%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP707-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 07:31:17 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.91s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 10
% Syntax : Number of formulae : 233 ( 233 unt; 0 def)
% Number of atoms : 233 ( 232 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 471 ( 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(VAR_0,mult(VAR_1,mult(VAR_1,VAR_2))) = mult(mult(mult(VAR_0,VAR_1),VAR_1),VAR_2),
file('theBenchmark.p',c07) ).
cnf(c_7,plain,
mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C),
inference(clausify,[status(thm)],[c07]) ).
cnf(c_8,plain,
mult(mult(mult(A,B),B),C) = mult(A,mult(B,mult(B,C))),
inference(copy,[status(thm)],[c_7]) ).
fof(c08,axiom,
! [VAR_0] : mult(VAR_0,mult(VAR_0,mult(VAR_0,VAR_0))) = unit,
file('theBenchmark.p',c08) ).
cnf(c_9,plain,
mult(A,mult(A,mult(A,A))) = unit,
inference(clausify,[status(thm)],[c08]) ).
fof(c09,axiom,
! [VAR_0,VAR_1] : mult(mult(VAR_0,VAR_0),VAR_1) = mult(VAR_1,mult(VAR_0,VAR_0)),
file('theBenchmark.p',c09) ).
cnf(c_10,plain,
mult(mult(A,A),B) = mult(B,mult(A,A)),
inference(clausify,[status(thm)],[c09]) ).
fof(goals,axiom,
mult(mult(a,b),a) != mult(a,mult(b,a)),
file('theBenchmark.p',goals) ).
cnf(c_11,plain,
mult(mult(a,b),a) != mult(a,mult(b,a)),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_12,plain,
ld(rd(A,B),A) = B,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_13,plain,
rd(A,ld(B,A)) = B,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_16,plain,
ld(unit,A) = A,
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_506,plain,
mult(mult(A,ld(B,A)),C) = mult(B,mult(ld(B,A),mult(ld(B,A),C))),
inference(paramod,[status(thm)],[c_1,c_8]) ).
cnf(c_19,plain,
mult(A,mult(ld(A,B),mult(ld(A,B),C))) = mult(mult(B,ld(A,B)),C),
inference(copy,[status(thm)],[c_506]) ).
cnf(c_507,plain,
mult(mult(A,B),C) = mult(rd(A,B),mult(B,mult(B,C))),
inference(paramod,[status(thm)],[c_3,c_8]) ).
cnf(c_21,plain,
mult(rd(A,B),mult(B,mult(B,C))) = mult(mult(A,B),C),
inference(copy,[status(thm)],[c_507]) ).
cnf(c_22,plain,
rd(mult(A,mult(B,mult(B,C))),C) = mult(mult(A,B),B),
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_508,plain,
mult(A,mult(B,mult(B,unit))) = mult(mult(A,B),B),
inference(paramod,[status(thm)],[c_8,c_5]) ).
cnf(c_509,plain,
mult(A,mult(B,B)) = mult(mult(A,B),B),
inference(paramod,[status(thm)],[c_5,c_508]) ).
cnf(c_23,plain,
mult(mult(A,B),B) = mult(A,mult(B,B)),
inference(copy,[status(thm)],[c_509]) ).
cnf(c_510,plain,
mult(mult(A,A),B) = mult(unit,mult(A,mult(A,B))),
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_24,plain,
mult(mult(A,A),B) = mult(A,mult(A,B)),
inference(paramod,[status(thm)],[c_6,c_510]) ).
cnf(c_30,plain,
rd(mult(A,mult(B,mult(B,C))),C) = mult(A,mult(B,B)),
inference(paramod,[status(thm)],[c_23,c_22]) ).
cnf(c_33,plain,
mult(mult(A,mult(B,B)),C) = mult(A,mult(B,mult(B,C))),
inference(paramod,[status(thm)],[c_23,c_8]) ).
cnf(c_511,plain,
mult(A,mult(A,B)) = mult(B,mult(A,A)),
inference(paramod,[status(thm)],[c_24,c_10]) ).
cnf(c_34,plain,
mult(A,mult(B,B)) = mult(B,mult(B,A)),
inference(copy,[status(thm)],[c_511]) ).
cnf(c_512,plain,
ld(A,unit) = mult(A,mult(A,A)),
inference(paramod,[status(thm)],[c_9,c_2]) ).
cnf(c_38,plain,
mult(A,mult(A,A)) = ld(A,unit),
inference(copy,[status(thm)],[c_512]) ).
cnf(c_40,plain,
ld(A,ld(A,unit)) = mult(A,A),
inference(paramod,[status(thm)],[c_38,c_2]) ).
cnf(c_43,plain,
ld(A,mult(mult(B,ld(A,B)),C)) = mult(ld(A,B),mult(ld(A,B),C)),
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_513,plain,
mult(A,ld(ld(A,B),unit)) = mult(mult(B,ld(A,B)),ld(A,B)),
inference(paramod,[status(thm)],[c_38,c_19]) ).
cnf(c_514,plain,
mult(A,ld(ld(A,B),unit)) = mult(B,mult(ld(A,B),ld(A,B))),
inference(paramod,[status(thm)],[c_23,c_513]) ).
cnf(c_47,plain,
mult(A,mult(ld(B,A),ld(B,A))) = mult(B,ld(ld(B,A),unit)),
inference(copy,[status(thm)],[c_514]) ).
cnf(c_515,plain,
ld(rd(unit,A),A) = mult(rd(unit,A),rd(unit,A)),
inference(paramod,[status(thm)],[c_12,c_40]) ).
cnf(c_50,plain,
mult(rd(unit,A),rd(unit,A)) = ld(rd(unit,A),A),
inference(copy,[status(thm)],[c_515]) ).
cnf(c_516,plain,
mult(mult(A,mult(B,B)),B) = mult(mult(A,B),mult(B,B)),
inference(paramod,[status(thm)],[c_23,c_23]) ).
cnf(c_517,plain,
mult(A,mult(B,mult(B,B))) = mult(mult(A,B),mult(B,B)),
inference(paramod,[status(thm)],[c_33,c_516]) ).
cnf(c_518,plain,
mult(A,ld(B,unit)) = mult(mult(A,B),mult(B,B)),
inference(paramod,[status(thm)],[c_38,c_517]) ).
cnf(c_519,plain,
mult(A,ld(B,unit)) = mult(B,mult(B,mult(A,B))),
inference(paramod,[status(thm)],[c_34,c_518]) ).
cnf(c_60,plain,
mult(A,mult(A,mult(B,A))) = mult(B,ld(A,unit)),
inference(copy,[status(thm)],[c_519]) ).
cnf(c_520,plain,
mult(mult(A,A),mult(A,mult(A,mult(A,A)))) = ld(mult(A,A),unit),
inference(paramod,[status(thm)],[c_24,c_38]) ).
cnf(c_521,plain,
mult(mult(A,A),mult(A,ld(A,unit))) = ld(mult(A,A),unit),
inference(paramod,[status(thm)],[c_38,c_520]) ).
cnf(c_522,plain,
mult(mult(A,A),unit) = ld(mult(A,A),unit),
inference(paramod,[status(thm)],[c_1,c_521]) ).
cnf(c_523,plain,
mult(A,A) = ld(mult(A,A),unit),
inference(paramod,[status(thm)],[c_5,c_522]) ).
cnf(c_66,plain,
ld(mult(A,A),unit) = mult(A,A),
inference(copy,[status(thm)],[c_523]) ).
cnf(c_524,plain,
mult(mult(A,mult(B,B)),mult(B,B)) = mult(A,mult(B,mult(B,mult(B,B)))),
inference(paramod,[status(thm)],[c_24,c_23]) ).
cnf(c_525,plain,
mult(B,mult(B,mult(A,mult(B,B)))) = mult(A,mult(B,mult(B,mult(B,B)))),
inference(paramod,[status(thm)],[c_34,c_524]) ).
cnf(c_526,plain,
mult(B,mult(B,mult(A,mult(B,B)))) = mult(A,mult(B,ld(B,unit))),
inference(paramod,[status(thm)],[c_38,c_525]) ).
cnf(c_527,plain,
mult(B,mult(B,mult(A,mult(B,B)))) = mult(A,unit),
inference(paramod,[status(thm)],[c_1,c_526]) ).
cnf(c_70,plain,
mult(A,mult(A,mult(B,mult(A,A)))) = B,
inference(paramod,[status(thm)],[c_5,c_527]) ).
cnf(c_528,plain,
mult(mult(A,mult(A,mult(A,A))),B) = mult(mult(A,A),mult(mult(A,A),B)),
inference(paramod,[status(thm)],[c_24,c_24]) ).
cnf(c_529,plain,
mult(mult(A,ld(A,unit)),B) = mult(mult(A,A),mult(mult(A,A),B)),
inference(paramod,[status(thm)],[c_38,c_528]) ).
cnf(c_530,plain,
mult(unit,B) = mult(mult(A,A),mult(mult(A,A),B)),
inference(paramod,[status(thm)],[c_1,c_529]) ).
cnf(c_531,plain,
B = mult(mult(A,A),mult(mult(A,A),B)),
inference(paramod,[status(thm)],[c_6,c_530]) ).
cnf(c_532,plain,
B = mult(mult(A,A),mult(A,mult(A,B))),
inference(paramod,[status(thm)],[c_24,c_531]) ).
cnf(c_533,plain,
B = mult(A,mult(A,mult(A,mult(A,B)))),
inference(paramod,[status(thm)],[c_24,c_532]) ).
cnf(c_71,plain,
mult(A,mult(A,mult(A,mult(A,B)))) = B,
inference(copy,[status(thm)],[c_533]) ).
cnf(c_73,plain,
rd(unit,mult(A,A)) = mult(A,A),
inference(paramod,[status(thm)],[c_66,c_13]) ).
cnf(c_534,plain,
mult(rd(A,B),mult(B,ld(B,unit))) = mult(mult(A,B),mult(B,B)),
inference(paramod,[status(thm)],[c_38,c_21]) ).
cnf(c_535,plain,
mult(rd(A,B),unit) = mult(mult(A,B),mult(B,B)),
inference(paramod,[status(thm)],[c_1,c_534]) ).
cnf(c_536,plain,
rd(A,B) = mult(mult(A,B),mult(B,B)),
inference(paramod,[status(thm)],[c_5,c_535]) ).
cnf(c_537,plain,
rd(A,B) = mult(B,mult(B,mult(A,B))),
inference(paramod,[status(thm)],[c_34,c_536]) ).
cnf(c_538,plain,
rd(A,B) = mult(A,ld(B,unit)),
inference(paramod,[status(thm)],[c_60,c_537]) ).
cnf(c_78,plain,
mult(A,ld(B,unit)) = rd(A,B),
inference(copy,[status(thm)],[c_538]) ).
cnf(c_539,plain,
mult(rd(A,B),ld(B,unit)) = mult(mult(A,B),B),
inference(paramod,[status(thm)],[c_38,c_21]) ).
cnf(c_540,plain,
rd(rd(A,B),B) = mult(mult(A,B),B),
inference(paramod,[status(thm)],[c_78,c_539]) ).
cnf(c_79,plain,
rd(rd(A,B),B) = mult(A,mult(B,B)),
inference(paramod,[status(thm)],[c_23,c_540]) ).
cnf(c_541,plain,
mult(rd(A,mult(A,A)),mult(mult(A,A),mult(mult(A,A),B))) = mult(ld(A,unit),B),
inference(paramod,[status(thm)],[c_38,c_21]) ).
cnf(c_542,plain,
mult(rd(A,mult(A,A)),mult(mult(A,A),mult(A,mult(A,B)))) = mult(ld(A,unit),B),
inference(paramod,[status(thm)],[c_24,c_541]) ).
cnf(c_543,plain,
mult(rd(A,mult(A,A)),mult(A,mult(A,mult(A,mult(A,B))))) = mult(ld(A,unit),B),
inference(paramod,[status(thm)],[c_24,c_542]) ).
cnf(c_80,plain,
mult(rd(A,mult(A,A)),B) = mult(ld(A,unit),B),
inference(paramod,[status(thm)],[c_71,c_543]) ).
cnf(c_544,plain,
mult(rd(A,mult(B,B)),mult(mult(B,B),mult(B,mult(B,C)))) = mult(mult(A,mult(B,B)),C),
inference(paramod,[status(thm)],[c_24,c_21]) ).
cnf(c_545,plain,
mult(rd(A,mult(B,B)),mult(B,mult(B,mult(B,mult(B,C))))) = mult(mult(A,mult(B,B)),C),
inference(paramod,[status(thm)],[c_24,c_544]) ).
cnf(c_546,plain,
mult(rd(A,mult(B,B)),C) = mult(mult(A,mult(B,B)),C),
inference(paramod,[status(thm)],[c_71,c_545]) ).
cnf(c_83,plain,
mult(rd(A,mult(B,B)),C) = mult(A,mult(B,mult(B,C))),
inference(paramod,[status(thm)],[c_33,c_546]) ).
cnf(c_85,plain,
mult(A,mult(ld(B,A),ld(B,A))) = rd(B,ld(B,A)),
inference(paramod,[status(thm)],[c_78,c_47]) ).
cnf(c_87,plain,
mult(A,mult(A,mult(A,B))) = mult(ld(A,unit),B),
inference(paramod,[status(thm)],[c_83,c_80]) ).
cnf(c_547,plain,
rd(unit,ld(rd(unit,A),A)) = mult(rd(unit,A),rd(unit,A)),
inference(paramod,[status(thm)],[c_50,c_73]) ).
cnf(c_89,plain,
rd(unit,ld(rd(unit,A),A)) = ld(rd(unit,A),A),
inference(paramod,[status(thm)],[c_50,c_547]) ).
cnf(c_90,plain,
ld(A,rd(A,B)) = ld(B,unit),
inference(paramod,[status(thm)],[c_78,c_2]) ).
cnf(c_93,plain,
rd(unit,A) = ld(A,unit),
inference(paramod,[status(thm)],[c_78,c_6]) ).
cnf(c_548,plain,
mult(rd(ld(A,unit),A),B) = mult(ld(A,unit),mult(ld(A,unit),B)),
inference(paramod,[status(thm)],[c_78,c_24]) ).
cnf(c_99,plain,
mult(ld(A,unit),mult(ld(A,unit),B)) = mult(rd(ld(A,unit),A),B),
inference(copy,[status(thm)],[c_548]) ).
cnf(c_549,plain,
rd(mult(A,A),B) = mult(A,mult(A,ld(B,unit))),
inference(paramod,[status(thm)],[c_78,c_24]) ).
cnf(c_100,plain,
rd(mult(A,A),B) = mult(A,rd(A,B)),
inference(paramod,[status(thm)],[c_78,c_549]) ).
cnf(c_550,plain,
mult(A,mult(B,B)) = rd(A,mult(B,B)),
inference(paramod,[status(thm)],[c_66,c_78]) ).
cnf(c_102,plain,
rd(A,mult(B,B)) = mult(A,mult(B,B)),
inference(copy,[status(thm)],[c_550]) ).
cnf(c_551,plain,
rd(unit,ld(ld(A,unit),A)) = ld(rd(unit,A),A),
inference(paramod,[status(thm)],[c_93,c_89]) ).
cnf(c_552,plain,
ld(ld(ld(A,unit),A),unit) = ld(rd(unit,A),A),
inference(paramod,[status(thm)],[c_93,c_551]) ).
cnf(c_103,plain,
ld(ld(ld(A,unit),A),unit) = ld(ld(A,unit),A),
inference(paramod,[status(thm)],[c_93,c_552]) ).
cnf(c_553,plain,
mult(ld(A,unit),rd(unit,A)) = ld(rd(unit,A),A),
inference(paramod,[status(thm)],[c_93,c_50]) ).
cnf(c_554,plain,
mult(ld(A,unit),ld(A,unit)) = ld(rd(unit,A),A),
inference(paramod,[status(thm)],[c_93,c_553]) ).
cnf(c_555,plain,
rd(ld(A,unit),A) = ld(rd(unit,A),A),
inference(paramod,[status(thm)],[c_78,c_554]) ).
cnf(c_109,plain,
rd(ld(A,unit),A) = ld(ld(A,unit),A),
inference(paramod,[status(thm)],[c_93,c_555]) ).
cnf(c_111,plain,
mult(ld(A,unit),mult(ld(A,unit),B)) = mult(ld(ld(A,unit),A),B),
inference(paramod,[status(thm)],[c_109,c_99]) ).
cnf(c_113,plain,
ld(mult(A,B),A) = ld(B,unit),
inference(paramod,[status(thm)],[c_4,c_90]) ).
cnf(c_556,plain,
ld(A,B) = ld(ld(B,A),unit),
inference(paramod,[status(thm)],[c_13,c_90]) ).
cnf(c_114,plain,
ld(ld(A,B),unit) = ld(B,A),
inference(copy,[status(thm)],[c_556]) ).
cnf(c_557,plain,
ld(A,ld(A,unit)) = ld(ld(A,unit),A),
inference(paramod,[status(thm)],[c_114,c_103]) ).
cnf(c_558,plain,
mult(A,A) = ld(ld(A,unit),A),
inference(paramod,[status(thm)],[c_40,c_557]) ).
cnf(c_116,plain,
ld(ld(A,unit),A) = mult(A,A),
inference(copy,[status(thm)],[c_558]) ).
cnf(c_559,plain,
mult(ld(A,unit),mult(ld(A,unit),B)) = mult(mult(A,A),B),
inference(paramod,[status(thm)],[c_116,c_111]) ).
cnf(c_117,plain,
mult(ld(A,unit),mult(ld(A,unit),B)) = mult(A,mult(A,B)),
inference(paramod,[status(thm)],[c_24,c_559]) ).
cnf(c_560,plain,
rd(mult(A,mult(A,mult(A,A))),B) = mult(mult(A,A),rd(mult(A,A),B)),
inference(paramod,[status(thm)],[c_24,c_100]) ).
cnf(c_561,plain,
rd(mult(A,ld(A,unit)),B) = mult(mult(A,A),rd(mult(A,A),B)),
inference(paramod,[status(thm)],[c_38,c_560]) ).
cnf(c_562,plain,
rd(unit,B) = mult(mult(A,A),rd(mult(A,A),B)),
inference(paramod,[status(thm)],[c_1,c_561]) ).
cnf(c_563,plain,
ld(B,unit) = mult(mult(A,A),rd(mult(A,A),B)),
inference(paramod,[status(thm)],[c_93,c_562]) ).
cnf(c_564,plain,
ld(B,unit) = mult(mult(A,A),mult(A,rd(A,B))),
inference(paramod,[status(thm)],[c_100,c_563]) ).
cnf(c_565,plain,
ld(B,unit) = mult(A,mult(A,mult(A,rd(A,B)))),
inference(paramod,[status(thm)],[c_24,c_564]) ).
cnf(c_566,plain,
ld(B,unit) = mult(ld(A,unit),rd(A,B)),
inference(paramod,[status(thm)],[c_87,c_565]) ).
cnf(c_137,plain,
mult(ld(A,unit),rd(A,B)) = ld(B,unit),
inference(copy,[status(thm)],[c_566]) ).
cnf(c_567,plain,
mult(A,ld(B,C)) = rd(A,ld(C,B)),
inference(paramod,[status(thm)],[c_114,c_78]) ).
cnf(c_143,plain,
rd(A,ld(B,C)) = mult(A,ld(C,B)),
inference(copy,[status(thm)],[c_567]) ).
cnf(c_146,plain,
mult(A,mult(ld(B,A),ld(B,A))) = mult(B,ld(A,B)),
inference(paramod,[status(thm)],[c_143,c_85]) ).
cnf(c_154,plain,
ld(ld(A,unit),ld(B,unit)) = rd(A,B),
inference(paramod,[status(thm)],[c_137,c_2]) ).
cnf(c_568,plain,
ld(ld(A,unit),ld(B,unit)) = ld(rd(B,A),unit),
inference(paramod,[status(thm)],[c_137,c_113]) ).
cnf(c_569,plain,
rd(A,B) = ld(rd(B,A),unit),
inference(paramod,[status(thm)],[c_154,c_568]) ).
cnf(c_163,plain,
ld(rd(A,B),unit) = rd(B,A),
inference(copy,[status(thm)],[c_569]) ).
cnf(c_570,plain,
ld(A,unit) = rd(B,mult(A,B)),
inference(paramod,[status(thm)],[c_4,c_163]) ).
cnf(c_166,plain,
rd(A,mult(B,A)) = ld(B,unit),
inference(copy,[status(thm)],[c_570]) ).
cnf(c_571,plain,
mult(A,rd(B,C)) = rd(A,rd(C,B)),
inference(paramod,[status(thm)],[c_163,c_78]) ).
cnf(c_169,plain,
rd(A,rd(B,C)) = mult(A,rd(C,B)),
inference(copy,[status(thm)],[c_571]) ).
cnf(c_572,plain,
ld(mult(A,mult(B,B)),unit) = rd(C,mult(A,mult(B,mult(B,C)))),
inference(paramod,[status(thm)],[c_30,c_163]) ).
cnf(c_170,plain,
rd(A,mult(B,mult(C,mult(C,A)))) = ld(mult(B,mult(C,C)),unit),
inference(copy,[status(thm)],[c_572]) ).
cnf(c_573,plain,
ld(rd(A,mult(B,B)),unit) = mult(B,rd(B,A)),
inference(paramod,[status(thm)],[c_100,c_163]) ).
cnf(c_173,plain,
ld(mult(A,mult(B,B)),unit) = mult(B,rd(B,A)),
inference(paramod,[status(thm)],[c_102,c_573]) ).
cnf(c_177,plain,
rd(A,mult(B,mult(C,mult(C,A)))) = mult(C,rd(C,B)),
inference(paramod,[status(thm)],[c_173,c_170]) ).
cnf(c_180,plain,
rd(ld(A,B),B) = ld(A,unit),
inference(paramod,[status(thm)],[c_1,c_166]) ).
cnf(c_574,plain,
ld(A,ld(B,unit)) = ld(mult(B,A),unit),
inference(paramod,[status(thm)],[c_166,c_90]) ).
cnf(c_185,plain,
ld(mult(A,B),unit) = ld(B,ld(A,unit)),
inference(copy,[status(thm)],[c_574]) ).
cnf(c_575,plain,
mult(ld(A,unit),ld(B,unit)) = ld(mult(B,A),unit),
inference(paramod,[status(thm)],[c_166,c_137]) ).
cnf(c_576,plain,
rd(ld(A,unit),B) = ld(mult(B,A),unit),
inference(paramod,[status(thm)],[c_78,c_575]) ).
cnf(c_186,plain,
rd(ld(A,unit),B) = ld(A,ld(B,unit)),
inference(paramod,[status(thm)],[c_185,c_576]) ).
cnf(c_188,plain,
ld(mult(A,A),ld(B,unit)) = mult(A,rd(A,B)),
inference(paramod,[status(thm)],[c_185,c_173]) ).
cnf(c_196,plain,
mult(ld(A,unit),B) = ld(A,B),
inference(paramod,[status(thm)],[c_180,c_3]) ).
cnf(c_577,plain,
mult(ld(A,unit),ld(A,B)) = mult(A,mult(A,B)),
inference(paramod,[status(thm)],[c_196,c_117]) ).
cnf(c_200,plain,
ld(A,ld(A,B)) = mult(A,mult(A,B)),
inference(paramod,[status(thm)],[c_196,c_577]) ).
cnf(c_201,plain,
mult(A,mult(A,mult(A,B))) = ld(A,B),
inference(paramod,[status(thm)],[c_196,c_87]) ).
cnf(c_578,plain,
mult(ld(A,B),B) = mult(ld(A,unit),mult(B,B)),
inference(paramod,[status(thm)],[c_196,c_23]) ).
cnf(c_579,plain,
mult(ld(A,B),B) = ld(A,mult(B,B)),
inference(paramod,[status(thm)],[c_196,c_578]) ).
cnf(c_210,plain,
ld(A,mult(B,B)) = mult(ld(A,B),B),
inference(copy,[status(thm)],[c_579]) ).
cnf(c_580,plain,
mult(ld(A,B),C) = ld(ld(B,A),C),
inference(paramod,[status(thm)],[c_114,c_196]) ).
cnf(c_212,plain,
ld(ld(A,B),C) = mult(ld(B,A),C),
inference(copy,[status(thm)],[c_580]) ).
cnf(c_581,plain,
mult(rd(A,B),C) = ld(rd(B,A),C),
inference(paramod,[status(thm)],[c_163,c_196]) ).
cnf(c_213,plain,
ld(rd(A,B),C) = mult(rd(B,A),C),
inference(copy,[status(thm)],[c_581]) ).
cnf(c_582,plain,
ld(mult(A,mult(B,B)),C) = mult(rd(D,mult(A,mult(B,mult(B,D)))),C),
inference(paramod,[status(thm)],[c_30,c_213]) ).
cnf(c_230,plain,
ld(mult(A,mult(B,B)),C) = mult(mult(B,rd(B,A)),C),
inference(paramod,[status(thm)],[c_177,c_582]) ).
cnf(c_248,plain,
ld(mult(A,rd(B,C)),D) = mult(rd(rd(C,B),A),D),
inference(paramod,[status(thm)],[c_169,c_213]) ).
cnf(c_583,plain,
mult(mult(A,mult(B,B)),mult(A,mult(B,mult(B,mult(A,mult(B,B)))))) = ld(mult(A,mult(B,B)),unit),
inference(paramod,[status(thm)],[c_33,c_38]) ).
cnf(c_584,plain,
mult(mult(A,mult(B,B)),mult(A,A)) = ld(mult(A,mult(B,B)),unit),
inference(paramod,[status(thm)],[c_70,c_583]) ).
cnf(c_585,plain,
mult(A,mult(A,mult(A,mult(B,B)))) = ld(mult(A,mult(B,B)),unit),
inference(paramod,[status(thm)],[c_34,c_584]) ).
cnf(c_586,plain,
ld(A,mult(B,B)) = ld(mult(A,mult(B,B)),unit),
inference(paramod,[status(thm)],[c_201,c_585]) ).
cnf(c_587,plain,
mult(ld(A,B),B) = ld(mult(A,mult(B,B)),unit),
inference(paramod,[status(thm)],[c_210,c_586]) ).
cnf(c_588,plain,
mult(ld(A,B),B) = ld(mult(B,B),ld(A,unit)),
inference(paramod,[status(thm)],[c_185,c_587]) ).
cnf(c_250,plain,
mult(ld(A,B),B) = mult(B,rd(B,A)),
inference(paramod,[status(thm)],[c_188,c_588]) ).
cnf(c_263,plain,
ld(A,mult(B,B)) = mult(B,rd(B,A)),
inference(paramod,[status(thm)],[c_250,c_210]) ).
cnf(c_270,plain,
mult(A,mult(ld(A,B),mult(B,rd(B,A)))) = mult(mult(B,ld(A,B)),B),
inference(paramod,[status(thm)],[c_250,c_19]) ).
cnf(c_589,plain,
mult(mult(A,rd(A,B)),A) = mult(ld(B,A),mult(A,A)),
inference(paramod,[status(thm)],[c_250,c_23]) ).
cnf(c_271,plain,
mult(mult(A,rd(A,B)),A) = mult(A,mult(A,ld(B,A))),
inference(paramod,[status(thm)],[c_34,c_589]) ).
cnf(c_590,plain,
ld(mult(A,mult(A,B)),unit) = ld(B,ld(mult(A,A),unit)),
inference(paramod,[status(thm)],[c_24,c_185]) ).
cnf(c_591,plain,
ld(mult(A,B),ld(A,unit)) = ld(B,ld(mult(A,A),unit)),
inference(paramod,[status(thm)],[c_185,c_590]) ).
cnf(c_592,plain,
ld(mult(A,B),ld(A,unit)) = ld(B,ld(A,ld(A,unit))),
inference(paramod,[status(thm)],[c_185,c_591]) ).
cnf(c_593,plain,
ld(mult(A,B),ld(A,unit)) = ld(B,mult(A,mult(A,unit))),
inference(paramod,[status(thm)],[c_200,c_592]) ).
cnf(c_594,plain,
ld(mult(A,B),ld(A,unit)) = ld(B,mult(A,A)),
inference(paramod,[status(thm)],[c_5,c_593]) ).
cnf(c_284,plain,
ld(mult(A,B),ld(A,unit)) = mult(A,rd(A,B)),
inference(paramod,[status(thm)],[c_263,c_594]) ).
cnf(c_285,plain,
mult(A,ld(B,ld(C,unit))) = rd(A,mult(C,B)),
inference(paramod,[status(thm)],[c_185,c_78]) ).
cnf(c_595,plain,
ld(mult(A,mult(B,mult(B,C))),unit) = ld(C,ld(mult(A,mult(B,B)),unit)),
inference(paramod,[status(thm)],[c_33,c_185]) ).
cnf(c_596,plain,
ld(mult(B,mult(B,C)),ld(A,unit)) = ld(C,ld(mult(A,mult(B,B)),unit)),
inference(paramod,[status(thm)],[c_185,c_595]) ).
cnf(c_597,plain,
ld(mult(B,mult(B,C)),ld(A,unit)) = ld(C,ld(mult(B,B),ld(A,unit))),
inference(paramod,[status(thm)],[c_185,c_596]) ).
cnf(c_288,plain,
ld(mult(A,mult(A,B)),ld(C,unit)) = ld(B,mult(A,rd(A,C))),
inference(paramod,[status(thm)],[c_188,c_597]) ).
cnf(c_598,plain,
ld(mult(A,mult(B,B)),B) = ld(mult(B,A),unit),
inference(paramod,[status(thm)],[c_34,c_113]) ).
cnf(c_599,plain,
mult(mult(B,rd(B,A)),B) = ld(mult(B,A),unit),
inference(paramod,[status(thm)],[c_230,c_598]) ).
cnf(c_600,plain,
mult(B,mult(B,ld(A,B))) = ld(mult(B,A),unit),
inference(paramod,[status(thm)],[c_271,c_599]) ).
cnf(c_317,plain,
mult(A,mult(A,ld(B,A))) = ld(B,ld(A,unit)),
inference(paramod,[status(thm)],[c_185,c_600]) ).
cnf(c_601,plain,
mult(A,mult(ld(B,A),ld(B,A))) = mult(ld(B,A),mult(A,rd(A,B))),
inference(paramod,[status(thm)],[c_250,c_34]) ).
cnf(c_602,plain,
mult(B,ld(A,B)) = mult(ld(B,A),mult(A,rd(A,B))),
inference(paramod,[status(thm)],[c_146,c_601]) ).
cnf(c_324,plain,
mult(ld(A,B),mult(B,rd(B,A))) = mult(A,ld(B,A)),
inference(copy,[status(thm)],[c_602]) ).
cnf(c_603,plain,
mult(A,mult(A,ld(B,A))) = mult(mult(B,ld(A,B)),B),
inference(paramod,[status(thm)],[c_324,c_270]) ).
cnf(c_604,plain,
ld(B,ld(A,unit)) = mult(mult(B,ld(A,B)),B),
inference(paramod,[status(thm)],[c_317,c_603]) ).
cnf(c_330,plain,
mult(mult(A,ld(B,A)),A) = ld(A,ld(B,unit)),
inference(copy,[status(thm)],[c_604]) ).
cnf(c_605,plain,
ld(ld(ld(A,unit),mult(B,B)),C) = mult(mult(B,rd(B,A)),C),
inference(paramod,[status(thm)],[c_188,c_212]) ).
cnf(c_606,plain,
ld(mult(B,rd(B,ld(A,unit))),C) = mult(mult(B,rd(B,A)),C),
inference(paramod,[status(thm)],[c_263,c_605]) ).
cnf(c_607,plain,
ld(mult(B,mult(B,ld(unit,A))),C) = mult(mult(B,rd(B,A)),C),
inference(paramod,[status(thm)],[c_143,c_606]) ).
cnf(c_397,plain,
ld(mult(A,mult(A,B)),C) = mult(mult(A,rd(A,B)),C),
inference(paramod,[status(thm)],[c_16,c_607]) ).
cnf(c_608,plain,
mult(mult(A,rd(A,B)),ld(C,unit)) = ld(B,mult(A,rd(A,C))),
inference(paramod,[status(thm)],[c_397,c_288]) ).
cnf(c_403,plain,
rd(mult(A,rd(A,B)),C) = ld(B,mult(A,rd(A,C))),
inference(paramod,[status(thm)],[c_78,c_608]) ).
cnf(c_609,plain,
ld(mult(mult(A,B),B),ld(mult(A,B),unit)) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_4,c_284]) ).
cnf(c_610,plain,
ld(mult(A,mult(B,B)),ld(mult(A,B),unit)) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_23,c_609]) ).
cnf(c_611,plain,
ld(mult(A,mult(B,B)),ld(B,ld(A,unit))) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_185,c_610]) ).
cnf(c_612,plain,
mult(mult(B,rd(B,A)),ld(B,ld(A,unit))) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_230,c_611]) ).
cnf(c_613,plain,
rd(mult(B,rd(B,A)),mult(A,B)) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_285,c_612]) ).
cnf(c_614,plain,
ld(A,mult(B,rd(B,mult(A,B)))) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_403,c_613]) ).
cnf(c_615,plain,
ld(A,mult(B,ld(A,unit))) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_166,c_614]) ).
cnf(c_411,plain,
ld(A,rd(B,A)) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_78,c_615]) ).
cnf(c_616,plain,
ld(mult(ld(A,B),B),ld(ld(A,B),unit)) = mult(ld(A,B),ld(A,unit)),
inference(paramod,[status(thm)],[c_180,c_284]) ).
cnf(c_617,plain,
ld(mult(B,rd(B,A)),ld(ld(A,B),unit)) = mult(ld(A,B),ld(A,unit)),
inference(paramod,[status(thm)],[c_250,c_616]) ).
cnf(c_618,plain,
ld(mult(B,rd(B,A)),mult(ld(B,A),unit)) = mult(ld(A,B),ld(A,unit)),
inference(paramod,[status(thm)],[c_212,c_617]) ).
cnf(c_619,plain,
ld(mult(B,rd(B,A)),ld(B,A)) = mult(ld(A,B),ld(A,unit)),
inference(paramod,[status(thm)],[c_5,c_618]) ).
cnf(c_620,plain,
mult(rd(rd(A,B),B),ld(B,A)) = mult(ld(A,B),ld(A,unit)),
inference(paramod,[status(thm)],[c_248,c_619]) ).
cnf(c_621,plain,
mult(mult(A,mult(B,B)),ld(B,A)) = mult(ld(A,B),ld(A,unit)),
inference(paramod,[status(thm)],[c_79,c_620]) ).
cnf(c_622,plain,
mult(A,mult(B,mult(B,ld(B,A)))) = mult(ld(A,B),ld(A,unit)),
inference(paramod,[status(thm)],[c_33,c_621]) ).
cnf(c_623,plain,
mult(A,mult(B,A)) = mult(ld(A,B),ld(A,unit)),
inference(paramod,[status(thm)],[c_1,c_622]) ).
cnf(c_624,plain,
mult(A,mult(B,A)) = rd(ld(A,B),A),
inference(paramod,[status(thm)],[c_78,c_623]) ).
cnf(c_414,plain,
rd(ld(A,B),A) = mult(A,mult(B,A)),
inference(copy,[status(thm)],[c_624]) ).
cnf(c_625,plain,
ld(A,mult(mult(B,ld(A,B)),B)) = mult(ld(A,B),mult(B,rd(B,A))),
inference(paramod,[status(thm)],[c_250,c_43]) ).
cnf(c_626,plain,
ld(A,ld(B,ld(A,unit))) = mult(ld(A,B),mult(B,rd(B,A))),
inference(paramod,[status(thm)],[c_330,c_625]) ).
cnf(c_434,plain,
ld(A,ld(B,ld(A,unit))) = mult(A,ld(B,A)),
inference(paramod,[status(thm)],[c_324,c_626]) ).
cnf(c_627,plain,
ld(A,rd(ld(B,unit),A)) = mult(rd(A,B),A),
inference(paramod,[status(thm)],[c_78,c_411]) ).
cnf(c_628,plain,
ld(A,ld(B,ld(A,unit))) = mult(rd(A,B),A),
inference(paramod,[status(thm)],[c_186,c_627]) ).
cnf(c_629,plain,
mult(A,ld(B,A)) = mult(rd(A,B),A),
inference(paramod,[status(thm)],[c_434,c_628]) ).
cnf(c_462,plain,
mult(rd(A,B),A) = mult(A,ld(B,A)),
inference(copy,[status(thm)],[c_629]) ).
cnf(c_630,plain,
ld(mult(A,ld(B,A)),unit) = ld(A,ld(rd(A,B),unit)),
inference(paramod,[status(thm)],[c_462,c_185]) ).
cnf(c_631,plain,
ld(ld(B,A),ld(A,unit)) = ld(A,ld(rd(A,B),unit)),
inference(paramod,[status(thm)],[c_185,c_630]) ).
cnf(c_632,plain,
mult(ld(A,B),ld(A,unit)) = ld(A,ld(rd(A,B),unit)),
inference(paramod,[status(thm)],[c_212,c_631]) ).
cnf(c_633,plain,
rd(ld(A,B),A) = ld(A,ld(rd(A,B),unit)),
inference(paramod,[status(thm)],[c_78,c_632]) ).
cnf(c_634,plain,
mult(A,mult(B,A)) = ld(A,ld(rd(A,B),unit)),
inference(paramod,[status(thm)],[c_414,c_633]) ).
cnf(c_635,plain,
mult(A,mult(B,A)) = ld(A,mult(rd(B,A),unit)),
inference(paramod,[status(thm)],[c_213,c_634]) ).
cnf(c_636,plain,
mult(A,mult(B,A)) = ld(A,rd(B,A)),
inference(paramod,[status(thm)],[c_5,c_635]) ).
cnf(c_637,plain,
mult(A,mult(B,A)) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_411,c_636]) ).
cnf(c_504,plain,
mult(mult(A,B),A) = mult(A,mult(B,A)),
inference(copy,[status(thm)],[c_637]) ).
cnf(c_505,plain,
$false,
inference(resolve,[status(thm)],[c_504,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP707-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.77 % Computer : n010.cluster.edu
% 0.08/0.77 % Model : x86_64 x86_64
% 0.08/0.77 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.77 % Memory : 8046.5625MB
% 0.08/0.77 % OS : Linux 6.8.0-71-generic
% 0.08/0.77 % CPULimit : 300
% 0.08/0.77 % WCLimit : 300
% 0.08/0.77 % DateTime : Fri Sep 25 15:39:32 UTC 2026
% 0.08/0.77 % CPUTime :
% 0.08/0.77 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.77 % Process 1127195 was started by sandbox on n010,
% 0.08/0.77 % Fri Sep 25 15:39:32 2026
% 0.08/0.77 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.78
% 0.08/0.78 % From the command line: assign(max_seconds, 300).
% 0.12/0.91
% 0.12/0.91 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.91
% 0.12/0.91 % Proof 1 at 0.09 (+ 0.03) seconds.
% 0.12/0.91 % Length of proof is 91.
% 0.12/0.91 % Level of proof is 21.
% 0.12/0.91 % Maximum clause weight is 50.000.
% 0.12/0.91 % Given clauses 68.
% 0.12/0.91
% 0.12/0.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------