%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP668-1 : 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 : n015.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 07:31:09 AM UTC 2026
% Result : Unsatisfiable 4.11s 1.06s
% Output : CNFRefutation 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 9
% Syntax : Number of formulae : 148 ( 148 unt; 0 def)
% Number of atoms : 148 ( 147 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 312 ( 0 sgn 15 !; 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,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(goals,axiom,
mult(mult(a,b),mult(mult(c,b),c)) != mult(mult(a,mult(mult(b,c),b)),c),
file('theBenchmark.p',goals) ).
cnf(c_10,plain,
mult(mult(a,b),mult(mult(c,b),c)) != mult(mult(a,mult(mult(b,c),b)),c),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_2519,plain,
mult(mult(a,b),mult(c,mult(b,c))) != mult(mult(a,mult(mult(b,c),b)),c),
inference(paramod,[status(thm)],[c_9,c_10]) ).
cnf(c_2520,plain,
mult(mult(a,b),mult(c,mult(b,c))) != mult(mult(a,mult(b,mult(c,b))),c),
inference(paramod,[status(thm)],[c_9,c_2519]) ).
cnf(c_11,plain,
mult(mult(a,mult(b,mult(c,b))),c) != mult(mult(a,b),mult(c,mult(b,c))),
inference(copy,[status(thm)],[c_2520]) ).
cnf(c_12,plain,
ld(rd(A,B),A) = B,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_14,plain,
ld(A,A) = unit,
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_16,plain,
ld(unit,A) = A,
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_19,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_2521,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_2521]) ).
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_2522,plain,
mult(A,mult(B,mult(B,unit))) = mult(mult(A,B),B),
inference(paramod,[status(thm)],[c_8,c_5]) ).
cnf(c_2523,plain,
mult(A,mult(B,B)) = mult(mult(A,B),B),
inference(paramod,[status(thm)],[c_5,c_2522]) ).
cnf(c_23,plain,
mult(mult(A,B),B) = mult(A,mult(B,B)),
inference(copy,[status(thm)],[c_2523]) ).
cnf(c_2524,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_2524]) ).
cnf(c_28,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_31,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_2525,plain,
mult(A,B) = mult(B,mult(ld(B,A),B)),
inference(paramod,[status(thm)],[c_1,c_9]) ).
cnf(c_34,plain,
mult(A,mult(ld(A,B),A)) = mult(B,A),
inference(copy,[status(thm)],[c_2525]) ).
cnf(c_2526,plain,
mult(A,ld(B,A)) = mult(B,mult(ld(B,A),ld(B,A))),
inference(paramod,[status(thm)],[c_1,c_23]) ).
cnf(c_39,plain,
mult(A,mult(ld(A,B),ld(A,B))) = mult(B,ld(A,B)),
inference(copy,[status(thm)],[c_2526]) ).
cnf(c_2527,plain,
mult(A,B) = mult(rd(A,B),mult(B,B)),
inference(paramod,[status(thm)],[c_3,c_23]) ).
cnf(c_41,plain,
mult(rd(A,B),mult(B,B)) = mult(A,B),
inference(copy,[status(thm)],[c_2527]) ).
cnf(c_48,plain,
rd(mult(A,B),mult(B,B)) = rd(A,B),
inference(paramod,[status(thm)],[c_41,c_4]) ).
cnf(c_2528,plain,
rd(A,mult(B,B)) = rd(rd(A,B),B),
inference(paramod,[status(thm)],[c_3,c_48]) ).
cnf(c_94,plain,
rd(rd(A,B),B) = rd(A,mult(B,B)),
inference(copy,[status(thm)],[c_2528]) ).
cnf(c_108,plain,
mult(rd(A,mult(B,B)),B) = rd(A,B),
inference(paramod,[status(thm)],[c_94,c_3]) ).
cnf(c_121,plain,
rd(mult(A,mult(B,C)),ld(B,C)) = mult(A,mult(B,B)),
inference(paramod,[status(thm)],[c_1,c_28]) ).
cnf(c_199,plain,
ld(A,mult(B,A)) = mult(ld(A,B),A),
inference(paramod,[status(thm)],[c_34,c_2]) ).
cnf(c_2529,plain,
ld(A,A) = mult(ld(A,unit),A),
inference(paramod,[status(thm)],[c_6,c_199]) ).
cnf(c_2530,plain,
unit = mult(ld(A,unit),A),
inference(paramod,[status(thm)],[c_14,c_2529]) ).
cnf(c_213,plain,
mult(ld(A,unit),A) = unit,
inference(copy,[status(thm)],[c_2530]) ).
cnf(c_227,plain,
ld(ld(A,unit),unit) = A,
inference(paramod,[status(thm)],[c_213,c_2]) ).
cnf(c_228,plain,
rd(unit,A) = ld(A,unit),
inference(paramod,[status(thm)],[c_213,c_4]) ).
cnf(c_2531,plain,
mult(unit,A) = mult(ld(A,unit),mult(A,A)),
inference(paramod,[status(thm)],[c_213,c_23]) ).
cnf(c_2532,plain,
A = mult(ld(A,unit),mult(A,A)),
inference(paramod,[status(thm)],[c_6,c_2531]) ).
cnf(c_229,plain,
mult(ld(A,unit),mult(A,A)) = A,
inference(copy,[status(thm)],[c_2532]) ).
cnf(c_2533,plain,
rd(unit,mult(A,A)) = rd(ld(A,unit),A),
inference(paramod,[status(thm)],[c_213,c_48]) ).
cnf(c_2534,plain,
ld(mult(A,A),unit) = rd(ld(A,unit),A),
inference(paramod,[status(thm)],[c_228,c_2533]) ).
cnf(c_232,plain,
rd(ld(A,unit),A) = ld(mult(A,A),unit),
inference(copy,[status(thm)],[c_2534]) ).
cnf(c_2535,plain,
mult(unit,A) = mult(ld(mult(B,B),unit),mult(B,mult(B,A))),
inference(paramod,[status(thm)],[c_213,c_31]) ).
cnf(c_2536,plain,
A = mult(ld(mult(B,B),unit),mult(B,mult(B,A))),
inference(paramod,[status(thm)],[c_6,c_2535]) ).
cnf(c_237,plain,
mult(ld(mult(A,A),unit),mult(A,mult(A,B))) = B,
inference(copy,[status(thm)],[c_2536]) ).
cnf(c_2537,plain,
mult(ld(A,unit),mult(A,mult(A,B))) = mult(mult(unit,A),B),
inference(paramod,[status(thm)],[c_228,c_21]) ).
cnf(c_255,plain,
mult(ld(A,unit),mult(A,mult(A,B))) = mult(A,B),
inference(paramod,[status(thm)],[c_6,c_2537]) ).
cnf(c_2538,plain,
rd(mult(A,mult(ld(B,unit),B)),mult(B,B)) = mult(A,mult(ld(B,unit),ld(B,unit))),
inference(paramod,[status(thm)],[c_229,c_28]) ).
cnf(c_2539,plain,
rd(mult(A,unit),mult(B,B)) = mult(A,mult(ld(B,unit),ld(B,unit))),
inference(paramod,[status(thm)],[c_213,c_2538]) ).
cnf(c_323,plain,
rd(A,mult(B,B)) = mult(A,mult(ld(B,unit),ld(B,unit))),
inference(paramod,[status(thm)],[c_5,c_2539]) ).
cnf(c_2540,plain,
mult(mult(A,mult(ld(B,unit),ld(B,unit))),B) = rd(A,B),
inference(paramod,[status(thm)],[c_323,c_108]) ).
cnf(c_2541,plain,
mult(A,mult(ld(B,unit),mult(ld(B,unit),B))) = rd(A,B),
inference(paramod,[status(thm)],[c_31,c_2540]) ).
cnf(c_2542,plain,
mult(A,mult(ld(B,unit),unit)) = rd(A,B),
inference(paramod,[status(thm)],[c_213,c_2541]) ).
cnf(c_2543,plain,
mult(A,ld(B,unit)) = rd(A,B),
inference(paramod,[status(thm)],[c_5,c_2542]) ).
cnf(c_353,plain,
rd(A,B) = mult(A,ld(B,unit)),
inference(copy,[status(thm)],[c_2543]) ).
cnf(c_2544,plain,
mult(ld(A,unit),ld(A,unit)) = ld(mult(A,A),unit),
inference(paramod,[status(thm)],[c_353,c_232]) ).
cnf(c_400,plain,
ld(mult(A,A),unit) = mult(ld(A,unit),ld(A,unit)),
inference(copy,[status(thm)],[c_2544]) ).
cnf(c_418,plain,
mult(mult(A,mult(B,C)),ld(ld(B,C),unit)) = mult(A,mult(B,B)),
inference(paramod,[status(thm)],[c_353,c_121]) ).
cnf(c_437,plain,
mult(mult(A,mult(B,mult(B,C))),ld(C,unit)) = mult(A,mult(B,B)),
inference(paramod,[status(thm)],[c_353,c_28]) ).
cnf(c_440,plain,
ld(mult(A,ld(B,unit)),A) = B,
inference(paramod,[status(thm)],[c_353,c_12]) ).
cnf(c_441,plain,
mult(mult(A,B),ld(B,unit)) = A,
inference(paramod,[status(thm)],[c_353,c_4]) ).
cnf(c_2545,plain,
mult(mult(ld(A,unit),ld(A,unit)),mult(A,mult(A,B))) = B,
inference(paramod,[status(thm)],[c_400,c_237]) ).
cnf(c_2546,plain,
mult(ld(A,unit),mult(ld(A,unit),mult(A,mult(A,B)))) = B,
inference(paramod,[status(thm)],[c_24,c_2545]) ).
cnf(c_448,plain,
mult(ld(A,unit),mult(A,B)) = B,
inference(paramod,[status(thm)],[c_255,c_2546]) ).
cnf(c_480,plain,
ld(mult(A,B),A) = ld(B,unit),
inference(paramod,[status(thm)],[c_227,c_440]) ).
cnf(c_2547,plain,
ld(A,B) = ld(ld(B,A),unit),
inference(paramod,[status(thm)],[c_1,c_480]) ).
cnf(c_483,plain,
ld(ld(A,B),unit) = ld(B,A),
inference(copy,[status(thm)],[c_2547]) ).
cnf(c_2548,plain,
mult(mult(A,ld(B,unit)),C) = mult(mult(A,B),mult(ld(mult(A,B),A),mult(ld(mult(A,B),A),C))),
inference(paramod,[status(thm)],[c_480,c_19]) ).
cnf(c_2549,plain,
mult(mult(A,ld(B,unit)),C) = mult(mult(A,B),mult(ld(B,unit),mult(ld(mult(A,B),A),C))),
inference(paramod,[status(thm)],[c_480,c_2548]) ).
cnf(c_486,plain,
mult(mult(A,ld(B,unit)),C) = mult(mult(A,B),mult(ld(B,unit),mult(ld(B,unit),C))),
inference(paramod,[status(thm)],[c_480,c_2549]) ).
cnf(c_497,plain,
mult(mult(A,mult(B,C)),ld(C,B)) = mult(A,mult(B,B)),
inference(paramod,[status(thm)],[c_483,c_418]) ).
cnf(c_514,plain,
mult(ld(A,unit),B) = ld(A,B),
inference(paramod,[status(thm)],[c_1,c_448]) ).
cnf(c_2550,plain,
mult(mult(unit,ld(A,unit)),mult(A,B)) = mult(A,mult(ld(A,unit),B)),
inference(paramod,[status(thm)],[c_448,c_19]) ).
cnf(c_2551,plain,
mult(ld(A,unit),mult(A,B)) = mult(A,mult(ld(A,unit),B)),
inference(paramod,[status(thm)],[c_6,c_2550]) ).
cnf(c_2552,plain,
B = mult(A,mult(ld(A,unit),B)),
inference(paramod,[status(thm)],[c_448,c_2551]) ).
cnf(c_520,plain,
mult(A,mult(ld(A,unit),B)) = B,
inference(copy,[status(thm)],[c_2552]) ).
cnf(c_2553,plain,
ld(A,ld(B,unit)) = ld(mult(B,A),unit),
inference(paramod,[status(thm)],[c_448,c_480]) ).
cnf(c_530,plain,
ld(mult(A,B),unit) = ld(B,ld(A,unit)),
inference(copy,[status(thm)],[c_2553]) ).
cnf(c_2554,plain,
rd(ld(A,unit),B) = ld(A,ld(B,unit)),
inference(paramod,[status(thm)],[c_514,c_353]) ).
cnf(c_2555,plain,
mult(ld(A,unit),ld(B,unit)) = ld(A,ld(B,unit)),
inference(paramod,[status(thm)],[c_353,c_2554]) ).
cnf(c_611,plain,
ld(A,ld(B,unit)) = mult(ld(A,unit),ld(B,unit)),
inference(copy,[status(thm)],[c_2555]) ).
cnf(c_2556,plain,
ld(ld(A,B),ld(A,unit)) = ld(B,unit),
inference(paramod,[status(thm)],[c_514,c_480]) ).
cnf(c_2557,plain,
mult(ld(ld(A,B),unit),ld(A,unit)) = ld(B,unit),
inference(paramod,[status(thm)],[c_611,c_2556]) ).
cnf(c_619,plain,
mult(ld(A,B),ld(B,unit)) = ld(A,unit),
inference(paramod,[status(thm)],[c_483,c_2557]) ).
cnf(c_652,plain,
ld(mult(A,B),unit) = mult(ld(B,unit),ld(A,unit)),
inference(paramod,[status(thm)],[c_611,c_530]) ).
cnf(c_2558,plain,
mult(mult(ld(A,unit),ld(B,unit)),C) = ld(mult(B,A),C),
inference(paramod,[status(thm)],[c_652,c_514]) ).
cnf(c_2559,plain,
mult(mult(ld(A,unit),B),mult(ld(B,unit),mult(ld(B,unit),C))) = ld(mult(B,A),C),
inference(paramod,[status(thm)],[c_486,c_2558]) ).
cnf(c_690,plain,
ld(mult(A,B),C) = mult(mult(ld(B,unit),A),mult(ld(A,unit),mult(ld(A,unit),C))),
inference(copy,[status(thm)],[c_2559]) ).
cnf(c_691,plain,
mult(ld(A,mult(B,C)),mult(ld(C,unit),ld(B,unit))) = ld(A,unit),
inference(paramod,[status(thm)],[c_652,c_619]) ).
cnf(c_2560,plain,
mult(ld(A,B),C) = ld(ld(B,A),C),
inference(paramod,[status(thm)],[c_483,c_514]) ).
cnf(c_725,plain,
ld(ld(A,B),C) = mult(ld(B,A),C),
inference(copy,[status(thm)],[c_2560]) ).
cnf(c_2561,plain,
mult(A,mult(B,ld(ld(A,unit),B))) = mult(ld(ld(A,unit),B),ld(ld(A,unit),B)),
inference(paramod,[status(thm)],[c_39,c_520]) ).
cnf(c_2562,plain,
mult(A,mult(B,mult(ld(unit,A),B))) = mult(ld(ld(A,unit),B),ld(ld(A,unit),B)),
inference(paramod,[status(thm)],[c_725,c_2561]) ).
cnf(c_2563,plain,
mult(A,mult(B,mult(A,B))) = mult(ld(ld(A,unit),B),ld(ld(A,unit),B)),
inference(paramod,[status(thm)],[c_16,c_2562]) ).
cnf(c_2564,plain,
mult(A,mult(B,mult(A,B))) = mult(mult(ld(unit,A),B),ld(ld(A,unit),B)),
inference(paramod,[status(thm)],[c_725,c_2563]) ).
cnf(c_2565,plain,
mult(A,mult(B,mult(A,B))) = mult(mult(A,B),ld(ld(A,unit),B)),
inference(paramod,[status(thm)],[c_16,c_2564]) ).
cnf(c_2566,plain,
mult(A,mult(B,mult(A,B))) = mult(mult(A,B),mult(ld(unit,A),B)),
inference(paramod,[status(thm)],[c_725,c_2565]) ).
cnf(c_2567,plain,
mult(A,mult(B,mult(A,B))) = mult(mult(A,B),mult(A,B)),
inference(paramod,[status(thm)],[c_16,c_2566]) ).
cnf(c_910,plain,
mult(mult(A,B),mult(A,B)) = mult(A,mult(B,mult(A,B))),
inference(copy,[status(thm)],[c_2567]) ).
cnf(c_2568,plain,
mult(ld(A,unit),ld(mult(ld(B,unit),ld(C,unit)),unit)) = ld(A,mult(C,B)),
inference(paramod,[status(thm)],[c_691,c_441]) ).
cnf(c_2569,plain,
mult(ld(A,unit),mult(mult(ld(ld(C,unit),unit),ld(B,unit)),mult(ld(ld(B,unit),unit),mult(ld(ld(B,unit),unit),unit)))) = ld(A,mult(C,B)),
inference(paramod,[status(thm)],[c_690,c_2568]) ).
cnf(c_2570,plain,
mult(ld(A,unit),mult(mult(mult(ld(unit,C),unit),ld(B,unit)),mult(ld(ld(B,unit),unit),mult(ld(ld(B,unit),unit),unit)))) = ld(A,mult(C,B)),
inference(paramod,[status(thm)],[c_725,c_2569]) ).
cnf(c_2571,plain,
mult(ld(A,unit),mult(mult(mult(C,unit),ld(B,unit)),mult(ld(ld(B,unit),unit),mult(ld(ld(B,unit),unit),unit)))) = ld(A,mult(C,B)),
inference(paramod,[status(thm)],[c_16,c_2570]) ).
cnf(c_2572,plain,
mult(ld(A,unit),mult(mult(C,ld(B,unit)),mult(ld(ld(B,unit),unit),mult(ld(ld(B,unit),unit),unit)))) = ld(A,mult(C,B)),
inference(paramod,[status(thm)],[c_5,c_2571]) ).
cnf(c_2573,plain,
mult(ld(A,unit),mult(mult(C,ld(B,unit)),mult(mult(ld(unit,B),unit),mult(ld(ld(B,unit),unit),unit)))) = ld(A,mult(C,B)),
inference(paramod,[status(thm)],[c_725,c_2572]) ).
cnf(c_2574,plain,
mult(ld(A,unit),mult(mult(C,ld(B,unit)),mult(mult(B,unit),mult(ld(ld(B,unit),unit),unit)))) = ld(A,mult(C,B)),
inference(paramod,[status(thm)],[c_16,c_2573]) ).
cnf(c_2575,plain,
mult(ld(A,unit),mult(mult(C,ld(B,unit)),mult(B,mult(ld(ld(B,unit),unit),unit)))) = ld(A,mult(C,B)),
inference(paramod,[status(thm)],[c_5,c_2574]) ).
cnf(c_2576,plain,
mult(ld(A,unit),mult(mult(C,ld(B,unit)),mult(B,mult(mult(ld(unit,B),unit),unit)))) = ld(A,mult(C,B)),
inference(paramod,[status(thm)],[c_725,c_2575]) ).
cnf(c_2577,plain,
mult(ld(A,unit),mult(mult(C,ld(B,unit)),mult(B,mult(mult(B,unit),unit)))) = ld(A,mult(C,B)),
inference(paramod,[status(thm)],[c_16,c_2576]) ).
cnf(c_2578,plain,
mult(ld(A,unit),mult(mult(C,ld(B,unit)),mult(B,mult(B,unit)))) = ld(A,mult(C,B)),
inference(paramod,[status(thm)],[c_5,c_2577]) ).
cnf(c_2579,plain,
mult(ld(A,unit),mult(mult(C,ld(B,unit)),mult(B,B))) = ld(A,mult(C,B)),
inference(paramod,[status(thm)],[c_5,c_2578]) ).
cnf(c_2580,plain,
mult(ld(A,unit),mult(mult(C,B),mult(ld(B,unit),mult(ld(B,unit),mult(B,B))))) = ld(A,mult(C,B)),
inference(paramod,[status(thm)],[c_486,c_2579]) ).
cnf(c_2581,plain,
mult(ld(A,unit),mult(mult(C,B),mult(ld(B,unit),B))) = ld(A,mult(C,B)),
inference(paramod,[status(thm)],[c_448,c_2580]) ).
cnf(c_2582,plain,
mult(ld(A,unit),mult(mult(C,B),unit)) = ld(A,mult(C,B)),
inference(paramod,[status(thm)],[c_213,c_2581]) ).
cnf(c_2583,plain,
mult(ld(A,unit),mult(C,B)) = ld(A,mult(C,B)),
inference(paramod,[status(thm)],[c_5,c_2582]) ).
cnf(c_1272,plain,
ld(A,mult(B,C)) = mult(ld(A,unit),mult(B,C)),
inference(copy,[status(thm)],[c_2583]) ).
cnf(c_2584,plain,
mult(mult(A,mult(mult(B,C),B)),ld(ld(C,unit),unit)) = mult(A,mult(mult(B,C),mult(B,C))),
inference(paramod,[status(thm)],[c_441,c_437]) ).
cnf(c_2585,plain,
mult(mult(A,mult(B,mult(C,B))),ld(ld(C,unit),unit)) = mult(A,mult(mult(B,C),mult(B,C))),
inference(paramod,[status(thm)],[c_9,c_2584]) ).
cnf(c_2586,plain,
mult(mult(A,mult(B,mult(C,B))),mult(ld(unit,C),unit)) = mult(A,mult(mult(B,C),mult(B,C))),
inference(paramod,[status(thm)],[c_725,c_2585]) ).
cnf(c_2587,plain,
mult(mult(A,mult(B,mult(C,B))),mult(C,unit)) = mult(A,mult(mult(B,C),mult(B,C))),
inference(paramod,[status(thm)],[c_16,c_2586]) ).
cnf(c_2588,plain,
mult(mult(A,mult(B,mult(C,B))),C) = mult(A,mult(mult(B,C),mult(B,C))),
inference(paramod,[status(thm)],[c_5,c_2587]) ).
cnf(c_1993,plain,
mult(mult(A,mult(B,mult(C,B))),C) = mult(A,mult(B,mult(C,mult(B,C)))),
inference(paramod,[status(thm)],[c_910,c_2588]) ).
cnf(c_2589,plain,
mult(a,mult(b,mult(c,mult(b,c)))) != mult(mult(a,b),mult(c,mult(b,c))),
inference(paramod,[status(thm)],[c_1993,c_11]) ).
cnf(c_2028,plain,
mult(mult(a,b),mult(c,mult(b,c))) != mult(a,mult(b,mult(c,mult(b,c)))),
inference(copy,[status(thm)],[c_2589]) ).
cnf(c_2590,plain,
mult(mult(A,B),ld(ld(C,unit),mult(B,C))) = mult(A,mult(mult(B,C),mult(B,C))),
inference(paramod,[status(thm)],[c_441,c_497]) ).
cnf(c_2591,plain,
mult(mult(A,B),mult(ld(ld(C,unit),unit),mult(B,C))) = mult(A,mult(mult(B,C),mult(B,C))),
inference(paramod,[status(thm)],[c_1272,c_2590]) ).
cnf(c_2592,plain,
mult(mult(A,B),mult(mult(ld(unit,C),unit),mult(B,C))) = mult(A,mult(mult(B,C),mult(B,C))),
inference(paramod,[status(thm)],[c_725,c_2591]) ).
cnf(c_2593,plain,
mult(mult(A,B),mult(mult(C,unit),mult(B,C))) = mult(A,mult(mult(B,C),mult(B,C))),
inference(paramod,[status(thm)],[c_16,c_2592]) ).
cnf(c_2594,plain,
mult(mult(A,B),mult(C,mult(B,C))) = mult(A,mult(mult(B,C),mult(B,C))),
inference(paramod,[status(thm)],[c_5,c_2593]) ).
cnf(c_2517,plain,
mult(mult(A,B),mult(C,mult(B,C))) = mult(A,mult(B,mult(C,mult(B,C)))),
inference(paramod,[status(thm)],[c_910,c_2594]) ).
cnf(c_2518,plain,
$false,
inference(resolve,[status(thm)],[c_2517,c_2028]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP668-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n015.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 15:38:12 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 1727035 was started by sandbox2 on n015,
% 0.07/0.35 % Fri Sep 25 15:38:12 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 4.11/1.06
% 4.11/1.06 % SZS status Unsatisfiable for theBenchmark
% 4.11/1.06
% 4.11/1.06 % Proof 1 at 0.55 (+ 0.13) seconds.
% 4.11/1.06 % Length of proof is 63.
% 4.11/1.06 % Level of proof is 16.
% 4.11/1.06 % Maximum clause weight is 74.000.
% 4.11/1.06 % Given clauses 164.
% 4.11/1.06
% 4.11/1.06 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------