%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP667-3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 : Sun Sep 27 07:31:08 AM UTC 2026
% Result : Unsatisfiable 32.16s 4.58s
% Output : CNFRefutation 32.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 64
% Number of leaves : 10
% Syntax : Number of formulae : 244 ( 244 unt; 0 def)
% Number of atoms : 244 ( 243 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 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 : 402 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c01,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,ld(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',c01) ).
cnf(c_1,plain,
mult(A,ld(A,B)) = B,
inference(clausify,[status(thm)],[c01]) ).
fof(c02,axiom,
! [VAR_0,VAR_1] : ld(VAR_0,mult(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',c02) ).
cnf(c_2,plain,
ld(A,mult(A,B)) = B,
inference(clausify,[status(thm)],[c02]) ).
fof(c03,axiom,
! [VAR_0,VAR_1] : mult(rd(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',c03) ).
cnf(c_3,plain,
mult(rd(A,B),B) = A,
inference(clausify,[status(thm)],[c03]) ).
fof(c04,axiom,
! [VAR_0,VAR_1] : rd(mult(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',c04) ).
cnf(c_4,plain,
rd(mult(A,B),B) = A,
inference(clausify,[status(thm)],[c04]) ).
fof(c05,axiom,
! [VAR_0] : mult(VAR_0,unit) = VAR_0,
file('theBenchmark.p',c05) ).
cnf(c_5,plain,
mult(A,unit) = A,
inference(clausify,[status(thm)],[c05]) ).
fof(c06,axiom,
! [VAR_0] : mult(unit,VAR_0) = VAR_0,
file('theBenchmark.p',c06) ).
cnf(c_6,plain,
mult(unit,A) = A,
inference(clausify,[status(thm)],[c06]) ).
fof(c07,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(mult(VAR_0,VAR_1),mult(mult(VAR_2,VAR_1),VAR_2)) = mult(mult(VAR_0,mult(mult(VAR_1,VAR_2),VAR_1)),VAR_2),
file('theBenchmark.p',c07) ).
cnf(c_7,plain,
mult(mult(A,B),mult(mult(C,B),C)) = mult(mult(A,mult(mult(B,C),B)),C),
inference(clausify,[status(thm)],[c07]) ).
cnf(c_8,plain,
mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C)),
inference(copy,[status(thm)],[c_7]) ).
fof(c08,axiom,
! [VAR_0,VAR_1] : mult(mult(VAR_0,VAR_1),VAR_0) = mult(VAR_0,mult(VAR_1,VAR_0)),
file('theBenchmark.p',c08) ).
cnf(c_9,plain,
mult(mult(A,B),A) = mult(A,mult(B,A)),
inference(clausify,[status(thm)],[c08]) ).
fof(c09,axiom,
! [VAR_0] : mult(f(VAR_0),f(VAR_0)) = VAR_0,
file('theBenchmark.p',c09) ).
cnf(c_10,plain,
mult(f(A),f(A)) = A,
inference(clausify,[status(thm)],[c09]) ).
fof(goals,axiom,
mult(a,mult(b,mult(c,b))) != mult(mult(mult(a,b),c),b),
file('theBenchmark.p',goals) ).
cnf(c_11,plain,
mult(a,mult(b,mult(c,b))) != mult(mult(mult(a,b),c),b),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_12,plain,
mult(mult(mult(a,b),c),b) != mult(a,mult(b,mult(c,b))),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_9385,plain,
mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(mult(C,B),C)),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_13,plain,
mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))),
inference(paramod,[status(thm)],[c_9,c_9385]) ).
cnf(c_14,plain,
ld(rd(A,B),A) = B,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_15,plain,
rd(A,ld(B,A)) = B,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_16,plain,
ld(A,A) = unit,
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_9386,plain,
mult(A,B) = mult(B,mult(ld(B,A),B)),
inference(paramod,[status(thm)],[c_1,c_9]) ).
cnf(c_20,plain,
mult(A,mult(ld(A,B),A)) = mult(B,A),
inference(copy,[status(thm)],[c_9386]) ).
cnf(c_21,plain,
ld(mult(A,B),mult(A,mult(B,A))) = A,
inference(paramod,[status(thm)],[c_9,c_2]) ).
cnf(c_9387,plain,
mult(A,rd(A,B)) = mult(rd(A,B),mult(B,rd(A,B))),
inference(paramod,[status(thm)],[c_3,c_9]) ).
cnf(c_22,plain,
mult(rd(A,B),mult(B,rd(A,B))) = mult(A,rd(A,B)),
inference(copy,[status(thm)],[c_9387]) ).
cnf(c_9388,plain,
mult(A,f(A)) = mult(f(A),mult(f(A),f(A))),
inference(paramod,[status(thm)],[c_10,c_9]) ).
cnf(c_9389,plain,
mult(A,f(A)) = mult(f(A),A),
inference(paramod,[status(thm)],[c_10,c_9388]) ).
cnf(c_27,plain,
mult(f(A),A) = mult(A,f(A)),
inference(copy,[status(thm)],[c_9389]) ).
cnf(c_9390,plain,
mult(mult(A,mult(ld(B,C),C)),B) = mult(mult(A,ld(B,C)),mult(B,mult(ld(B,C),B))),
inference(paramod,[status(thm)],[c_1,c_13]) ).
cnf(c_28,plain,
mult(mult(A,mult(ld(B,C),C)),B) = mult(mult(A,ld(B,C)),mult(C,B)),
inference(paramod,[status(thm)],[c_20,c_9390]) ).
cnf(c_9391,plain,
mult(mult(A,mult(B,C)),rd(C,B)) = mult(mult(A,B),mult(rd(C,B),mult(B,rd(C,B)))),
inference(paramod,[status(thm)],[c_3,c_13]) ).
cnf(c_31,plain,
mult(mult(A,mult(B,C)),rd(C,B)) = mult(mult(A,B),mult(C,rd(C,B))),
inference(paramod,[status(thm)],[c_22,c_9391]) ).
cnf(c_9392,plain,
mult(A,B) = mult(mult(rd(A,mult(C,mult(B,C))),C),mult(B,mult(C,B))),
inference(paramod,[status(thm)],[c_3,c_13]) ).
cnf(c_32,plain,
mult(mult(rd(A,mult(B,mult(C,B))),B),mult(C,mult(B,C))) = mult(A,C),
inference(copy,[status(thm)],[c_9392]) ).
cnf(c_34,plain,
rd(mult(mult(A,B),mult(C,mult(B,C))),C) = mult(A,mult(B,mult(C,B))),
inference(paramod,[status(thm)],[c_13,c_4]) ).
cnf(c_9393,plain,
mult(mult(A,B),mult(unit,mult(B,unit))) = mult(A,mult(B,mult(unit,B))),
inference(paramod,[status(thm)],[c_13,c_5]) ).
cnf(c_9394,plain,
mult(mult(A,B),mult(unit,B)) = mult(A,mult(B,mult(unit,B))),
inference(paramod,[status(thm)],[c_5,c_9393]) ).
cnf(c_9395,plain,
mult(mult(A,B),B) = mult(A,mult(B,mult(unit,B))),
inference(paramod,[status(thm)],[c_6,c_9394]) ).
cnf(c_35,plain,
mult(mult(A,B),B) = mult(A,mult(B,B)),
inference(paramod,[status(thm)],[c_6,c_9395]) ).
cnf(c_39,plain,
ld(A,mult(B,A)) = mult(ld(A,B),A),
inference(paramod,[status(thm)],[c_20,c_2]) ).
cnf(c_9396,plain,
ld(A,B) = mult(ld(A,rd(B,A)),A),
inference(paramod,[status(thm)],[c_3,c_39]) ).
cnf(c_51,plain,
mult(ld(A,rd(B,A)),A) = ld(A,B),
inference(copy,[status(thm)],[c_9396]) ).
cnf(c_9397,plain,
ld(A,A) = mult(ld(A,unit),A),
inference(paramod,[status(thm)],[c_6,c_39]) ).
cnf(c_9398,plain,
unit = mult(ld(A,unit),A),
inference(paramod,[status(thm)],[c_16,c_9397]) ).
cnf(c_52,plain,
mult(ld(A,unit),A) = unit,
inference(copy,[status(thm)],[c_9398]) ).
cnf(c_9399,plain,
ld(A,mult(A,f(A))) = mult(ld(A,f(A)),A),
inference(paramod,[status(thm)],[c_27,c_39]) ).
cnf(c_9400,plain,
f(A) = mult(ld(A,f(A)),A),
inference(paramod,[status(thm)],[c_2,c_9399]) ).
cnf(c_55,plain,
mult(ld(A,f(A)),A) = f(A),
inference(copy,[status(thm)],[c_9400]) ).
cnf(c_57,plain,
ld(ld(A,unit),unit) = A,
inference(paramod,[status(thm)],[c_52,c_2]) ).
cnf(c_58,plain,
rd(unit,A) = ld(A,unit),
inference(paramod,[status(thm)],[c_52,c_4]) ).
cnf(c_61,plain,
ld(mult(ld(A,B),A),mult(ld(A,B),B)) = ld(A,B),
inference(paramod,[status(thm)],[c_1,c_21]) ).
cnf(c_62,plain,
ld(mult(A,rd(B,A)),mult(A,B)) = A,
inference(paramod,[status(thm)],[c_3,c_21]) ).
cnf(c_72,plain,
rd(f(A),A) = ld(A,f(A)),
inference(paramod,[status(thm)],[c_55,c_4]) ).
cnf(c_9401,plain,
mult(f(A),ld(A,f(A))) = mult(ld(A,f(A)),mult(A,ld(A,f(A)))),
inference(paramod,[status(thm)],[c_55,c_9]) ).
cnf(c_9402,plain,
mult(f(A),ld(A,f(A))) = mult(ld(A,f(A)),f(A)),
inference(paramod,[status(thm)],[c_1,c_9401]) ).
cnf(c_73,plain,
mult(ld(A,f(A)),f(A)) = mult(f(A),ld(A,f(A))),
inference(copy,[status(thm)],[c_9402]) ).
cnf(c_9403,plain,
mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(mult(A,B),mult(ld(B,f(B)),mult(B,ld(B,f(B))))),
inference(paramod,[status(thm)],[c_55,c_13]) ).
cnf(c_9404,plain,
mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(mult(A,B),mult(ld(B,f(B)),f(B))),
inference(paramod,[status(thm)],[c_1,c_9403]) ).
cnf(c_74,plain,
mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(mult(A,B),mult(f(B),ld(B,f(B)))),
inference(paramod,[status(thm)],[c_73,c_9404]) ).
cnf(c_82,plain,
rd(ld(A,B),A) = ld(A,rd(B,A)),
inference(paramod,[status(thm)],[c_51,c_4]) ).
cnf(c_9405,plain,
mult(ld(A,B),ld(A,rd(B,A))) = mult(ld(A,rd(B,A)),mult(A,ld(A,rd(B,A)))),
inference(paramod,[status(thm)],[c_51,c_9]) ).
cnf(c_9406,plain,
mult(ld(A,B),ld(A,rd(B,A))) = mult(ld(A,rd(B,A)),rd(B,A)),
inference(paramod,[status(thm)],[c_1,c_9405]) ).
cnf(c_83,plain,
mult(ld(A,rd(B,A)),rd(B,A)) = mult(ld(A,B),ld(A,rd(B,A))),
inference(copy,[status(thm)],[c_9406]) ).
cnf(c_9407,plain,
mult(mult(A,mult(B,ld(B,C))),ld(B,rd(C,B))) = mult(mult(A,B),mult(ld(B,rd(C,B)),mult(B,ld(B,rd(C,B))))),
inference(paramod,[status(thm)],[c_51,c_13]) ).
cnf(c_9408,plain,
mult(mult(A,C),ld(B,rd(C,B))) = mult(mult(A,B),mult(ld(B,rd(C,B)),mult(B,ld(B,rd(C,B))))),
inference(paramod,[status(thm)],[c_1,c_9407]) ).
cnf(c_9409,plain,
mult(mult(A,C),ld(B,rd(C,B))) = mult(mult(A,B),mult(ld(B,rd(C,B)),rd(C,B))),
inference(paramod,[status(thm)],[c_1,c_9408]) ).
cnf(c_9410,plain,
mult(mult(A,C),ld(B,rd(C,B))) = mult(mult(A,B),mult(ld(B,C),ld(B,rd(C,B)))),
inference(paramod,[status(thm)],[c_83,c_9409]) ).
cnf(c_84,plain,
mult(mult(A,B),mult(ld(B,C),ld(B,rd(C,B)))) = mult(mult(A,C),ld(B,rd(C,B))),
inference(copy,[status(thm)],[c_9410]) ).
cnf(c_9411,plain,
rd(A,ld(A,unit)) = ld(ld(A,unit),rd(unit,ld(A,unit))),
inference(paramod,[status(thm)],[c_57,c_82]) ).
cnf(c_90,plain,
rd(A,ld(A,unit)) = ld(ld(A,unit),A),
inference(paramod,[status(thm)],[c_15,c_9411]) ).
cnf(c_98,plain,
rd(mult(A,B),A) = mult(A,rd(B,A)),
inference(paramod,[status(thm)],[c_62,c_15]) ).
cnf(c_9412,plain,
mult(mult(f(A),ld(A,f(A))),ld(A,f(A))) = mult(ld(A,f(A)),mult(f(A),ld(A,f(A)))),
inference(paramod,[status(thm)],[c_73,c_9]) ).
cnf(c_9413,plain,
mult(f(A),mult(ld(A,f(A)),ld(A,f(A)))) = mult(ld(A,f(A)),mult(f(A),ld(A,f(A)))),
inference(paramod,[status(thm)],[c_35,c_9412]) ).
cnf(c_137,plain,
mult(ld(A,f(A)),mult(f(A),ld(A,f(A)))) = mult(f(A),mult(ld(A,f(A)),ld(A,f(A)))),
inference(copy,[status(thm)],[c_9413]) ).
cnf(c_9414,plain,
ld(f(A),mult(f(A),ld(A,f(A)))) = mult(ld(f(A),ld(A,f(A))),f(A)),
inference(paramod,[status(thm)],[c_73,c_39]) ).
cnf(c_9415,plain,
ld(A,f(A)) = mult(ld(f(A),ld(A,f(A))),f(A)),
inference(paramod,[status(thm)],[c_2,c_9414]) ).
cnf(c_140,plain,
mult(ld(f(A),ld(A,f(A))),f(A)) = ld(A,f(A)),
inference(copy,[status(thm)],[c_9415]) ).
cnf(c_9416,plain,
mult(A,B) = mult(rd(A,B),mult(B,B)),
inference(paramod,[status(thm)],[c_3,c_35]) ).
cnf(c_169,plain,
mult(rd(A,B),mult(B,B)) = mult(A,B),
inference(copy,[status(thm)],[c_9416]) ).
cnf(c_9417,plain,
mult(mult(A,mult(B,A)),A) = mult(mult(A,B),mult(A,A)),
inference(paramod,[status(thm)],[c_9,c_35]) ).
cnf(c_9418,plain,
mult(A,mult(mult(B,A),A)) = mult(mult(A,B),mult(A,A)),
inference(paramod,[status(thm)],[c_9,c_9417]) ).
cnf(c_9419,plain,
mult(A,mult(B,mult(A,A))) = mult(mult(A,B),mult(A,A)),
inference(paramod,[status(thm)],[c_35,c_9418]) ).
cnf(c_171,plain,
mult(mult(A,B),mult(A,A)) = mult(A,mult(B,mult(A,A))),
inference(copy,[status(thm)],[c_9419]) ).
cnf(c_9420,plain,
mult(unit,A) = mult(ld(A,unit),mult(A,A)),
inference(paramod,[status(thm)],[c_52,c_35]) ).
cnf(c_9421,plain,
A = mult(ld(A,unit),mult(A,A)),
inference(paramod,[status(thm)],[c_6,c_9420]) ).
cnf(c_175,plain,
mult(ld(A,unit),mult(A,A)) = A,
inference(copy,[status(thm)],[c_9421]) ).
cnf(c_193,plain,
ld(ld(A,unit),A) = mult(A,A),
inference(paramod,[status(thm)],[c_175,c_2]) ).
cnf(c_194,plain,
rd(A,mult(A,A)) = ld(A,unit),
inference(paramod,[status(thm)],[c_175,c_4]) ).
cnf(c_9422,plain,
mult(A,ld(A,unit)) = mult(ld(A,unit),mult(mult(A,A),ld(A,unit))),
inference(paramod,[status(thm)],[c_175,c_9]) ).
cnf(c_9423,plain,
unit = mult(ld(A,unit),mult(mult(A,A),ld(A,unit))),
inference(paramod,[status(thm)],[c_1,c_9422]) ).
cnf(c_195,plain,
mult(ld(A,unit),mult(mult(A,A),ld(A,unit))) = unit,
inference(copy,[status(thm)],[c_9423]) ).
cnf(c_9424,plain,
mult(mult(A,mult(mult(B,B),B)),ld(B,unit)) = mult(mult(A,mult(B,B)),mult(ld(B,unit),mult(mult(B,B),ld(B,unit)))),
inference(paramod,[status(thm)],[c_175,c_13]) ).
cnf(c_9425,plain,
mult(mult(A,mult(B,mult(B,B))),ld(B,unit)) = mult(mult(A,mult(B,B)),mult(ld(B,unit),mult(mult(B,B),ld(B,unit)))),
inference(paramod,[status(thm)],[c_9,c_9424]) ).
cnf(c_9426,plain,
mult(mult(A,mult(B,mult(B,B))),ld(B,unit)) = mult(mult(A,mult(B,B)),unit),
inference(paramod,[status(thm)],[c_195,c_9425]) ).
cnf(c_197,plain,
mult(mult(A,mult(B,mult(B,B))),ld(B,unit)) = mult(A,mult(B,B)),
inference(paramod,[status(thm)],[c_5,c_9426]) ).
cnf(c_206,plain,
rd(A,ld(A,unit)) = mult(A,A),
inference(paramod,[status(thm)],[c_193,c_90]) ).
cnf(c_9427,plain,
rd(f(A),A) = ld(f(A),unit),
inference(paramod,[status(thm)],[c_10,c_194]) ).
cnf(c_9428,plain,
ld(A,f(A)) = ld(f(A),unit),
inference(paramod,[status(thm)],[c_72,c_9427]) ).
cnf(c_208,plain,
ld(f(A),unit) = ld(A,f(A)),
inference(copy,[status(thm)],[c_9428]) ).
cnf(c_9429,plain,
rd(mult(mult(A,A),A),mult(A,A)) = mult(mult(A,A),ld(A,unit)),
inference(paramod,[status(thm)],[c_194,c_98]) ).
cnf(c_9430,plain,
rd(mult(A,mult(A,A)),mult(A,A)) = mult(mult(A,A),ld(A,unit)),
inference(paramod,[status(thm)],[c_9,c_9429]) ).
cnf(c_9431,plain,
A = mult(mult(A,A),ld(A,unit)),
inference(paramod,[status(thm)],[c_4,c_9430]) ).
cnf(c_210,plain,
mult(mult(A,A),ld(A,unit)) = A,
inference(copy,[status(thm)],[c_9431]) ).
cnf(c_9432,plain,
rd(rd(unit,A),A) = mult(rd(unit,A),rd(unit,A)),
inference(paramod,[status(thm)],[c_14,c_206]) ).
cnf(c_9433,plain,
rd(ld(A,unit),A) = mult(rd(unit,A),rd(unit,A)),
inference(paramod,[status(thm)],[c_58,c_9432]) ).
cnf(c_9434,plain,
ld(A,rd(unit,A)) = mult(rd(unit,A),rd(unit,A)),
inference(paramod,[status(thm)],[c_82,c_9433]) ).
cnf(c_9435,plain,
ld(A,ld(A,unit)) = mult(rd(unit,A),rd(unit,A)),
inference(paramod,[status(thm)],[c_58,c_9434]) ).
cnf(c_9436,plain,
ld(A,ld(A,unit)) = mult(ld(A,unit),rd(unit,A)),
inference(paramod,[status(thm)],[c_58,c_9435]) ).
cnf(c_9437,plain,
ld(A,ld(A,unit)) = mult(ld(A,unit),ld(A,unit)),
inference(paramod,[status(thm)],[c_58,c_9436]) ).
cnf(c_213,plain,
mult(ld(A,unit),ld(A,unit)) = ld(A,ld(A,unit)),
inference(copy,[status(thm)],[c_9437]) ).
cnf(c_9438,plain,
rd(ld(ld(A,unit),A),ld(A,unit)) = ld(ld(A,unit),mult(A,A)),
inference(paramod,[status(thm)],[c_206,c_82]) ).
cnf(c_214,plain,
rd(mult(A,A),ld(A,unit)) = ld(ld(A,unit),mult(A,A)),
inference(paramod,[status(thm)],[c_193,c_9438]) ).
cnf(c_215,plain,
mult(f(A),ld(A,f(A))) = unit,
inference(paramod,[status(thm)],[c_208,c_1]) ).
cnf(c_216,plain,
mult(A,ld(f(A),unit)) = f(A),
inference(paramod,[status(thm)],[c_208,c_1]) ).
cnf(c_9439,plain,
rd(ld(A,f(A)),f(A)) = ld(f(A),rd(unit,f(A))),
inference(paramod,[status(thm)],[c_208,c_82]) ).
cnf(c_218,plain,
rd(ld(A,f(A)),f(A)) = ld(f(A),ld(f(A),unit)),
inference(paramod,[status(thm)],[c_58,c_9439]) ).
cnf(c_9440,plain,
mult(ld(A,f(A)),unit) = mult(f(A),mult(ld(A,f(A)),ld(A,f(A)))),
inference(paramod,[status(thm)],[c_215,c_137]) ).
cnf(c_9441,plain,
ld(A,f(A)) = mult(f(A),mult(ld(A,f(A)),ld(A,f(A)))),
inference(paramod,[status(thm)],[c_5,c_9440]) ).
cnf(c_223,plain,
mult(f(A),mult(ld(A,f(A)),ld(A,f(A)))) = ld(A,f(A)),
inference(copy,[status(thm)],[c_9441]) ).
cnf(c_9442,plain,
mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(mult(A,B),unit),
inference(paramod,[status(thm)],[c_215,c_74]) ).
cnf(c_224,plain,
mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(A,B),
inference(paramod,[status(thm)],[c_5,c_9442]) ).
cnf(c_225,plain,
mult(ld(A,f(A)),f(A)) = unit,
inference(paramod,[status(thm)],[c_215,c_73]) ).
cnf(c_300,plain,
ld(rd(A,B),mult(A,B)) = mult(B,B),
inference(paramod,[status(thm)],[c_169,c_2]) ).
cnf(c_301,plain,
rd(mult(A,B),mult(B,B)) = rd(A,B),
inference(paramod,[status(thm)],[c_169,c_4]) ).
cnf(c_9443,plain,
mult(rd(A,ld(f(A),unit)),mult(ld(f(A),unit),ld(f(A),unit))) = f(A),
inference(paramod,[status(thm)],[c_216,c_169]) ).
cnf(c_318,plain,
mult(rd(A,ld(f(A),unit)),ld(f(A),ld(f(A),unit))) = f(A),
inference(paramod,[status(thm)],[c_213,c_9443]) ).
cnf(c_9444,plain,
ld(mult(A,A),mult(A,ld(A,unit))) = mult(ld(A,unit),ld(A,unit)),
inference(paramod,[status(thm)],[c_206,c_300]) ).
cnf(c_9445,plain,
ld(mult(A,A),unit) = mult(ld(A,unit),ld(A,unit)),
inference(paramod,[status(thm)],[c_1,c_9444]) ).
cnf(c_344,plain,
ld(mult(A,A),unit) = ld(A,ld(A,unit)),
inference(paramod,[status(thm)],[c_213,c_9445]) ).
cnf(c_9446,plain,
ld(rd(f(A),ld(A,f(A))),unit) = mult(ld(A,f(A)),ld(A,f(A))),
inference(paramod,[status(thm)],[c_215,c_300]) ).
cnf(c_9447,plain,
ld(A,unit) = mult(ld(A,f(A)),ld(A,f(A))),
inference(paramod,[status(thm)],[c_15,c_9446]) ).
cnf(c_348,plain,
mult(ld(A,f(A)),ld(A,f(A))) = ld(A,unit),
inference(copy,[status(thm)],[c_9447]) ).
cnf(c_352,plain,
mult(f(A),ld(A,unit)) = ld(A,f(A)),
inference(paramod,[status(thm)],[c_348,c_223]) ).
cnf(c_9448,plain,
rd(A,mult(B,B)) = rd(rd(A,B),B),
inference(paramod,[status(thm)],[c_3,c_301]) ).
cnf(c_354,plain,
rd(rd(A,B),B) = rd(A,mult(B,B)),
inference(copy,[status(thm)],[c_9448]) ).
cnf(c_9449,plain,
rd(A,mult(ld(A,unit),ld(A,unit))) = rd(mult(A,A),ld(A,unit)),
inference(paramod,[status(thm)],[c_210,c_301]) ).
cnf(c_9450,plain,
rd(A,ld(A,ld(A,unit))) = rd(mult(A,A),ld(A,unit)),
inference(paramod,[status(thm)],[c_213,c_9449]) ).
cnf(c_369,plain,
rd(A,ld(A,ld(A,unit))) = ld(ld(A,unit),mult(A,A)),
inference(paramod,[status(thm)],[c_214,c_9450]) ).
cnf(c_9451,plain,
rd(f(A),mult(ld(f(A),unit),ld(f(A),unit))) = rd(A,ld(f(A),unit)),
inference(paramod,[status(thm)],[c_216,c_301]) ).
cnf(c_9452,plain,
rd(f(A),ld(f(A),ld(f(A),unit))) = rd(A,ld(f(A),unit)),
inference(paramod,[status(thm)],[c_213,c_9451]) ).
cnf(c_9453,plain,
ld(ld(f(A),unit),mult(f(A),f(A))) = rd(A,ld(f(A),unit)),
inference(paramod,[status(thm)],[c_369,c_9452]) ).
cnf(c_9454,plain,
ld(ld(f(A),unit),A) = rd(A,ld(f(A),unit)),
inference(paramod,[status(thm)],[c_10,c_9453]) ).
cnf(c_370,plain,
rd(A,ld(f(A),unit)) = ld(ld(f(A),unit),A),
inference(copy,[status(thm)],[c_9454]) ).
cnf(c_9455,plain,
rd(unit,mult(f(A),f(A))) = rd(ld(A,f(A)),f(A)),
inference(paramod,[status(thm)],[c_225,c_301]) ).
cnf(c_9456,plain,
rd(unit,A) = rd(ld(A,f(A)),f(A)),
inference(paramod,[status(thm)],[c_10,c_9455]) ).
cnf(c_9457,plain,
ld(A,unit) = rd(ld(A,f(A)),f(A)),
inference(paramod,[status(thm)],[c_58,c_9456]) ).
cnf(c_371,plain,
rd(ld(A,f(A)),f(A)) = ld(A,unit),
inference(copy,[status(thm)],[c_9457]) ).
cnf(c_379,plain,
mult(ld(ld(f(A),unit),A),ld(f(A),ld(f(A),unit))) = f(A),
inference(paramod,[status(thm)],[c_370,c_318]) ).
cnf(c_9458,plain,
ld(A,unit) = ld(f(A),ld(f(A),unit)),
inference(paramod,[status(thm)],[c_371,c_218]) ).
cnf(c_380,plain,
ld(f(A),ld(f(A),unit)) = ld(A,unit),
inference(copy,[status(thm)],[c_9458]) ).
cnf(c_385,plain,
mult(ld(ld(f(A),unit),A),ld(A,unit)) = f(A),
inference(paramod,[status(thm)],[c_380,c_379]) ).
cnf(c_387,plain,
ld(f(A),ld(A,f(A))) = ld(A,unit),
inference(paramod,[status(thm)],[c_352,c_2]) ).
cnf(c_407,plain,
mult(ld(A,unit),f(A)) = ld(A,f(A)),
inference(paramod,[status(thm)],[c_387,c_140]) ).
cnf(c_9459,plain,
rd(mult(A,A),ld(A,ld(A,unit))) = mult(mult(A,A),mult(A,A)),
inference(paramod,[status(thm)],[c_344,c_206]) ).
cnf(c_504,plain,
rd(mult(A,A),ld(A,ld(A,unit))) = mult(A,mult(A,mult(A,A))),
inference(paramod,[status(thm)],[c_171,c_9459]) ).
cnf(c_511,plain,
mult(rd(A,mult(B,B)),B) = rd(A,B),
inference(paramod,[status(thm)],[c_354,c_3]) ).
cnf(c_575,plain,
mult(rd(A,B),f(B)) = rd(A,f(B)),
inference(paramod,[status(thm)],[c_10,c_511]) ).
cnf(c_601,plain,
ld(rd(A,B),rd(A,f(B))) = f(B),
inference(paramod,[status(thm)],[c_575,c_2]) ).
cnf(c_9460,plain,
mult(A,f(B)) = rd(mult(A,B),f(B)),
inference(paramod,[status(thm)],[c_4,c_575]) ).
cnf(c_602,plain,
rd(mult(A,B),f(B)) = mult(A,f(B)),
inference(copy,[status(thm)],[c_9460]) ).
cnf(c_636,plain,
ld(mult(A,f(B)),mult(A,B)) = f(B),
inference(paramod,[status(thm)],[c_602,c_14]) ).
cnf(c_9461,plain,
rd(f(A),mult(B,f(A))) = ld(mult(B,f(A)),rd(mult(B,A),mult(B,f(A)))),
inference(paramod,[status(thm)],[c_636,c_82]) ).
cnf(c_732,plain,
ld(mult(A,f(B)),rd(mult(A,B),mult(A,f(B)))) = rd(f(B),mult(A,f(B))),
inference(copy,[status(thm)],[c_9461]) ).
cnf(c_9462,plain,
mult(mult(ld(A,f(A)),mult(ld(A,f(A)),f(A))),A) = mult(ld(A,unit),mult(f(A),A)),
inference(paramod,[status(thm)],[c_348,c_28]) ).
cnf(c_9463,plain,
mult(mult(ld(A,f(A)),unit),A) = mult(ld(A,unit),mult(f(A),A)),
inference(paramod,[status(thm)],[c_225,c_9462]) ).
cnf(c_9464,plain,
mult(ld(A,f(A)),A) = mult(ld(A,unit),mult(f(A),A)),
inference(paramod,[status(thm)],[c_5,c_9463]) ).
cnf(c_9465,plain,
f(A) = mult(ld(A,unit),mult(f(A),A)),
inference(paramod,[status(thm)],[c_55,c_9464]) ).
cnf(c_9466,plain,
f(A) = mult(ld(A,unit),mult(A,f(A))),
inference(paramod,[status(thm)],[c_27,c_9465]) ).
cnf(c_776,plain,
mult(ld(A,unit),mult(A,f(A))) = f(A),
inference(copy,[status(thm)],[c_9466]) ).
cnf(c_9467,plain,
rd(mult(unit,mult(A,mult(B,A))),A) = mult(ld(B,unit),mult(B,mult(A,B))),
inference(paramod,[status(thm)],[c_52,c_34]) ).
cnf(c_9468,plain,
rd(mult(A,mult(B,A)),A) = mult(ld(B,unit),mult(B,mult(A,B))),
inference(paramod,[status(thm)],[c_6,c_9467]) ).
cnf(c_9469,plain,
mult(A,rd(mult(B,A),A)) = mult(ld(B,unit),mult(B,mult(A,B))),
inference(paramod,[status(thm)],[c_98,c_9468]) ).
cnf(c_9470,plain,
mult(A,B) = mult(ld(B,unit),mult(B,mult(A,B))),
inference(paramod,[status(thm)],[c_4,c_9469]) ).
cnf(c_887,plain,
mult(ld(A,unit),mult(A,mult(B,A))) = mult(B,A),
inference(copy,[status(thm)],[c_9470]) ).
cnf(c_9471,plain,
mult(rd(mult(A,A),mult(ld(A,unit),ld(A,unit))),ld(A,unit)) = ld(ld(A,unit),mult(A,A)),
inference(paramod,[status(thm)],[c_214,c_511]) ).
cnf(c_9472,plain,
mult(rd(mult(A,A),ld(A,ld(A,unit))),ld(A,unit)) = ld(ld(A,unit),mult(A,A)),
inference(paramod,[status(thm)],[c_213,c_9471]) ).
cnf(c_9473,plain,
mult(mult(A,mult(A,mult(A,A))),ld(A,unit)) = ld(ld(A,unit),mult(A,A)),
inference(paramod,[status(thm)],[c_504,c_9472]) ).
cnf(c_9474,plain,
mult(A,mult(A,A)) = ld(ld(A,unit),mult(A,A)),
inference(paramod,[status(thm)],[c_197,c_9473]) ).
cnf(c_1540,plain,
ld(ld(A,unit),mult(A,A)) = mult(A,mult(A,A)),
inference(copy,[status(thm)],[c_9474]) ).
cnf(c_1552,plain,
rd(mult(A,A),ld(A,unit)) = mult(A,mult(A,A)),
inference(paramod,[status(thm)],[c_1540,c_214]) ).
cnf(c_9475,plain,
rd(A,ld(f(A),unit)) = mult(f(A),mult(f(A),f(A))),
inference(paramod,[status(thm)],[c_10,c_1552]) ).
cnf(c_9476,plain,
ld(ld(f(A),unit),A) = mult(f(A),mult(f(A),f(A))),
inference(paramod,[status(thm)],[c_370,c_9475]) ).
cnf(c_9477,plain,
ld(ld(f(A),unit),A) = mult(f(A),A),
inference(paramod,[status(thm)],[c_10,c_9476]) ).
cnf(c_1553,plain,
ld(ld(f(A),unit),A) = mult(A,f(A)),
inference(paramod,[status(thm)],[c_27,c_9477]) ).
cnf(c_1564,plain,
mult(mult(A,f(A)),ld(A,unit)) = f(A),
inference(paramod,[status(thm)],[c_1553,c_385]) ).
cnf(c_9478,plain,
mult(mult(rd(A,mult(mult(B,f(B)),f(B))),mult(B,f(B))),mult(ld(B,unit),mult(mult(B,f(B)),ld(B,unit)))) = mult(A,ld(B,unit)),
inference(paramod,[status(thm)],[c_776,c_32]) ).
cnf(c_9479,plain,
mult(mult(rd(A,mult(B,mult(f(B),f(B)))),mult(B,f(B))),mult(ld(B,unit),mult(mult(B,f(B)),ld(B,unit)))) = mult(A,ld(B,unit)),
inference(paramod,[status(thm)],[c_35,c_9478]) ).
cnf(c_9480,plain,
mult(mult(rd(A,mult(B,B)),mult(B,f(B))),mult(ld(B,unit),mult(mult(B,f(B)),ld(B,unit)))) = mult(A,ld(B,unit)),
inference(paramod,[status(thm)],[c_10,c_9479]) ).
cnf(c_9481,plain,
mult(mult(rd(A,mult(B,B)),mult(B,f(B))),mult(ld(B,unit),f(B))) = mult(A,ld(B,unit)),
inference(paramod,[status(thm)],[c_1564,c_9480]) ).
cnf(c_9482,plain,
mult(mult(rd(A,mult(B,B)),mult(B,f(B))),ld(B,f(B))) = mult(A,ld(B,unit)),
inference(paramod,[status(thm)],[c_407,c_9481]) ).
cnf(c_9483,plain,
mult(rd(A,mult(B,B)),B) = mult(A,ld(B,unit)),
inference(paramod,[status(thm)],[c_224,c_9482]) ).
cnf(c_9484,plain,
rd(A,B) = mult(A,ld(B,unit)),
inference(paramod,[status(thm)],[c_511,c_9483]) ).
cnf(c_2263,plain,
mult(A,ld(B,unit)) = rd(A,B),
inference(copy,[status(thm)],[c_9484]) ).
cnf(c_2598,plain,
ld(A,rd(A,B)) = ld(B,unit),
inference(paramod,[status(thm)],[c_2263,c_2]) ).
cnf(c_9485,plain,
mult(A,B) = rd(A,rd(unit,B)),
inference(paramod,[status(thm)],[c_14,c_2263]) ).
cnf(c_9486,plain,
mult(A,B) = rd(A,ld(B,unit)),
inference(paramod,[status(thm)],[c_58,c_9485]) ).
cnf(c_2605,plain,
rd(A,ld(B,unit)) = mult(A,B),
inference(copy,[status(thm)],[c_9486]) ).
cnf(c_2762,plain,
ld(mult(A,B),A) = ld(B,unit),
inference(paramod,[status(thm)],[c_4,c_2598]) ).
cnf(c_9487,plain,
ld(A,B) = ld(ld(B,A),unit),
inference(paramod,[status(thm)],[c_15,c_2598]) ).
cnf(c_2763,plain,
ld(ld(A,B),unit) = ld(B,A),
inference(copy,[status(thm)],[c_9487]) ).
cnf(c_9488,plain,
mult(mult(ld(A,unit),B),A) = mult(ld(A,unit),rd(B,ld(A,unit))),
inference(paramod,[status(thm)],[c_2605,c_98]) ).
cnf(c_2790,plain,
mult(mult(ld(A,unit),B),A) = mult(ld(A,unit),mult(B,A)),
inference(paramod,[status(thm)],[c_2605,c_9488]) ).
cnf(c_2804,plain,
ld(mult(A,mult(B,A)),mult(A,B)) = ld(A,unit),
inference(paramod,[status(thm)],[c_9,c_2762]) ).
cnf(c_9489,plain,
ld(ld(A,B),unit) = ld(mult(ld(A,B),B),mult(ld(A,B),A)),
inference(paramod,[status(thm)],[c_61,c_2763]) ).
cnf(c_9490,plain,
ld(B,A) = ld(mult(ld(A,B),B),mult(ld(A,B),A)),
inference(paramod,[status(thm)],[c_2763,c_9489]) ).
cnf(c_2828,plain,
ld(mult(ld(A,B),B),mult(ld(A,B),A)) = ld(B,A),
inference(copy,[status(thm)],[c_9490]) ).
cnf(c_9491,plain,
ld(mult(ld(mult(A,mult(B,A)),mult(A,B)),mult(A,B)),mult(ld(mult(A,mult(B,A)),mult(A,B)),mult(A,mult(B,A)))) = A,
inference(paramod,[status(thm)],[c_21,c_2828]) ).
cnf(c_9492,plain,
ld(mult(ld(A,unit),mult(A,B)),mult(ld(mult(A,mult(B,A)),mult(A,B)),mult(A,mult(B,A)))) = A,
inference(paramod,[status(thm)],[c_2804,c_9491]) ).
cnf(c_9493,plain,
ld(mult(ld(A,unit),mult(A,B)),mult(ld(A,unit),mult(A,mult(B,A)))) = A,
inference(paramod,[status(thm)],[c_2804,c_9492]) ).
cnf(c_3608,plain,
ld(mult(ld(A,unit),mult(A,B)),mult(B,A)) = A,
inference(paramod,[status(thm)],[c_887,c_9493]) ).
cnf(c_6173,plain,
ld(mult(ld(A,unit),B),mult(ld(A,B),A)) = A,
inference(paramod,[status(thm)],[c_1,c_3608]) ).
cnf(c_9494,plain,
mult(mult(ld(A,unit),B),A) = mult(ld(A,B),A),
inference(paramod,[status(thm)],[c_6173,c_1]) ).
cnf(c_6265,plain,
mult(ld(A,unit),mult(B,A)) = mult(ld(A,B),A),
inference(paramod,[status(thm)],[c_2790,c_9494]) ).
cnf(c_9495,plain,
mult(ld(A,unit),B) = mult(ld(A,rd(B,A)),A),
inference(paramod,[status(thm)],[c_3,c_6265]) ).
cnf(c_6457,plain,
mult(ld(A,unit),B) = ld(A,B),
inference(paramod,[status(thm)],[c_51,c_9495]) ).
cnf(c_7636,plain,
rd(ld(A,B),B) = ld(A,unit),
inference(paramod,[status(thm)],[c_6457,c_4]) ).
cnf(c_9496,plain,
mult(mult(A,mult(B,f(C))),mult(f(C),ld(mult(B,f(C)),rd(mult(B,C),mult(B,f(C)))))) = mult(mult(A,mult(B,C)),ld(mult(B,f(C)),rd(mult(B,C),mult(B,f(C))))),
inference(paramod,[status(thm)],[c_636,c_84]) ).
cnf(c_9497,plain,
mult(mult(A,mult(B,f(C))),mult(f(C),rd(f(C),mult(B,f(C))))) = mult(mult(A,mult(B,C)),ld(mult(B,f(C)),rd(mult(B,C),mult(B,f(C))))),
inference(paramod,[status(thm)],[c_732,c_9496]) ).
cnf(c_8189,plain,
mult(mult(A,mult(B,f(C))),mult(f(C),rd(f(C),mult(B,f(C))))) = mult(mult(A,mult(B,C)),rd(f(C),mult(B,f(C)))),
inference(paramod,[status(thm)],[c_732,c_9497]) ).
cnf(c_8234,plain,
rd(A,mult(B,A)) = ld(B,unit),
inference(paramod,[status(thm)],[c_2,c_7636]) ).
cnf(c_9498,plain,
rd(A,B) = ld(rd(B,A),unit),
inference(paramod,[status(thm)],[c_14,c_7636]) ).
cnf(c_8235,plain,
ld(rd(A,B),unit) = rd(B,A),
inference(copy,[status(thm)],[c_9498]) ).
cnf(c_9499,plain,
rd(f(A),rd(B,f(A))) = ld(rd(B,A),unit),
inference(paramod,[status(thm)],[c_601,c_7636]) ).
cnf(c_8244,plain,
rd(f(A),rd(B,f(A))) = rd(A,B),
inference(paramod,[status(thm)],[c_8235,c_9499]) ).
cnf(c_9500,plain,
mult(mult(A,mult(B,f(C))),mult(f(C),ld(B,unit))) = mult(mult(A,mult(B,C)),rd(f(C),mult(B,f(C)))),
inference(paramod,[status(thm)],[c_8234,c_8189]) ).
cnf(c_9501,plain,
mult(mult(A,mult(B,f(C))),rd(f(C),B)) = mult(mult(A,mult(B,C)),rd(f(C),mult(B,f(C)))),
inference(paramod,[status(thm)],[c_2263,c_9500]) ).
cnf(c_9502,plain,
mult(mult(A,B),mult(f(C),rd(f(C),B))) = mult(mult(A,mult(B,C)),rd(f(C),mult(B,f(C)))),
inference(paramod,[status(thm)],[c_31,c_9501]) ).
cnf(c_9503,plain,
mult(mult(A,B),mult(f(C),rd(f(C),B))) = mult(mult(A,mult(B,C)),ld(B,unit)),
inference(paramod,[status(thm)],[c_8234,c_9502]) ).
cnf(c_8281,plain,
mult(mult(A,B),mult(f(C),rd(f(C),B))) = rd(mult(A,mult(B,C)),B),
inference(paramod,[status(thm)],[c_2263,c_9503]) ).
cnf(c_9504,plain,
mult(A,rd(B,C)) = rd(A,rd(C,B)),
inference(paramod,[status(thm)],[c_8235,c_2263]) ).
cnf(c_8869,plain,
rd(A,rd(B,C)) = mult(A,rd(C,B)),
inference(copy,[status(thm)],[c_9504]) ).
cnf(c_8972,plain,
mult(f(A),rd(f(A),B)) = rd(A,B),
inference(paramod,[status(thm)],[c_8869,c_8244]) ).
cnf(c_9505,plain,
mult(mult(A,B),rd(C,B)) = rd(mult(A,mult(B,C)),B),
inference(paramod,[status(thm)],[c_8972,c_8281]) ).
cnf(c_9276,plain,
rd(mult(A,mult(B,C)),B) = mult(mult(A,B),rd(C,B)),
inference(copy,[status(thm)],[c_9505]) ).
cnf(c_9506,plain,
mult(mult(mult(A,B),C),rd(mult(B,C),C)) = mult(A,mult(B,mult(C,B))),
inference(paramod,[status(thm)],[c_9276,c_34]) ).
cnf(c_9383,plain,
mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B))),
inference(paramod,[status(thm)],[c_4,c_9506]) ).
cnf(c_9384,plain,
$false,
inference(resolve,[status(thm)],[c_9383,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP667-3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n020.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 15:35:18 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 3270081 was started by sandbox2 on n020,
% 0.18/0.45 % Fri Sep 25 15:35:18 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 32.16/4.58
% 32.16/4.58 % Assigning unary symbol f kb_weight 0 and highest precedence (9).
% 32.16/4.58
% 32.16/4.58 % SZS status Unsatisfiable for theBenchmark
% 32.16/4.58
% 32.16/4.58 % Proof 1 at 3.22 (+ 0.83) seconds.
% 32.16/4.58 % Length of proof is 112.
% 32.16/4.58 % Level of proof is 28.
% 32.16/4.58 % Maximum clause weight is 86.000.
% 32.16/4.58 % Given clauses 246.
% 32.16/4.58
% 32.16/4.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------