
! [X0,X1] : ld(X1,X0) = mult(ld(X1,rd(X0,X1)),X1),
inference(superposition,[],[f626,f3]) ).
fof(f980,plain,
! [X0,X1] : mult(mult(X0,X1),mult(i(X1),mult(X0,X1))) = rd(mult(X0,X0),i(X1)),
inference(superposition,[],[f106,f8]) ).
fof(f992,plain,
! [X0,X1] : mult(mult(X0,X1),mult(i(X1),mult(X0,X1))) = mult(mult(X0,X0),X1),
inference(forward_demodulation,[],[f980,f108]) ).
fof(f1010,plain,
! [X0,X1] : mult(X0,mult(X0,X1)) = mult(mult(X0,X0),X1),
inference(forward_demodulation,[],[f992,f100]) ).
fof(f1325,plain,
! [X0,X1] : mult(mult(X1,mult(i(X1),X0)),mult(X1,mult(i(X1),X0))) = mult(mult(X0,X0),ld(X0,mult(X1,mult(i(X1),X0)))),
inference(superposition,[],[f651,f155]) ).
fof(f1331,plain,
! [X0,X1] : mult(mult(X0,X1),mult(X0,X1)) = mult(X0,ld(i(X1),mult(X0,X1))),
inference(superposition,[],[f651,f8]) ).
fof(f1373,plain,
! [X0,X1] : mult(mult(X0,X1),mult(X0,X1)) = mult(X0,mult(X1,mult(X0,X1))),
inference(forward_demodulation,[],[f1331,f182]) ).
fof(f1378,plain,
! [X0,X1] : mult(mult(X1,mult(i(X1),X0)),mult(X1,mult(i(X1),X0))) = mult(X0,mult(X0,ld(X0,mult(X1,mult(i(X1),X0))))),
inference(forward_demodulation,[],[f1325,f1010]) ).
fof(f1397,plain,
! [X0,X1] : mult(X0,mult(X1,mult(i(X1),X0))) = mult(mult(X1,mult(i(X1),X0)),mult(X1,mult(i(X1),X0))),
inference(forward_demodulation,[],[f1378,f1]) ).
fof(f1405,plain,
! [X0,X1] : mult(X0,mult(X1,mult(i(X1),X0))) = mult(X1,mult(mult(i(X1),X0),mult(X1,mult(i(X1),X0)))),
inference(forward_demodulation,[],[f1397,f1373]) ).
fof(f1409,plain,
! [X0,X1] : mult(X0,X0) = mult(X1,mult(mult(i(X1),X0),X0)),
inference(forward_demodulation,[],[f1405,f164]) ).
fof(f1413,plain,
! [X0,X1] : mult(X0,X0) = mult(X1,mult(ld(X1,X0),X0)),
inference(forward_demodulation,[],[f1409,f193]) ).
fof(f1626,plain,
! [X0,X1] : i(ld(X0,rd(X1,X0))) = rd(X0,ld(X0,X1)),
inference(superposition,[],[f345,f691]) ).
fof(f1641,plain,
! [X0,X1] : rd(X0,ld(X0,X1)) = ld(rd(X1,X0),X0),
inference(forward_demodulation,[],[f1626,f440]) ).
fof(f1846,plain,
! [X0,X1] : mult(ld(X1,X0),X0) = ld(X1,mult(X0,X0)),
inference(superposition,[],[f2,f1413]) ).
fof(f1871,plain,
! [X0,X1] : mult(X1,mult(X0,X0)) = mult(ld(i(X1),X0),X0),
inference(superposition,[],[f164,f1413]) ).
fof(f1872,plain,
! [X0,X1] : mult(X1,mult(X0,X0)) = mult(mult(X1,X0),X0),
inference(forward_demodulation,[],[f1871,f182]) ).
fof(f6965,plain,
! [X0,X1] : i(X0) = mult(ld(X0,i(X1)),X1),
inference(superposition,[],[f108,f388]) ).
fof(f9641,plain,
! [X0,X1] : mult(X1,ld(X0,X1)) = ld(rd(X0,X1),X1),
inference(superposition,[],[f369,f3]) ).
fof(f10148,plain,
! [X2,X0,X1] : mult(X2,ld(X0,X1)) = rd(X2,ld(X1,X0)),
inference(superposition,[],[f113,f440]) ).
fof(f10153,plain,
! [X2,X0,X1] : mult(ld(X0,X1),X2) = ld(ld(X1,X0),X2),
inference(superposition,[],[f193,f440]) ).
fof(f10264,plain,
! [X2,X0,X1] : mult(X1,mult(mult(X2,rd(X0,mult(X1,X2))),X1)) = rd(mult(mult(X1,X2),X0),X2),
inference(superposition,[],[f111,f3]) ).
fof(f12720,plain,
! [X2,X0,X1] : ld(rd(X2,ld(X1,X0)),ld(X1,X0)) = rd(ld(X1,X0),mult(ld(X0,X1),X2)),
inference(superposition,[],[f1641,f10153]) ).
fof(f12746,plain,
! [X2,X0,X1] : rd(ld(X1,X0),mult(ld(X0,X1),X2)) = mult(ld(X1,X0),ld(X2,ld(X1,X0))),
inference(forward_demodulation,[],[f12720,f9641]) ).
fof(f27351,plain,
! [X2,X0,X1] : rd(X2,mult(X1,X0)) = mult(X2,rd(i(X0),X1)),
inference(superposition,[],[f113,f397]) ).
fof(f27378,plain,
! [X2,X0,X1] : rd(X2,mult(X1,X0)) = mult(X2,ld(X0,i(X1))),
inference(forward_demodulation,[],[f27351,f572]) ).
fof(f29582,plain,
! [X2,X0,X1] : mult(X1,mult(mult(ld(X1,X0),rd(X2,X0)),X1)) = rd(mult(X0,X2),ld(X1,X0)),
inference(superposition,[],[f10264,f1]) ).
fof(f29944,plain,
! [X2,X0,X1] : mult(X1,mult(mult(ld(X1,X0),rd(X2,X0)),X1)) = mult(mult(X0,X2),ld(X0,X1)),
inference(forward_demodulation,[],[f29582,f10148]) ).
fof(f40253,plain,
! [X2,X0,X1] : rd(i(ld(X0,i(X1))),mult(ld(X0,i(X1)),mult(X1,X2))) = rd(X1,mult(i(X0),mult(X2,i(X0)))),
inference(superposition,[],[f408,f6965]) ).
fof(f40578,plain,
! [X2,X0,X1] : rd(i(ld(X0,i(X1))),mult(ld(X0,i(X1)),mult(X1,X2))) = rd(X1,ld(X0,mult(X2,i(X0)))),
inference(forward_demodulation,[],[f40253,f193]) ).
fof(f40764,plain,
! [X2,X0,X1] : rd(i(ld(X0,i(X1))),mult(ld(X0,i(X1)),mult(X1,X2))) = mult(X1,ld(mult(X2,i(X0)),X0)),
inference(forward_demodulation,[],[f40578,f10148]) ).
fof(f40949,plain,
! [X2,X0,X1] : rd(i(ld(X0,i(X1))),mult(ld(X0,i(X1)),mult(X1,X2))) = mult(X1,ld(rd(X2,X0),X0)),
inference(forward_demodulation,[],[f40764,f113]) ).
fof(f41112,plain,
! [X2,X0,X1] : mult(X1,mult(X0,ld(X2,X0))) = rd(i(ld(X0,i(X1))),mult(ld(X0,i(X1)),mult(X1,X2))),
inference(forward_demodulation,[],[f40949,f9641]) ).
fof(f41239,plain,
! [X2,X0,X1] : mult(X1,mult(X0,ld(X2,X0))) = ld(ld(X0,i(X1)),i(mult(ld(X0,i(X1)),mult(X1,X2)))),
inference(forward_demodulation,[],[f41112,f572]) ).
fof(f41342,plain,
! [X2,X0,X1] : mult(X1,mult(X0,ld(X2,X0))) = mult(ld(i(X1),X0),i(mult(ld(X0,i(X1)),mult(X1,X2)))),
inference(forward_demodulation,[],[f41239,f10153]) ).
fof(f41421,plain,
! [X2,X0,X1] : mult(X1,mult(X0,ld(X2,X0))) = rd(ld(i(X1),X0),mult(ld(X0,i(X1)),mult(X1,X2))),
inference(forward_demodulation,[],[f41342,f113]) ).
fof(f41481,plain,
! [X2,X0,X1] : mult(X1,mult(X0,ld(X2,X0))) = mult(ld(i(X1),X0),ld(mult(X1,X2),ld(i(X1),X0))),
inference(forward_demodulation,[],[f41421,f12746]) ).
fof(f41526,plain,
! [X2,X0,X1] : mult(X1,mult(X0,ld(X2,X0))) = mult(mult(X1,X0),ld(mult(X1,X2),mult(X1,X0))),
inference(forward_demodulation,[],[f41481,f182]) ).
fof(f134438,plain,
! [X2,X0,X1] : mult(mult(mult(ld(i(X2),X0),rd(X1,X0)),i(X2)),X2) = mult(X2,mult(mult(mult(X0,X1),ld(X0,i(X2))),X2)),
inference(superposition,[],[f194,f29944]) ).
fof(f134447,plain,
! [X2,X0,X1] : mult(mult(mult(ld(i(X2),X0),rd(X1,X0)),i(X2)),X2) = mult(X2,mult(rd(mult(X0,X1),mult(X2,X0)),X2)),
inference(forward_demodulation,[],[f134438,f27378]) ).
fof(f134702,plain,
! [X2,X0,X1] : mult(X2,mult(rd(mult(X0,X1),mult(X2,X0)),X2)) = mult(rd(mult(ld(i(X2),X0),rd(X1,X0)),X2),X2),
inference(forward_demodulation,[],[f134447,f113]) ).
fof(f134902,plain,
! [X2,X0,X1] : mult(ld(i(X2),X0),rd(X1,X0)) = mult(X2,mult(rd(mult(X0,X1),mult(X2,X0)),X2)),
inference(forward_demodulation,[],[f134702,f3]) ).
fof(f135048,plain,
! [X2,X0,X1] : mult(mult(X2,X0),rd(X1,X0)) = mult(X2,mult(rd(mult(X0,X1),mult(X2,X0)),X2)),
inference(forward_demodulation,[],[f134902,f182]) ).
fof(f243620,plain,
! [X2,X0,X1] : mult(mult(X0,mult(X1,X2)),ld(mult(X0,X1),mult(X0,mult(X1,X2)))) = mult(mult(mult(X0,X1),rd(X2,X1)),mult(X1,X2)),
inference(superposition,[],[f557,f135048]) ).
fof(f244084,plain,
! [X2,X0,X1] : mult(mult(mult(X0,X1),rd(X2,X1)),mult(X1,X2)) = mult(X0,mult(mult(X1,X2),ld(X1,mult(X1,X2)))),
inference(forward_demodulation,[],[f243620,f41526]) ).
fof(f244638,plain,
! [X2,X0,X1] : mult(X0,mult(mult(X1,X2),X2)) = mult(mult(mult(X0,X1),rd(X2,X1)),mult(X1,X2)),
inference(forward_demodulation,[],[f244084,f2]) ).
fof(f245060,plain,
! [X2,X0,X1] : mult(X0,mult(X1,mult(X2,X2))) = mult(mult(mult(X0,X1),rd(X2,X1)),mult(X1,X2)),
inference(forward_demodulation,[],[f244638,f1872]) ).
fof(f321198,plain,
! [X2,X0,X1] : mult(rd(X0,X1),mult(X1,mult(X2,X2))) = mult(mult(X0,rd(X2,X1)),mult(X1,X2)),
inference(superposition,[],[f245060,f3]) ).
fof(f324567,plain,
! [X2,X0,X1] : mult(rd(X1,i(X2)),mult(i(X2),mult(mult(X2,X0),mult(X2,X0)))) = mult(mult(X1,rd(mult(X2,X0),i(X2))),X0),
inference(superposition,[],[f321198,f7]) ).
fof(f325069,plain,
! [X2,X0,X1] : mult(rd(X1,i(X2)),mult(i(X2),mult(mult(X2,X0),mult(X2,X0)))) = mult(mult(X1,mult(mult(X2,X0),X2)),X0),
inference(forward_demodulation,[],[f324567,f108]) ).
fof(f325623,plain,
! [X2,X0,X1] : mult(rd(X1,i(X2)),mult(i(X2),mult(mult(X2,X0),mult(X2,X0)))) = mult(mult(X1,mult(X2,mult(X0,X2))),X0),
inference(forward_demodulation,[],[f325069,f17]) ).
fof(f326084,plain,
! [X2,X0,X1] : mult(mult(X1,mult(X2,mult(X0,X2))),X0) = mult(rd(X1,i(X2)),ld(X2,mult(mult(X2,X0),mult(X2,X0)))),
inference(forward_demodulation,[],[f325623,f193]) ).
fof(f326451,plain,
! [X2,X0,X1] : mult(mult(X1,mult(X2,mult(X0,X2))),X0) = mult(rd(X1,i(X2)),mult(ld(X2,mult(X2,X0)),mult(X2,X0))),
inference(forward_demodulation,[],[f326084,f1846]) ).
fof(f326728,plain,
! [X2,X0,X1] : mult(mult(X1,mult(X2,mult(X0,X2))),X0) = mult(rd(X1,i(X2)),mult(X0,mult(X2,X0))),
inference(forward_demodulation,[],[f326451,f2]) ).
fof(f326937,plain,
! [X2,X0,X1] : mult(mult(X1,mult(X2,mult(X0,X2))),X0) = mult(mult(X1,X2),mult(X0,mult(X2,X0))),
inference(forward_demodulation,[],[f326728,f108]) ).
fof(f327731,plain,
mult(mult(a,b),mult(c,mult(b,c))) != mult(mult(a,b),mult(c,mult(b,c))),
inference(superposition,[],[f27,f326937]) ).
fof(f327977,plain,
$false,
inference(trivial_inequality_removal,[],[f327731]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP670-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n006.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 10:34:26 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 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
% 72.15/12.74 % (2781618)Detected a unit-equality problem, will run specialized UEQ schedule.
% 72.15/12.74 % (2781626)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2769502755:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 72.15/12.74 % (2781624)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=1615261277:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 72.15/12.74 % (2781628)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3000424016:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 72.15/12.74 % (2781627)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3438433989:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 72.15/12.74 % (2781623)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=1817045001:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 72.15/12.74 % (2781625)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3931837973:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 72.15/12.74 % (2781626)Instruction limit reached!
% 72.15/12.74 % (2781626)------------------------------
% 72.15/12.74 % (2781626)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 72.15/12.74 % (2781626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.15/12.74 % (2781626)CaDiCaL version: 2.1.3
% 72.15/12.74 % (2781626)Termination reason: Instruction limit
% 72.15/12.74 % (2781626)Termination phase: Saturation
% 72.15/12.74 % (2781626)Time elapsed: 0.046 s
% 72.15/12.74 % (2781626)Peak memory usage: 88 MB
% 72.15/12.74 % (2781626)Instructions burned: 136 (million)
% 72.15/12.74 % (2781629)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=651737720:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 72.15/12.74 % (2781636)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3341904275:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 72.15/12.74 % (2781627)Instruction limit reached!
% 72.15/12.74 % (2781627)------------------------------
% 72.15/12.74 % (2781627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 72.15/12.74 % (2781627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.15/12.74 % (2781627)CaDiCaL version: 2.1.3
% 72.15/12.74 % (2781627)Termination reason: Instruction limit
% 72.15/12.74 % (2781627)Termination phase: Saturation
% 72.15/12.74 % (2781627)Time elapsed: 0.101 s
% 72.15/12.74 % (2781627)Peak memory usage: 89 MB
% 72.15/12.74 % (2781627)Instructions burned: 181 (million)
% 72.15/12.74 % (2781628)Instruction limit reached!
% 72.15/12.74 % (2781628)------------------------------
% 72.15/12.74 % (2781628)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 72.15/12.74 % (2781628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.15/12.74 % (2781628)CaDiCaL version: 2.1.3
% 72.15/12.74 % (2781628)Termination reason: Instruction limit
% 72.15/12.74 % (2781628)Termination phase: Saturation
% 72.15/12.74 % (2781628)Time elapsed: 0.162 s
% 72.15/12.74 % (2781628)Peak memory usage: 89 MB
% 72.15/12.74 % (2781628)Instructions burned: 258 (million)
% 72.15/12.74 % (2781639)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3448987059:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 72.15/12.74 % (2781640)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1436858935:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 72.15/12.74 % (2781640)Instruction limit reached!
% 72.15/12.74 % (2781640)------------------------------
% 72.15/12.74 % (2781640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 72.15/12.74 % (2781640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.15/12.74 % (2781640)CaDiCaL version: 2.1.3
% 72.15/12.74 % (2781640)Termination reason: Instruction limit
% 72.15/12.74 % (2781640)Termination phase: Saturation
% 72.15/12.74 % (2781640)Time elapsed: 0.114 s
% 72.15/12.74 % (2781640)Peak memory usage: 89 MB
% 72.15/12.74 % (2781640)Instructions burned: 216 (million)
% 72.15/12.74 % (2781643)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=4247396397:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 72.15/12.74 % (2781629)Instruction limit reached!
% 72.15/12.74 % (2781629)------------------------------
% 72.15/12.74 % (2781629)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 72.15/12.74 % (2781629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.15/12.74 % (2781629)CaDiCaL version: 2.1.3
% 72.15/12.74 % (2781629)Termination reason: Instruction limit
% 72.15/12.74 % (2781629)Termination phase: Saturation
% 72.15/12.74 % (2781629)Time elapsed: 0.651 s
% 72.15/12.74 % (2781629)Peak memory usage: 101 MB
% 72.15/12.74 % (2781629)Instructions burned: 1188 (million)
% 72.15/12.74 % (2781643)Instruction limit reached!
% 72.15/12.74 % (2781643)------------------------------
% 72.15/12.74 % (2781643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 72.15/12.74 % (2781643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.15/12.74 % (2781643)CaDiCaL version: 2.1.3
% 72.15/12.74 % (2781643)Termination reason: Instruction limit
% 72.15/12.74 % (2781643)Termination phase: Saturation
% 72.15/12.74 % (2781643)Time elapsed: 0.209 s
% 72.15/12.74 % (2781643)Peak memory usage: 94 MB
% 72.15/12.74 % (2781643)Instructions burned: 317 (million)
% 72.15/12.74 % (2781645)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=238605284:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 72.15/12.74 % (2781646)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=1292039075:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2991 on theBenchmark for (2991ds/2836Mi)
% 72.15/12.74 % (2781636)Instruction limit reached!
% 72.15/12.74 % (2781636)------------------------------
% 72.15/12.74 % (2781636)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 72.15/12.74 % (2781636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.15/12.74 % (2781636)CaDiCaL version: 2.1.3
% 72.15/12.74 % (2781636)Termination reason: Instruction limit
% 72.15/12.74 % (2781636)Termination phase: Saturation
% 72.15/12.74 % (2781636)Time elapsed: 1.058 s
% 72.15/12.74 % (2781636)Peak memory usage: 140 MB
% 72.15/12.74 % (2781636)Instructions burned: 2051 (million)
% 72.15/12.74 % (2781649)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=754747530:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2987 on theBenchmark for (2987ds/14534Mi)
% 72.15/12.74 % (2781646)Instruction limit reached!
% 72.15/12.74 % (2781646)------------------------------
% 72.15/12.74 % (2781646)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 72.15/12.74 % (2781646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.15/12.74 % (2781646)CaDiCaL version: 2.1.3
% 72.15/12.74 % (2781646)Termination reason: Instruction limit
% 72.15/12.74 % (2781646)Termination phase: Saturation
% 72.15/12.74 % (2781646)Time elapsed: 1.828 s
% 72.15/12.74 % (2781646)Peak memory usage: 131 MB
% 72.15/12.74 % (2781646)Instructions burned: 2836 (million)
% 72.15/12.74 % (2781651)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:sas=cadical:sp=reverse_frequency:bsr=on:alpa=false:sac=on:random_seed=964934050:i=11832:s2at=3:bs=on:bd=preordered:fsd=on_2971 on theBenchmark for (2971ds/11832Mi)
% 72.15/12.74 % (2781639)Instruction limit reached!
% 72.15/12.74 % (2781639)------------------------------
% 72.15/12.74 % (2781639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 72.15/12.74 % (2781639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.15/12.74 % (2781639)CaDiCaL version: 2.1.3
% 72.15/12.74 % (2781639)Termination reason: Instruction limit
% 72.15/12.74 % (2781639)Termination phase: Saturation
% 72.15/12.74 % (2781639)Time elapsed: 2.990 s
% 72.15/12.74 % (2781639)Peak memory usage: 167 MB
% 72.15/12.74 % (2781639)Instructions burned: 4949 (million)
% 72.15/12.74 % (2781653)lrs+10_1_to=lpo:ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:drc=off:fde=unused:sp=const_min:spb=goal:fd=preordered:random_seed=3979429820:i=2279:fgj=on:bd=all_2966 on theBenchmark for (2966ds/2279Mi)
% 72.15/12.74 % (2781653)Instruction limit reached!
% 72.15/12.74 % (2781653)------------------------------
% 72.15/12.74 % (2781653)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 72.15/12.74 % (2781653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.15/12.74 % (2781653)CaDiCaL version: 2.1.3
% 72.15/12.74 % (2781653)Termination reason: Instruction limit
% 72.15/12.74 % (2781653)Termination phase: Saturation
% 72.15/12.74 % (2781653)Time elapsed: 1.395 s
% 72.15/12.74 % (2781653)Peak memory usage: 139 MB
% 72.15/12.74 % (2781653)Instructions burned: 2281 (million)
% 72.15/12.74 % (2781655)lrs-1010_1_to=lpo:ncem=casc2026/models/loop8.pt:sil=32000:tgt=ground:npcc=on:drc=off:fde=none:sp=reverse_arity:urr=ec_only:gs=on:s2agt=16:random_seed=2530535700:st=3:i=6225:bd=all:gtg=exists_all:ss=included:er=filter:sgt=10_2950 on theBenchmark for (2950ds/6225Mi)
% 72.15/12.74 % (2781655)Instruction limit reached!
% 72.15/12.74 % (2781655)------------------------------
% 72.15/12.74 % (2781655)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 72.15/12.74 % (2781655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.15/12.74 % (2781655)CaDiCaL version: 2.1.3
% 72.15/12.74 % (2781655)Termination reason: Instruction limit
% 72.15/12.74 % (2781655)Termination phase: Saturation
% 72.15/12.74 % (2781655)Time elapsed: 3.049 s
% 72.15/12.74 % (2781655)Peak memory usage: 158 MB
% 72.15/12.74 % (2781655)Instructions burned: 6225 (million)
% 72.15/12.74 % (2781645)Instruction limit reached!
% 72.15/12.74 % (2781645)------------------------------
% 72.15/12.74 % (2781645)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 72.15/12.74 % (2781645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.15/12.74 % (2781645)CaDiCaL version: 2.1.3
% 72.15/12.74 % (2781645)Termination reason: Instruction limit
% 72.15/12.74 % (2781645)Termination phase: Saturation
% 72.15/12.74 % (2781645)Time elapsed: 7.278 s
% 72.15/12.74 % (2781645)Peak memory usage: 246 MB
% 72.15/12.74 % (2781645)Instructions burned: 12125 (million)
% 72.15/12.74 % (2781657)lrs-1010_1_sil=32000:tgt=ground:etr=on:sp=const_frequency:spb=goal_then_units:rnwc=on:lwlo=on:random_seed=974026686:lrd=on:i=21755:kws=frequency:fgj=on:bd=preordered:nm=4:ins=20:av=off_2918 on theBenchmark for (2918ds/21755Mi)
% 72.15/12.74 % (2781659)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:drc=off:flr=on:random_seed=4025278942:s2pl=no:i=16427:s2at=1.5:bd=all:fsr=off_2917 on theBenchmark for (2917ds/16427Mi)
% 72.15/12.74 % (2781651)Instruction limit reached!
% 72.15/12.74 % (2781651)------------------------------
% 72.15/12.74 % (2781651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 72.15/12.74 % (2781651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.15/12.74 % (2781651)CaDiCaL version: 2.1.3
% 72.15/12.74 % (2781651)Termination reason: Instruction limit
% 72.15/12.74 % (2781651)Termination phase: Saturation
% 72.15/12.74 % (2781651)Time elapsed: 7.423 s
% 72.15/12.74 % (2781651)Peak memory usage: 231 MB
% 72.15/12.74 % (2781651)Instructions burned: 11832 (million)
% 72.15/12.74 % (2781661)lrs+1011_1_to=lpo:ncem=casc2026/models/loop7.pt:sil=32000:npcc=on:drc=off:fde=none:sp=const_frequency:spb=goal:fd=preordered:random_seed=688635228:i=9356:fgj=on:bd=preordered:av=off_2895 on theBenchmark for (2895ds/9356Mi)
% 72.15/12.74 % (2781649)Instruction limit reached!
% 72.15/12.74 % (2781649)------------------------------
% 72.15/12.74 % (2781649)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 72.15/12.74 % (2781649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.15/12.74 % (2781649)CaDiCaL version: 2.1.3
% 72.15/12.74 % (2781649)Termination reason: Instruction limit
% 72.15/12.74 % (2781649)Termination phase: Saturation
% 72.15/12.74 % (2781649)Time elapsed: 9.142 s
% 72.15/12.74 % (2781649)Peak memory usage: 244 MB
% 72.15/12.74 % (2781649)Instructions burned: 14535 (million)
% 72.15/12.74 % (2781663)dis+10_6_sil=8000:tgt=ground:prc=on:drc=ordering:spb=non_intro:fd=preordered:foolp=on:slsqc=1:slsq=on:random_seed=1955326870:i=2070:kws=inv_precedence:slsql=off:bd=all_2894 on theBenchmark for (2894ds/2070Mi)
% 72.15/12.74 % (2781624)First to succeed.
% 72.15/12.74 % (2781624)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2781618"
% 72.15/12.74 % (2781624)Refutation found. Thanks to Tanya!
% 72.15/12.74 % SZS status Unsatisfiable for theBenchmark
% 72.15/12.74 % SZS output start Proof for theBenchmark
% See solution above
% 84.55/12.94 % (2781624)------------------------------
% 84.55/12.94 % (2781624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 84.55/12.94 % (2781624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 84.55/12.94 % (2781624)CaDiCaL version: 2.1.3
% 84.55/12.94 % (2781624)Termination reason: Refutation
% 84.55/12.94 % (2781624)Time elapsed: 11.575 s
% 84.55/12.94 % (2781624)Peak memory usage: 430 MB
% 84.55/12.94 % (2781624)Instructions burned: 32956 (million)
% 84.55/12.94 % (2781624)------------------------------
% 84.55/12.94 % (2781624)------------------------------
% 84.55/12.94 % (2781618)Success in time 11.92 s
% 84.55/12.94 % Vampire exiting
%------------------------------------------------------------------------------