%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP720-2 : 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 : n018.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 07:31:19 AM UTC 2026
% Result : Unsatisfiable 35.14s 15.10s
% Output : CNFRefutation 35.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 7
% Syntax : Number of formulae : 114 ( 114 unt; 0 def)
% Number of atoms : 114 ( 113 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 16 ( 16 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 255 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c01,axiom,
! [VAR_0] : mult(VAR_0,unit) = VAR_0,
file('theBenchmark.p',c01) ).
cnf(c_1,plain,
mult(A,unit) = A,
inference(clausify,[status(thm)],[c01]) ).
fof(c02,axiom,
! [VAR_0] : mult(unit,VAR_0) = VAR_0,
file('theBenchmark.p',c02) ).
cnf(c_2,plain,
mult(unit,A) = A,
inference(clausify,[status(thm)],[c02]) ).
fof(c03,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,ld(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',c03) ).
cnf(c_3,plain,
mult(A,ld(A,B)) = B,
inference(clausify,[status(thm)],[c03]) ).
fof(c04,axiom,
! [VAR_0,VAR_1] : ld(VAR_0,mult(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',c04) ).
cnf(c_4,plain,
ld(A,mult(A,B)) = B,
inference(clausify,[status(thm)],[c04]) ).
fof(c05,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,VAR_1) = mult(VAR_1,VAR_0),
file('theBenchmark.p',c05) ).
cnf(c_5,plain,
mult(A,B) = mult(B,A),
inference(clausify,[status(thm)],[c05]) ).
fof(c06,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : ld(mult(VAR_0,VAR_1),mult(VAR_0,mult(VAR_1,mult(VAR_2,VAR_3)))) = mult(ld(mult(VAR_0,VAR_1),mult(VAR_0,mult(VAR_1,VAR_2))),ld(mult(VAR_0,VAR_1),mult(VAR_0,mult(VAR_1,VAR_3)))),
file('theBenchmark.p',c06) ).
cnf(c_6,plain,
ld(mult(A,B),mult(A,mult(B,mult(C,D)))) = mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,D)))),
inference(clausify,[status(thm)],[c06]) ).
fof(c08,axiom,
! [VAR_0] : mult(mult(op_a,op_a),mult(op_b,op_b)) != mult(VAR_0,VAR_0),
file('theBenchmark.p',c08) ).
cnf(c_8,plain,
mult(mult(op_a,op_a),mult(op_b,op_b)) != mult(A,A),
inference(clausify,[status(thm)],[c08]) ).
cnf(c_2863,plain,
A = ld(unit,A),
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_9,plain,
ld(unit,A) = A,
inference(copy,[status(thm)],[c_2863]) ).
cnf(c_10,plain,
ld(A,A) = unit,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_11,plain,
ld(A,mult(B,A)) = B,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_12,plain,
mult(mult(A,B),mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,D))))) = mult(A,mult(B,mult(C,D))),
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_2864,plain,
ld(mult(A,B),mult(A,mult(B,C))) = mult(ld(mult(A,B),mult(A,mult(B,D))),ld(mult(A,B),mult(A,mult(B,ld(D,C))))),
inference(paramod,[status(thm)],[c_3,c_6]) ).
cnf(c_14,plain,
mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,ld(C,D))))) = ld(mult(A,B),mult(A,mult(B,D))),
inference(copy,[status(thm)],[c_2864]) ).
cnf(c_16,plain,
ld(mult(A,B),mult(A,mult(mult(C,D),B))) = mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,D)))),
inference(paramod,[status(thm)],[c_5,c_6]) ).
cnf(c_19,plain,
ld(ld(A,B),B) = A,
inference(paramod,[status(thm)],[c_3,c_11]) ).
cnf(c_2865,plain,
mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,C))) = ld(mult(A,B),mult(A,mult(B,C))),
inference(paramod,[status(thm)],[c_3,c_14]) ).
cnf(c_23,plain,
ld(mult(A,B),mult(A,mult(B,C))) = mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,C))),
inference(copy,[status(thm)],[c_2865]) ).
cnf(c_2866,plain,
mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(B,A),mult(A,mult(B,ld(C,D))))) = ld(mult(A,B),mult(A,mult(B,D))),
inference(paramod,[status(thm)],[c_5,c_14]) ).
cnf(c_28,plain,
ld(mult(A,B),mult(A,mult(B,C))) = mult(ld(mult(A,B),mult(A,mult(B,D))),ld(mult(B,A),mult(A,mult(B,ld(D,C))))),
inference(copy,[status(thm)],[c_2866]) ).
cnf(c_2867,plain,
mult(A,ld(mult(A,A),mult(A,mult(A,ld(A,B))))) = ld(mult(A,A),mult(A,mult(A,B))),
inference(paramod,[status(thm)],[c_11,c_14]) ).
cnf(c_2868,plain,
mult(A,ld(mult(A,A),mult(A,B))) = ld(mult(A,A),mult(A,mult(A,B))),
inference(paramod,[status(thm)],[c_3,c_2867]) ).
cnf(c_31,plain,
ld(mult(A,A),mult(A,mult(A,B))) = mult(A,ld(mult(A,A),mult(A,B))),
inference(copy,[status(thm)],[c_2868]) ).
cnf(c_2869,plain,
ld(mult(A,A),mult(A,A)) = mult(A,ld(mult(A,A),mult(A,unit))),
inference(paramod,[status(thm)],[c_1,c_31]) ).
cnf(c_2870,plain,
unit = mult(A,ld(mult(A,A),mult(A,unit))),
inference(paramod,[status(thm)],[c_10,c_2869]) ).
cnf(c_2871,plain,
unit = mult(A,ld(mult(A,A),A)),
inference(paramod,[status(thm)],[c_1,c_2870]) ).
cnf(c_34,plain,
mult(A,ld(mult(A,A),A)) = unit,
inference(copy,[status(thm)],[c_2871]) ).
cnf(c_2872,plain,
ld(A,unit) = ld(mult(A,A),A),
inference(paramod,[status(thm)],[c_34,c_4]) ).
cnf(c_42,plain,
ld(mult(A,A),A) = ld(A,unit),
inference(copy,[status(thm)],[c_2872]) ).
cnf(c_2873,plain,
mult(ld(mult(A,B),mult(A,mult(B,mult(B,B)))),ld(mult(A,B),mult(A,unit))) = ld(mult(A,B),mult(A,mult(B,B))),
inference(paramod,[status(thm)],[c_34,c_14]) ).
cnf(c_2874,plain,
mult(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))),ld(mult(A,B),mult(A,unit))) = ld(mult(A,B),mult(A,mult(B,B))),
inference(paramod,[status(thm)],[c_6,c_2873]) ).
cnf(c_2875,plain,
mult(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))),ld(mult(A,B),A)) = ld(mult(A,B),mult(A,mult(B,B))),
inference(paramod,[status(thm)],[c_1,c_2874]) ).
cnf(c_45,plain,
mult(ld(mult(A,B),A),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B))))) = ld(mult(A,B),mult(A,mult(B,B))),
inference(paramod,[status(thm)],[c_5,c_2875]) ).
cnf(c_46,plain,
mult(mult(A,A),ld(A,unit)) = A,
inference(paramod,[status(thm)],[c_42,c_3]) ).
cnf(c_2876,plain,
mult(mult(ld(A,unit),ld(A,unit)),A) = ld(A,unit),
inference(paramod,[status(thm)],[c_19,c_46]) ).
cnf(c_49,plain,
mult(A,mult(ld(A,unit),ld(A,unit))) = ld(A,unit),
inference(paramod,[status(thm)],[c_5,c_2876]) ).
cnf(c_2877,plain,
mult(A,mult(ld(mult(B,ld(B,A)),mult(B,mult(ld(B,A),C))),ld(mult(B,ld(B,A)),mult(B,mult(ld(B,A),D))))) = mult(B,mult(ld(B,A),mult(C,D))),
inference(paramod,[status(thm)],[c_3,c_12]) ).
cnf(c_2878,plain,
mult(A,mult(ld(A,mult(B,mult(ld(B,A),C))),ld(mult(B,ld(B,A)),mult(B,mult(ld(B,A),D))))) = mult(B,mult(ld(B,A),mult(C,D))),
inference(paramod,[status(thm)],[c_3,c_2877]) ).
cnf(c_52,plain,
mult(A,mult(ld(A,mult(B,mult(ld(B,A),C))),ld(A,mult(B,mult(ld(B,A),D))))) = mult(B,mult(ld(B,A),mult(C,D))),
inference(paramod,[status(thm)],[c_3,c_2878]) ).
cnf(c_2879,plain,
mult(mult(op_a,op_a),mult(op_b,op_b)) != ld(mult(A,B),mult(A,mult(mult(C,C),B))),
inference(paramod,[status(thm)],[c_16,c_8]) ).
cnf(c_77,plain,
ld(mult(A,B),mult(A,mult(mult(C,C),B))) != mult(mult(op_a,op_a),mult(op_b,op_b)),
inference(copy,[status(thm)],[c_2879]) ).
cnf(c_85,plain,
ld(mult(A,ld(mult(B,B),C)),mult(A,C)) != mult(mult(op_a,op_a),mult(op_b,op_b)),
inference(paramod,[status(thm)],[c_3,c_77]) ).
cnf(c_94,plain,
ld(mult(ld(mult(A,A),B),C),mult(C,B)) != mult(mult(op_a,op_a),mult(op_b,op_b)),
inference(paramod,[status(thm)],[c_5,c_85]) ).
cnf(c_180,plain,
ld(mult(ld(A,unit),B),mult(B,A)) != mult(mult(op_a,op_a),mult(op_b,op_b)),
inference(paramod,[status(thm)],[c_42,c_94]) ).
cnf(c_189,plain,
ld(mult(ld(A,unit),B),mult(A,B)) != mult(mult(op_a,op_a),mult(op_b,op_b)),
inference(paramod,[status(thm)],[c_5,c_180]) ).
cnf(c_194,plain,
ld(mult(ld(A,unit),ld(A,B)),B) != mult(mult(op_a,op_a),mult(op_b,op_b)),
inference(paramod,[status(thm)],[c_3,c_189]) ).
cnf(c_2880,plain,
ld(mult(A,B),mult(A,ld(B,unit))) = mult(ld(mult(A,B),mult(A,mult(B,ld(B,unit)))),ld(mult(A,B),mult(A,mult(B,ld(B,unit))))),
inference(paramod,[status(thm)],[c_49,c_6]) ).
cnf(c_2881,plain,
ld(mult(A,B),mult(A,ld(B,unit))) = mult(ld(mult(A,B),mult(A,unit)),ld(mult(A,B),mult(A,mult(B,ld(B,unit))))),
inference(paramod,[status(thm)],[c_3,c_2880]) ).
cnf(c_2882,plain,
ld(mult(A,B),mult(A,ld(B,unit))) = mult(ld(mult(A,B),A),ld(mult(A,B),mult(A,mult(B,ld(B,unit))))),
inference(paramod,[status(thm)],[c_1,c_2881]) ).
cnf(c_2883,plain,
ld(mult(A,B),mult(A,ld(B,unit))) = mult(ld(mult(A,B),A),ld(mult(A,B),mult(A,unit))),
inference(paramod,[status(thm)],[c_3,c_2882]) ).
cnf(c_199,plain,
ld(mult(A,B),mult(A,ld(B,unit))) = mult(ld(mult(A,B),A),ld(mult(A,B),A)),
inference(paramod,[status(thm)],[c_1,c_2883]) ).
cnf(c_2884,plain,
mult(ld(mult(A,ld(A,unit)),ld(A,unit)),ld(mult(A,ld(A,unit)),mult(A,mult(ld(A,unit),ld(ld(A,unit),B))))) = ld(mult(A,ld(A,unit)),mult(A,mult(ld(A,unit),B))),
inference(paramod,[status(thm)],[c_49,c_14]) ).
cnf(c_2885,plain,
mult(ld(unit,ld(A,unit)),ld(mult(A,ld(A,unit)),mult(A,mult(ld(A,unit),ld(ld(A,unit),B))))) = ld(mult(A,ld(A,unit)),mult(A,mult(ld(A,unit),B))),
inference(paramod,[status(thm)],[c_3,c_2884]) ).
cnf(c_2886,plain,
mult(ld(A,unit),ld(mult(A,ld(A,unit)),mult(A,mult(ld(A,unit),ld(ld(A,unit),B))))) = ld(mult(A,ld(A,unit)),mult(A,mult(ld(A,unit),B))),
inference(paramod,[status(thm)],[c_9,c_2885]) ).
cnf(c_2887,plain,
mult(ld(A,unit),ld(unit,mult(A,mult(ld(A,unit),ld(ld(A,unit),B))))) = ld(mult(A,ld(A,unit)),mult(A,mult(ld(A,unit),B))),
inference(paramod,[status(thm)],[c_3,c_2886]) ).
cnf(c_2888,plain,
mult(ld(A,unit),ld(unit,mult(A,B))) = ld(mult(A,ld(A,unit)),mult(A,mult(ld(A,unit),B))),
inference(paramod,[status(thm)],[c_3,c_2887]) ).
cnf(c_2889,plain,
mult(ld(A,unit),mult(A,B)) = ld(mult(A,ld(A,unit)),mult(A,mult(ld(A,unit),B))),
inference(paramod,[status(thm)],[c_9,c_2888]) ).
cnf(c_2890,plain,
mult(ld(A,unit),mult(A,B)) = ld(unit,mult(A,mult(ld(A,unit),B))),
inference(paramod,[status(thm)],[c_3,c_2889]) ).
cnf(c_201,plain,
mult(ld(A,unit),mult(A,B)) = mult(A,mult(ld(A,unit),B)),
inference(paramod,[status(thm)],[c_9,c_2890]) ).
cnf(c_230,plain,
ld(mult(A,B),mult(B,ld(A,unit))) = mult(ld(mult(B,A),B),ld(mult(B,A),B)),
inference(paramod,[status(thm)],[c_5,c_199]) ).
cnf(c_332,plain,
ld(mult(A,B),mult(B,ld(A,unit))) = mult(ld(mult(A,B),B),ld(mult(B,A),B)),
inference(paramod,[status(thm)],[c_5,c_230]) ).
cnf(c_418,plain,
ld(mult(ld(mult(A,B),B),ld(mult(B,A),B)),mult(B,ld(A,unit))) = mult(A,B),
inference(paramod,[status(thm)],[c_332,c_19]) ).
cnf(c_2891,plain,
ld(mult(A,B),mult(A,B)) = mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(B,A),mult(A,mult(B,ld(C,unit))))),
inference(paramod,[status(thm)],[c_1,c_28]) ).
cnf(c_2892,plain,
unit = mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(B,A),mult(A,mult(B,ld(C,unit))))),
inference(paramod,[status(thm)],[c_10,c_2891]) ).
cnf(c_497,plain,
mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(B,A),mult(A,mult(B,ld(C,unit))))) = unit,
inference(copy,[status(thm)],[c_2892]) ).
cnf(c_2893,plain,
ld(mult(A,B),mult(B,mult(A,C))) = mult(ld(mult(B,A),mult(B,mult(A,D))),ld(mult(A,B),mult(B,mult(A,ld(D,C))))),
inference(paramod,[status(thm)],[c_5,c_28]) ).
cnf(c_499,plain,
mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(B,A),mult(A,mult(B,ld(C,D))))) = ld(mult(B,A),mult(A,mult(B,D))),
inference(copy,[status(thm)],[c_2893]) ).
cnf(c_2894,plain,
ld(mult(B,A),mult(A,mult(B,unit))) = unit,
inference(paramod,[status(thm)],[c_499,c_497]) ).
cnf(c_511,plain,
ld(mult(A,B),mult(B,A)) = unit,
inference(paramod,[status(thm)],[c_1,c_2894]) ).
cnf(c_2895,plain,
mult(ld(A,unit),B) = mult(A,mult(ld(A,unit),ld(A,B))),
inference(paramod,[status(thm)],[c_3,c_201]) ).
cnf(c_542,plain,
mult(A,mult(ld(A,unit),ld(A,B))) = mult(ld(A,unit),B),
inference(copy,[status(thm)],[c_2895]) ).
cnf(c_576,plain,
ld(A,mult(ld(A,unit),B)) = mult(ld(A,unit),ld(A,B)),
inference(paramod,[status(thm)],[c_542,c_4]) ).
cnf(c_579,plain,
ld(mult(ld(A,unit),ld(A,B)),mult(ld(A,unit),B)) = A,
inference(paramod,[status(thm)],[c_542,c_11]) ).
cnf(c_2896,plain,
ld(ld(A,unit),mult(A,B)) = mult(ld(ld(A,unit),unit),ld(ld(A,unit),B)),
inference(paramod,[status(thm)],[c_19,c_576]) ).
cnf(c_625,plain,
ld(ld(A,unit),mult(A,B)) = mult(A,ld(ld(A,unit),B)),
inference(paramod,[status(thm)],[c_19,c_2896]) ).
cnf(c_652,plain,
ld(mult(ld(A,unit),ld(A,B)),mult(B,ld(A,unit))) = A,
inference(paramod,[status(thm)],[c_5,c_579]) ).
cnf(c_762,plain,
ld(mult(ld(A,unit),B),mult(mult(B,A),ld(A,unit))) = A,
inference(paramod,[status(thm)],[c_11,c_652]) ).
cnf(c_2897,plain,
ld(mult(A,B),mult(mult(B,ld(A,unit)),ld(ld(A,unit),unit))) = ld(A,unit),
inference(paramod,[status(thm)],[c_19,c_762]) ).
cnf(c_2898,plain,
ld(mult(A,B),mult(mult(B,ld(A,unit)),A)) = ld(A,unit),
inference(paramod,[status(thm)],[c_19,c_2897]) ).
cnf(c_932,plain,
ld(mult(A,B),mult(A,mult(B,ld(A,unit)))) = ld(A,unit),
inference(paramod,[status(thm)],[c_5,c_2898]) ).
cnf(c_2899,plain,
mult(mult(A,B),mult(ld(mult(A,B),mult(mult(B,A),mult(unit,C))),ld(mult(A,B),mult(mult(B,A),mult(ld(mult(B,A),mult(A,B)),D))))) = mult(mult(B,A),mult(ld(mult(B,A),mult(A,B)),mult(C,D))),
inference(paramod,[status(thm)],[c_511,c_52]) ).
cnf(c_2900,plain,
mult(mult(A,B),mult(ld(mult(A,B),mult(mult(B,A),C)),ld(mult(A,B),mult(mult(B,A),mult(ld(mult(B,A),mult(A,B)),D))))) = mult(mult(B,A),mult(ld(mult(B,A),mult(A,B)),mult(C,D))),
inference(paramod,[status(thm)],[c_2,c_2899]) ).
cnf(c_2901,plain,
mult(mult(A,B),mult(ld(mult(A,B),mult(mult(B,A),C)),ld(mult(A,B),mult(mult(B,A),mult(unit,D))))) = mult(mult(B,A),mult(ld(mult(B,A),mult(A,B)),mult(C,D))),
inference(paramod,[status(thm)],[c_511,c_2900]) ).
cnf(c_2902,plain,
mult(mult(A,B),mult(ld(mult(A,B),mult(mult(B,A),C)),ld(mult(A,B),mult(mult(B,A),D)))) = mult(mult(B,A),mult(ld(mult(B,A),mult(A,B)),mult(C,D))),
inference(paramod,[status(thm)],[c_2,c_2901]) ).
cnf(c_2903,plain,
mult(mult(A,B),mult(ld(mult(A,B),mult(mult(B,A),C)),ld(mult(A,B),mult(mult(B,A),D)))) = mult(mult(B,A),mult(unit,mult(C,D))),
inference(paramod,[status(thm)],[c_511,c_2902]) ).
cnf(c_1164,plain,
mult(mult(A,B),mult(ld(mult(A,B),mult(mult(B,A),C)),ld(mult(A,B),mult(mult(B,A),D)))) = mult(mult(B,A),mult(C,D)),
inference(paramod,[status(thm)],[c_2,c_2903]) ).
cnf(c_2904,plain,
ld(A,unit) = mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,ld(A,unit)))),
inference(paramod,[status(thm)],[c_932,c_23]) ).
cnf(c_2905,plain,
ld(A,unit) = mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),unit)),
inference(paramod,[status(thm)],[c_3,c_2904]) ).
cnf(c_2906,plain,
ld(A,unit) = mult(ld(mult(A,B),unit),ld(mult(A,B),mult(A,mult(B,B)))),
inference(paramod,[status(thm)],[c_5,c_2905]) ).
cnf(c_1396,plain,
mult(ld(mult(A,B),unit),ld(mult(A,B),mult(A,mult(B,B)))) = ld(A,unit),
inference(copy,[status(thm)],[c_2906]) ).
cnf(c_2907,plain,
ld(mult(ld(ld(mult(A,B),mult(A,mult(B,B))),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B))))),ld(mult(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))),ld(mult(A,B),A)),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))))),mult(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))),ld(ld(mult(A,B),A),unit))) = mult(ld(mult(A,B),A),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B))))),
inference(paramod,[status(thm)],[c_45,c_418]) ).
cnf(c_2908,plain,
ld(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))),ld(mult(A,B),A)),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))))),mult(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))),ld(ld(mult(A,B),A),unit))) = mult(ld(mult(A,B),A),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B))))),
inference(paramod,[status(thm)],[c_4,c_2907]) ).
cnf(c_2909,plain,
ld(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(ld(mult(A,B),A),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B))))),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))))),mult(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))),ld(ld(mult(A,B),A),unit))) = mult(ld(mult(A,B),A),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B))))),
inference(paramod,[status(thm)],[c_5,c_2908]) ).
cnf(c_2910,plain,
ld(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(ld(mult(A,B),mult(A,mult(B,B))),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))))),mult(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))),ld(ld(mult(A,B),A),unit))) = mult(ld(mult(A,B),A),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B))))),
inference(paramod,[status(thm)],[c_45,c_2909]) ).
cnf(c_2911,plain,
ld(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))),mult(mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B)))),ld(ld(mult(A,B),A),unit))) = mult(ld(mult(A,B),A),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B))))),
inference(paramod,[status(thm)],[c_4,c_2910]) ).
cnf(c_2912,plain,
ld(ld(mult(A,B),A),unit) = mult(ld(mult(A,B),A),mult(ld(mult(A,B),mult(A,mult(B,B))),ld(mult(A,B),mult(A,mult(B,B))))),
inference(paramod,[status(thm)],[c_4,c_2911]) ).
cnf(c_1608,plain,
ld(ld(mult(A,B),A),unit) = ld(mult(A,B),mult(A,mult(B,B))),
inference(paramod,[status(thm)],[c_45,c_2912]) ).
cnf(c_2913,plain,
ld(ld(A,B),unit) = ld(mult(B,ld(B,A)),mult(B,mult(ld(B,A),ld(B,A)))),
inference(paramod,[status(thm)],[c_3,c_1608]) ).
cnf(c_2018,plain,
ld(ld(A,B),unit) = ld(A,mult(B,mult(ld(B,A),ld(B,A)))),
inference(paramod,[status(thm)],[c_3,c_2913]) ).
cnf(c_2914,plain,
ld(ld(A,unit),mult(A,mult(B,B))) != mult(mult(op_a,op_a),mult(op_b,op_b)),
inference(paramod,[status(thm)],[c_1396,c_194]) ).
cnf(c_2662,plain,
mult(A,ld(ld(A,unit),mult(B,B))) != mult(mult(op_a,op_a),mult(op_b,op_b)),
inference(paramod,[status(thm)],[c_625,c_2914]) ).
cnf(c_2851,plain,
mult(ld(A,unit),ld(A,mult(B,B))) != mult(mult(op_a,op_a),mult(op_b,op_b)),
inference(paramod,[status(thm)],[c_19,c_2662]) ).
cnf(c_2915,plain,
mult(ld(ld(A,mult(B,B)),unit),A) != mult(mult(op_a,op_a),mult(op_b,op_b)),
inference(paramod,[status(thm)],[c_19,c_2851]) ).
cnf(c_2916,plain,
mult(ld(A,mult(mult(B,B),mult(ld(mult(B,B),A),ld(mult(B,B),A)))),A) != mult(mult(op_a,op_a),mult(op_b,op_b)),
inference(paramod,[status(thm)],[c_2018,c_2915]) ).
cnf(c_2917,plain,
mult(A,ld(A,mult(mult(B,B),mult(ld(mult(B,B),A),ld(mult(B,B),A))))) != mult(mult(op_a,op_a),mult(op_b,op_b)),
inference(paramod,[status(thm)],[c_5,c_2916]) ).
cnf(c_2861,plain,
mult(mult(A,A),mult(ld(mult(A,A),B),ld(mult(A,A),B))) != mult(mult(op_a,op_a),mult(op_b,op_b)),
inference(paramod,[status(thm)],[c_3,c_2917]) ).
cnf(c_2862,plain,
$false,
inference(resolve,[status(thm)],[c_2861,c_1164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP720-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.59 % Computer : n018.cluster.edu
% 0.10/10.59 % Model : x86_64 x86_64
% 0.10/10.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.59 % Memory : 8046.5625MB
% 0.10/10.59 % OS : Linux 6.8.0-71-generic
% 0.10/10.59 % CPULimit : 300
% 0.10/10.59 % WCLimit : 300
% 0.10/10.59 % DateTime : Fri Sep 25 15:43:01 UTC 2026
% 0.10/10.59 % CPUTime :
% 0.10/10.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/10.59 % Process 2330949 was started by sandbox on n018,
% 0.10/10.59 % Fri Sep 25 15:43:01 2026
% 0.10/10.59 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/10.59
% 0.10/10.59 % From the command line: assign(max_seconds, 300).
% 35.14/15.10
% 35.14/15.10 % SZS status Unsatisfiable for theBenchmark
% 35.14/15.10
% 35.14/15.10 % Proof 1 at 3.92 (+ 0.55) seconds.
% 35.14/15.10 % Length of proof is 52.
% 35.14/15.10 % Level of proof is 17.
% 35.14/15.10 % Maximum clause weight is 91.000.
% 35.14/15.10 % Given clauses 217.
% 35.14/15.10
% 35.14/15.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------