%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP731-1 : 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 : n001.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 07:31:20 AM UTC 2026
% Result : Unsatisfiable 6.55s 1.61s
% Output : CNFRefutation 6.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 14
% Syntax : Number of formulae : 163 ( 163 unt; 0 def)
% Number of atoms : 163 ( 162 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 350 ( 17 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c01,axiom,
! [VAR_0] : mult(unit,VAR_0) = VAR_0,
file('theBenchmark.p',c01) ).
cnf(c_1,plain,
mult(unit,A) = A,
inference(clausify,[status(thm)],[c01]) ).
fof(c02,axiom,
! [VAR_0] : mult(VAR_0,unit) = VAR_0,
file('theBenchmark.p',c02) ).
cnf(c_2,plain,
mult(A,unit) = A,
inference(clausify,[status(thm)],[c02]) ).
fof(c03,axiom,
! [VAR_0] : mult(VAR_0,i(VAR_0)) = unit,
file('theBenchmark.p',c03) ).
cnf(c_3,plain,
mult(A,i(A)) = unit,
inference(clausify,[status(thm)],[c03]) ).
fof(c04,axiom,
! [VAR_0] : mult(i(VAR_0),VAR_0) = unit,
file('theBenchmark.p',c04) ).
cnf(c_4,plain,
mult(i(A),A) = unit,
inference(clausify,[status(thm)],[c04]) ).
fof(c05,axiom,
! [VAR_0,VAR_1] : i(mult(VAR_0,VAR_1)) = mult(i(VAR_0),i(VAR_1)),
file('theBenchmark.p',c05) ).
cnf(c_5,plain,
i(mult(A,B)) = mult(i(A),i(B)),
inference(clausify,[status(thm)],[c05]) ).
fof(c06,axiom,
! [VAR_0,VAR_1] : mult(i(VAR_0),mult(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',c06) ).
cnf(c_6,plain,
mult(i(A),mult(A,B)) = B,
inference(clausify,[status(thm)],[c06]) ).
fof(c07,axiom,
! [VAR_0,VAR_1] : rd(mult(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',c07) ).
cnf(c_7,plain,
rd(mult(A,B),B) = A,
inference(clausify,[status(thm)],[c07]) ).
fof(c08,axiom,
! [VAR_0,VAR_1] : mult(rd(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',c08) ).
cnf(c_8,plain,
mult(rd(A,B),B) = A,
inference(clausify,[status(thm)],[c08]) ).
fof(c09,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(mult(VAR_0,mult(VAR_1,VAR_0)),VAR_2) = mult(VAR_0,mult(VAR_1,mult(VAR_0,VAR_2))),
file('theBenchmark.p',c09) ).
cnf(c_9,plain,
mult(mult(A,mult(B,A)),C) = mult(A,mult(B,mult(A,C))),
inference(clausify,[status(thm)],[c09]) ).
fof(c10,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(mult(VAR_0,VAR_1),VAR_2) = mult(mult(VAR_0,mult(VAR_1,VAR_2)),asoc(VAR_0,VAR_1,VAR_2)),
file('theBenchmark.p',c10) ).
cnf(c_10,plain,
mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)),
inference(clausify,[status(thm)],[c10]) ).
cnf(c_11,plain,
mult(mult(A,mult(B,C)),asoc(A,B,C)) = mult(mult(A,B),C),
inference(copy,[status(thm)],[c_10]) ).
fof(c11,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,VAR_1) = mult(mult(VAR_1,VAR_0),op_k(VAR_0,VAR_1)),
file('theBenchmark.p',c11) ).
cnf(c_12,plain,
mult(A,B) = mult(mult(B,A),op_k(A,B)),
inference(clausify,[status(thm)],[c11]) ).
cnf(c_13,plain,
mult(mult(A,B),op_k(B,A)) = mult(B,A),
inference(copy,[status(thm)],[c_12]) ).
fof(c21,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : asoc(asoc(VAR_0,VAR_1,VAR_2),VAR_3,VAR_4) = unit,
file('theBenchmark.p',c21) ).
cnf(c_30,plain,
asoc(asoc(A,B,C),D,E) = unit,
inference(clausify,[status(thm)],[c21]) ).
fof(c22,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : asoc(VAR_0,VAR_1,asoc(VAR_2,VAR_3,VAR_4)) = unit,
file('theBenchmark.p',c22) ).
cnf(c_31,plain,
asoc(A,B,asoc(C,D,E)) = unit,
inference(clausify,[status(thm)],[c22]) ).
fof(goals,axiom,
op_k(asoc(a,b,c),d) != unit,
file('theBenchmark.p',goals) ).
cnf(c_32,plain,
op_k(asoc(a,b,c),d) != unit,
inference(clausify,[status(thm)],[goals]) ).
cnf(c_3398,plain,
mult(i(i(A)),unit) = A,
inference(paramod,[status(thm)],[c_4,c_6]) ).
cnf(c_36,plain,
i(i(A)) = A,
inference(paramod,[status(thm)],[c_2,c_3398]) ).
cnf(c_40,plain,
rd(A,unit) = A,
inference(paramod,[status(thm)],[c_2,c_7]) ).
cnf(c_43,plain,
rd(A,mult(B,A)) = i(B),
inference(paramod,[status(thm)],[c_6,c_7]) ).
cnf(c_3399,plain,
i(A) = mult(i(rd(A,B)),i(B)),
inference(paramod,[status(thm)],[c_8,c_5]) ).
cnf(c_44,plain,
mult(i(rd(A,B)),i(B)) = i(A),
inference(copy,[status(thm)],[c_3399]) ).
cnf(c_3400,plain,
mult(mult(A,B),C) = mult(A,mult(rd(B,A),mult(A,C))),
inference(paramod,[status(thm)],[c_8,c_9]) ).
cnf(c_50,plain,
mult(A,mult(rd(B,A),mult(A,C))) = mult(mult(A,B),C),
inference(copy,[status(thm)],[c_3400]) ).
cnf(c_3401,plain,
mult(unit,asoc(i(mult(A,B)),A,B)) = mult(mult(i(mult(A,B)),A),B),
inference(paramod,[status(thm)],[c_4,c_11]) ).
cnf(c_3402,plain,
mult(unit,asoc(mult(i(A),i(B)),A,B)) = mult(mult(i(mult(A,B)),A),B),
inference(paramod,[status(thm)],[c_5,c_3401]) ).
cnf(c_3403,plain,
asoc(mult(i(A),i(B)),A,B) = mult(mult(i(mult(A,B)),A),B),
inference(paramod,[status(thm)],[c_1,c_3402]) ).
cnf(c_3404,plain,
asoc(mult(i(A),i(B)),A,B) = mult(mult(mult(i(A),i(B)),A),B),
inference(paramod,[status(thm)],[c_5,c_3403]) ).
cnf(c_57,plain,
mult(mult(mult(i(A),i(B)),A),B) = asoc(mult(i(A),i(B)),A,B),
inference(copy,[status(thm)],[c_3404]) ).
cnf(c_3405,plain,
i(mult(mult(A,B),C)) = mult(i(mult(A,mult(B,C))),i(asoc(A,B,C))),
inference(paramod,[status(thm)],[c_11,c_5]) ).
cnf(c_3406,plain,
mult(i(mult(A,B)),i(C)) = mult(i(mult(A,mult(B,C))),i(asoc(A,B,C))),
inference(paramod,[status(thm)],[c_5,c_3405]) ).
cnf(c_3407,plain,
mult(mult(i(A),i(B)),i(C)) = mult(i(mult(A,mult(B,C))),i(asoc(A,B,C))),
inference(paramod,[status(thm)],[c_5,c_3406]) ).
cnf(c_3408,plain,
mult(mult(i(A),i(B)),i(C)) = mult(mult(i(A),i(mult(B,C))),i(asoc(A,B,C))),
inference(paramod,[status(thm)],[c_5,c_3407]) ).
cnf(c_3409,plain,
mult(mult(i(A),i(B)),i(C)) = mult(mult(i(A),mult(i(B),i(C))),i(asoc(A,B,C))),
inference(paramod,[status(thm)],[c_5,c_3408]) ).
cnf(c_59,plain,
mult(mult(i(A),mult(i(B),i(C))),i(asoc(A,B,C))) = mult(mult(i(A),i(B)),i(C)),
inference(copy,[status(thm)],[c_3409]) ).
cnf(c_3410,plain,
mult(i(mult(A,mult(B,C))),mult(mult(A,B),C)) = asoc(A,B,C),
inference(paramod,[status(thm)],[c_11,c_6]) ).
cnf(c_3411,plain,
mult(mult(i(A),i(mult(B,C))),mult(mult(A,B),C)) = asoc(A,B,C),
inference(paramod,[status(thm)],[c_5,c_3410]) ).
cnf(c_60,plain,
mult(mult(i(A),mult(i(B),i(C))),mult(mult(A,B),C)) = asoc(A,B,C),
inference(paramod,[status(thm)],[c_5,c_3411]) ).
cnf(c_3412,plain,
mult(i(mult(A,B)),mult(B,A)) = op_k(B,A),
inference(paramod,[status(thm)],[c_13,c_6]) ).
cnf(c_76,plain,
mult(mult(i(A),i(B)),mult(B,A)) = op_k(B,A),
inference(paramod,[status(thm)],[c_5,c_3412]) ).
cnf(c_78,plain,
rd(mult(A,B),op_k(A,B)) = mult(B,A),
inference(paramod,[status(thm)],[c_13,c_7]) ).
cnf(c_79,plain,
mult(A,op_k(B,rd(A,B))) = mult(B,rd(A,B)),
inference(paramod,[status(thm)],[c_8,c_13]) ).
cnf(c_3413,plain,
rd(A,B) = i(rd(B,A)),
inference(paramod,[status(thm)],[c_8,c_43]) ).
cnf(c_147,plain,
i(rd(A,B)) = rd(B,A),
inference(copy,[status(thm)],[c_3413]) ).
cnf(c_3414,plain,
rd(op_k(A,B),mult(A,B)) = i(mult(B,A)),
inference(paramod,[status(thm)],[c_13,c_43]) ).
cnf(c_149,plain,
rd(op_k(A,B),mult(A,B)) = mult(i(B),i(A)),
inference(paramod,[status(thm)],[c_5,c_3414]) ).
cnf(c_151,plain,
mult(rd(A,B),i(A)) = i(B),
inference(paramod,[status(thm)],[c_147,c_44]) ).
cnf(c_164,plain,
rd(i(A),i(B)) = rd(B,A),
inference(paramod,[status(thm)],[c_151,c_7]) ).
cnf(c_217,plain,
mult(A,mult(i(A),B)) = B,
inference(paramod,[status(thm)],[c_36,c_6]) ).
cnf(c_221,plain,
mult(rd(i(A),B),A) = i(B),
inference(paramod,[status(thm)],[c_36,c_151]) ).
cnf(c_222,plain,
rd(A,i(B)) = rd(B,i(A)),
inference(paramod,[status(thm)],[c_36,c_164]) ).
cnf(c_231,plain,
rd(A,op_k(i(B),mult(B,A))) = mult(mult(B,A),i(B)),
inference(paramod,[status(thm)],[c_6,c_78]) ).
cnf(c_232,plain,
rd(A,op_k(rd(A,B),B)) = mult(B,rd(A,B)),
inference(paramod,[status(thm)],[c_8,c_78]) ).
cnf(c_3415,plain,
rd(op_k(rd(A,B),B),A) = mult(i(B),i(rd(A,B))),
inference(paramod,[status(thm)],[c_8,c_149]) ).
cnf(c_238,plain,
rd(op_k(rd(A,B),B),A) = mult(i(B),rd(B,A)),
inference(paramod,[status(thm)],[c_147,c_3415]) ).
cnf(c_416,plain,
mult(i(A),mult(B,rd(A,B))) = op_k(B,rd(A,B)),
inference(paramod,[status(thm)],[c_79,c_6]) ).
cnf(c_3416,plain,
mult(A,op_k(B,rd(A,B))) = mult(B,rd(i(B),i(A))),
inference(paramod,[status(thm)],[c_164,c_79]) ).
cnf(c_3417,plain,
mult(B,rd(A,B)) = mult(B,rd(i(B),i(A))),
inference(paramod,[status(thm)],[c_79,c_3416]) ).
cnf(c_422,plain,
mult(A,rd(i(A),i(B))) = mult(A,rd(B,A)),
inference(copy,[status(thm)],[c_3417]) ).
cnf(c_3418,plain,
mult(A,mult(rd(B,A),unit)) = mult(mult(A,B),i(A)),
inference(paramod,[status(thm)],[c_3,c_50]) ).
cnf(c_3419,plain,
mult(A,rd(B,A)) = mult(mult(A,B),i(A)),
inference(paramod,[status(thm)],[c_2,c_3418]) ).
cnf(c_438,plain,
mult(mult(A,B),i(A)) = mult(A,rd(B,A)),
inference(copy,[status(thm)],[c_3419]) ).
cnf(c_3420,plain,
mult(i(A),mult(rd(B,i(A)),unit)) = mult(mult(i(A),B),A),
inference(paramod,[status(thm)],[c_4,c_50]) ).
cnf(c_3421,plain,
mult(i(A),rd(B,i(A))) = mult(mult(i(A),B),A),
inference(paramod,[status(thm)],[c_2,c_3420]) ).
cnf(c_439,plain,
mult(mult(i(A),B),A) = mult(i(A),rd(B,i(A))),
inference(copy,[status(thm)],[c_3421]) ).
cnf(c_3422,plain,
mult(i(A),mult(rd(B,i(A)),C)) = mult(mult(i(A),B),mult(A,C)),
inference(paramod,[status(thm)],[c_6,c_50]) ).
cnf(c_441,plain,
mult(mult(i(A),B),mult(A,C)) = mult(i(A),mult(rd(B,i(A)),C)),
inference(copy,[status(thm)],[c_3422]) ).
cnf(c_472,plain,
rd(A,op_k(i(B),mult(B,A))) = mult(B,rd(A,B)),
inference(paramod,[status(thm)],[c_438,c_231]) ).
cnf(c_477,plain,
mult(mult(i(A),rd(i(B),i(A))),B) = asoc(mult(i(A),i(B)),A,B),
inference(paramod,[status(thm)],[c_439,c_57]) ).
cnf(c_3423,plain,
rd(mult(A,rd(B,A)),i(A)) = mult(A,B),
inference(paramod,[status(thm)],[c_438,c_7]) ).
cnf(c_3424,plain,
rd(A,i(mult(A,rd(B,A)))) = mult(A,B),
inference(paramod,[status(thm)],[c_222,c_3423]) ).
cnf(c_3425,plain,
rd(A,mult(i(A),i(rd(B,A)))) = mult(A,B),
inference(paramod,[status(thm)],[c_5,c_3424]) ).
cnf(c_487,plain,
rd(A,mult(i(A),rd(A,B))) = mult(A,B),
inference(paramod,[status(thm)],[c_147,c_3425]) ).
cnf(c_575,plain,
mult(A,mult(B,rd(i(A),B))) = op_k(B,rd(i(A),B)),
inference(paramod,[status(thm)],[c_79,c_217]) ).
cnf(c_576,plain,
mult(mult(A,rd(B,A)),i(B)) = i(op_k(rd(B,A),A)),
inference(paramod,[status(thm)],[c_232,c_151]) ).
cnf(c_580,plain,
mult(mult(A,rd(i(B),A)),B) = i(op_k(rd(i(B),A),A)),
inference(paramod,[status(thm)],[c_232,c_221]) ).
cnf(c_3426,plain,
rd(A,mult(i(A),mult(B,rd(A,B)))) = mult(A,op_k(rd(A,B),B)),
inference(paramod,[status(thm)],[c_232,c_487]) ).
cnf(c_595,plain,
rd(A,op_k(B,rd(A,B))) = mult(A,op_k(rd(A,B),B)),
inference(paramod,[status(thm)],[c_416,c_3426]) ).
cnf(c_3427,plain,
i(op_k(rd(i(B),i(A)),i(A))) = asoc(mult(i(A),i(B)),A,B),
inference(paramod,[status(thm)],[c_580,c_477]) ).
cnf(c_599,plain,
asoc(mult(i(A),i(B)),A,B) = i(op_k(rd(i(B),i(A)),i(A))),
inference(copy,[status(thm)],[c_3427]) ).
cnf(c_3428,plain,
mult(unit,i(asoc(mult(i(A),i(B)),A,B))) = mult(mult(i(mult(i(A),i(B))),i(A)),i(B)),
inference(paramod,[status(thm)],[c_4,c_59]) ).
cnf(c_3429,plain,
mult(unit,i(i(op_k(rd(i(B),i(A)),i(A))))) = mult(mult(i(mult(i(A),i(B))),i(A)),i(B)),
inference(paramod,[status(thm)],[c_599,c_3428]) ).
cnf(c_3430,plain,
mult(unit,op_k(rd(i(B),i(A)),i(A))) = mult(mult(i(mult(i(A),i(B))),i(A)),i(B)),
inference(paramod,[status(thm)],[c_36,c_3429]) ).
cnf(c_3431,plain,
op_k(rd(i(B),i(A)),i(A)) = mult(mult(i(mult(i(A),i(B))),i(A)),i(B)),
inference(paramod,[status(thm)],[c_1,c_3430]) ).
cnf(c_3432,plain,
op_k(rd(i(B),i(A)),i(A)) = mult(mult(mult(i(i(A)),i(i(B))),i(A)),i(B)),
inference(paramod,[status(thm)],[c_5,c_3431]) ).
cnf(c_3433,plain,
op_k(rd(i(B),i(A)),i(A)) = mult(mult(mult(A,i(i(B))),i(A)),i(B)),
inference(paramod,[status(thm)],[c_36,c_3432]) ).
cnf(c_3434,plain,
op_k(rd(i(B),i(A)),i(A)) = mult(mult(mult(A,B),i(A)),i(B)),
inference(paramod,[status(thm)],[c_36,c_3433]) ).
cnf(c_3435,plain,
op_k(rd(i(B),i(A)),i(A)) = mult(mult(A,rd(B,A)),i(B)),
inference(paramod,[status(thm)],[c_438,c_3434]) ).
cnf(c_3436,plain,
op_k(rd(i(B),i(A)),i(A)) = i(op_k(rd(B,A),A)),
inference(paramod,[status(thm)],[c_576,c_3435]) ).
cnf(c_1011,plain,
i(op_k(rd(A,B),B)) = op_k(rd(i(A),i(B)),i(B)),
inference(copy,[status(thm)],[c_3436]) ).
cnf(c_3437,plain,
asoc(mult(i(A),i(B)),A,B) = op_k(rd(i(i(B)),i(i(A))),i(i(A))),
inference(paramod,[status(thm)],[c_1011,c_599]) ).
cnf(c_3438,plain,
asoc(mult(i(A),i(B)),A,B) = op_k(rd(B,i(i(A))),i(i(A))),
inference(paramod,[status(thm)],[c_36,c_3437]) ).
cnf(c_3439,plain,
asoc(mult(i(A),i(B)),A,B) = op_k(rd(B,A),i(i(A))),
inference(paramod,[status(thm)],[c_36,c_3438]) ).
cnf(c_1036,plain,
asoc(mult(i(A),i(B)),A,B) = op_k(rd(B,A),A),
inference(paramod,[status(thm)],[c_36,c_3439]) ).
cnf(c_3440,plain,
rd(op_k(rd(A,B),B),op_k(mult(i(B),rd(B,A)),A)) = mult(A,rd(op_k(rd(A,B),B),A)),
inference(paramod,[status(thm)],[c_238,c_232]) ).
cnf(c_1085,plain,
rd(op_k(rd(A,B),B),op_k(mult(i(B),rd(B,A)),A)) = mult(A,mult(i(B),rd(B,A))),
inference(paramod,[status(thm)],[c_238,c_3440]) ).
cnf(c_3441,plain,
mult(A,rd(i(A),i(op_k(rd(A,B),B)))) = mult(A,mult(i(B),rd(B,A))),
inference(paramod,[status(thm)],[c_238,c_422]) ).
cnf(c_3442,plain,
mult(A,rd(i(A),op_k(rd(i(A),i(B)),i(B)))) = mult(A,mult(i(B),rd(B,A))),
inference(paramod,[status(thm)],[c_1011,c_3441]) ).
cnf(c_3443,plain,
mult(A,mult(i(B),rd(i(A),i(B)))) = mult(A,mult(i(B),rd(B,A))),
inference(paramod,[status(thm)],[c_232,c_3442]) ).
cnf(c_3444,plain,
op_k(i(B),rd(i(A),i(B))) = mult(A,mult(i(B),rd(B,A))),
inference(paramod,[status(thm)],[c_575,c_3443]) ).
cnf(c_1090,plain,
mult(A,mult(i(B),rd(B,A))) = op_k(i(B),rd(i(A),i(B))),
inference(copy,[status(thm)],[c_3444]) ).
cnf(c_1099,plain,
rd(op_k(rd(A,B),B),op_k(mult(i(B),rd(B,A)),A)) = op_k(i(B),rd(i(A),i(B))),
inference(paramod,[status(thm)],[c_1090,c_1085]) ).
cnf(c_3445,plain,
mult(mult(i(mult(A,B)),mult(i(i(A)),i(C))),mult(mult(A,rd(B,A)),C)) = asoc(mult(A,B),i(A),C),
inference(paramod,[status(thm)],[c_438,c_60]) ).
cnf(c_3446,plain,
mult(mult(mult(i(A),i(B)),mult(i(i(A)),i(C))),mult(mult(A,rd(B,A)),C)) = asoc(mult(A,B),i(A),C),
inference(paramod,[status(thm)],[c_5,c_3445]) ).
cnf(c_3447,plain,
mult(mult(mult(i(A),i(B)),mult(A,i(C))),mult(mult(A,rd(B,A)),C)) = asoc(mult(A,B),i(A),C),
inference(paramod,[status(thm)],[c_36,c_3446]) ).
cnf(c_1207,plain,
mult(mult(i(A),mult(rd(i(B),i(A)),i(C))),mult(mult(A,rd(B,A)),C)) = asoc(mult(A,B),i(A),C),
inference(paramod,[status(thm)],[c_441,c_3447]) ).
cnf(c_3448,plain,
mult(mult(i(A),mult(i(rd(i(A),i(B))),i(C))),mult(mult(A,rd(B,A)),C)) = asoc(A,rd(i(A),i(B)),C),
inference(paramod,[status(thm)],[c_422,c_60]) ).
cnf(c_3449,plain,
mult(mult(i(A),mult(rd(i(B),i(A)),i(C))),mult(mult(A,rd(B,A)),C)) = asoc(A,rd(i(A),i(B)),C),
inference(paramod,[status(thm)],[c_147,c_3448]) ).
cnf(c_1218,plain,
asoc(mult(A,B),i(A),C) = asoc(A,rd(i(A),i(B)),C),
inference(paramod,[status(thm)],[c_1207,c_3449]) ).
cnf(c_3450,plain,
rd(A,mult(i(A),mult(B,rd(A,B)))) = mult(A,op_k(i(B),mult(B,A))),
inference(paramod,[status(thm)],[c_472,c_487]) ).
cnf(c_3451,plain,
rd(A,op_k(B,rd(A,B))) = mult(A,op_k(i(B),mult(B,A))),
inference(paramod,[status(thm)],[c_416,c_3450]) ).
cnf(c_1241,plain,
mult(A,op_k(rd(A,B),B)) = mult(A,op_k(i(B),mult(B,A))),
inference(paramod,[status(thm)],[c_595,c_3451]) ).
cnf(c_1726,plain,
asoc(A,B,op_k(rd(C,D),D)) = unit,
inference(paramod,[status(thm)],[c_1036,c_31]) ).
cnf(c_3452,plain,
asoc(mult(i(i(A)),i(i(B))),i(A),i(B)) = op_k(rd(A,B),i(A)),
inference(paramod,[status(thm)],[c_164,c_1036]) ).
cnf(c_3453,plain,
asoc(mult(A,i(i(B))),i(A),i(B)) = op_k(rd(A,B),i(A)),
inference(paramod,[status(thm)],[c_36,c_3452]) ).
cnf(c_3454,plain,
asoc(mult(A,B),i(A),i(B)) = op_k(rd(A,B),i(A)),
inference(paramod,[status(thm)],[c_36,c_3453]) ).
cnf(c_1730,plain,
asoc(A,rd(i(A),i(B)),i(B)) = op_k(rd(A,B),i(A)),
inference(paramod,[status(thm)],[c_1218,c_3454]) ).
cnf(c_3455,plain,
asoc(mult(A,i(B)),i(A),B) = op_k(rd(B,i(A)),i(A)),
inference(paramod,[status(thm)],[c_36,c_1036]) ).
cnf(c_3456,plain,
asoc(A,rd(i(A),i(i(B))),B) = op_k(rd(B,i(A)),i(A)),
inference(paramod,[status(thm)],[c_1218,c_3455]) ).
cnf(c_1732,plain,
asoc(A,rd(i(A),B),B) = op_k(rd(B,i(A)),i(A)),
inference(paramod,[status(thm)],[c_36,c_3456]) ).
cnf(c_3457,plain,
asoc(mult(i(A),i(op_k(rd(A,B),B))),A,op_k(rd(A,B),B)) = op_k(mult(i(B),rd(B,A)),A),
inference(paramod,[status(thm)],[c_238,c_1036]) ).
cnf(c_3458,plain,
asoc(mult(i(A),op_k(rd(i(A),i(B)),i(B))),A,op_k(rd(A,B),B)) = op_k(mult(i(B),rd(B,A)),A),
inference(paramod,[status(thm)],[c_1011,c_3457]) ).
cnf(c_3459,plain,
asoc(mult(i(A),op_k(i(i(B)),mult(i(B),i(A)))),A,op_k(rd(A,B),B)) = op_k(mult(i(B),rd(B,A)),A),
inference(paramod,[status(thm)],[c_1241,c_3458]) ).
cnf(c_3460,plain,
asoc(mult(i(A),op_k(B,mult(i(B),i(A)))),A,op_k(rd(A,B),B)) = op_k(mult(i(B),rd(B,A)),A),
inference(paramod,[status(thm)],[c_36,c_3459]) ).
cnf(c_3461,plain,
unit = op_k(mult(i(B),rd(B,A)),A),
inference(paramod,[status(thm)],[c_1726,c_3460]) ).
cnf(c_1747,plain,
op_k(mult(i(A),rd(A,B)),B) = unit,
inference(copy,[status(thm)],[c_3461]) ).
cnf(c_1758,plain,
op_k(rd(i(A),i(B)),i(B)) = op_k(rd(B,A),i(B)),
inference(paramod,[status(thm)],[c_1732,c_1730]) ).
cnf(c_3462,plain,
rd(op_k(rd(A,B),B),unit) = op_k(i(B),rd(i(A),i(B))),
inference(paramod,[status(thm)],[c_1747,c_1099]) ).
cnf(c_1759,plain,
op_k(rd(A,B),B) = op_k(i(B),rd(i(A),i(B))),
inference(paramod,[status(thm)],[c_40,c_3462]) ).
cnf(c_3463,plain,
op_k(i(i(B)),rd(i(i(A)),i(i(B)))) = op_k(rd(B,A),i(B)),
inference(paramod,[status(thm)],[c_1759,c_1758]) ).
cnf(c_3464,plain,
op_k(B,rd(i(i(A)),i(i(B)))) = op_k(rd(B,A),i(B)),
inference(paramod,[status(thm)],[c_36,c_3463]) ).
cnf(c_3465,plain,
op_k(B,rd(A,i(i(B)))) = op_k(rd(B,A),i(B)),
inference(paramod,[status(thm)],[c_36,c_3464]) ).
cnf(c_3466,plain,
op_k(B,rd(A,B)) = op_k(rd(B,A),i(B)),
inference(paramod,[status(thm)],[c_36,c_3465]) ).
cnf(c_1761,plain,
op_k(rd(A,B),i(A)) = op_k(A,rd(B,A)),
inference(copy,[status(thm)],[c_3466]) ).
cnf(c_3467,plain,
op_k(rd(A,mult(B,A)),i(A)) = op_k(A,B),
inference(paramod,[status(thm)],[c_7,c_1761]) ).
cnf(c_1826,plain,
op_k(i(A),i(B)) = op_k(B,A),
inference(paramod,[status(thm)],[c_43,c_3467]) ).
cnf(c_3468,plain,
mult(mult(i(i(A)),mult(i(i(B)),i(mult(B,A)))),op_k(B,A)) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_76,c_60]) ).
cnf(c_3469,plain,
mult(mult(A,mult(i(i(B)),i(mult(B,A)))),op_k(B,A)) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_36,c_3468]) ).
cnf(c_3470,plain,
mult(mult(A,mult(B,i(mult(B,A)))),op_k(B,A)) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_36,c_3469]) ).
cnf(c_3471,plain,
mult(mult(A,mult(B,mult(i(B),i(A)))),op_k(B,A)) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_5,c_3470]) ).
cnf(c_3472,plain,
mult(mult(A,i(A)),op_k(B,A)) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_217,c_3471]) ).
cnf(c_3473,plain,
mult(unit,op_k(B,A)) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_3,c_3472]) ).
cnf(c_3474,plain,
op_k(B,A) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_1,c_3473]) ).
cnf(c_2309,plain,
asoc(i(A),i(B),mult(B,A)) = op_k(B,A),
inference(copy,[status(thm)],[c_3474]) ).
cnf(c_3475,plain,
asoc(i(i(A)),i(i(B)),mult(i(B),i(A))) = op_k(A,B),
inference(paramod,[status(thm)],[c_1826,c_2309]) ).
cnf(c_3476,plain,
asoc(A,i(i(B)),mult(i(B),i(A))) = op_k(A,B),
inference(paramod,[status(thm)],[c_36,c_3475]) ).
cnf(c_2435,plain,
asoc(A,B,mult(i(B),i(A))) = op_k(A,B),
inference(paramod,[status(thm)],[c_36,c_3476]) ).
cnf(c_3396,plain,
op_k(asoc(A,B,C),D) = unit,
inference(paramod,[status(thm)],[c_2435,c_30]) ).
cnf(c_3397,plain,
$false,
inference(resolve,[status(thm)],[c_3396,c_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP731-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n001.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Fri Sep 25 15:46:40 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.43 % Process 3725864 was started by sandbox2 on n001,
% 0.18/0.43 % Fri Sep 25 15:46:40 2026
% 0.18/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.43
% 0.18/0.43 % From the command line: assign(max_seconds, 300).
% 6.55/1.61
% 6.55/1.61 % Assigning unary symbol i kb_weight 0 and highest precedence (14).
% 6.55/1.61
% 6.55/1.61 % SZS status Unsatisfiable for theBenchmark
% 6.55/1.61
% 6.55/1.61 % Proof 1 at 0.77 (+ 0.29) seconds.
% 6.55/1.61 % Length of proof is 70.
% 6.55/1.61 % Level of proof is 16.
% 6.55/1.61 % Maximum clause weight is 77.000.
% 6.55/1.61 % Given clauses 188.
% 6.55/1.61
% 6.55/1.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------