%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP669-1 : 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 : n009.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 0.67s 0.50s
% Output : CNFRefutation 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 74 ( 74 unt; 0 def)
% Number of atoms : 74 ( 73 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 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 : 143 ( 0 sgn 20 !; 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(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_0,VAR_2))) = mult(mult(mult(VAR_0,VAR_1),VAR_0),VAR_2),
file('theBenchmark.p',c07) ).
cnf(c_7,plain,
mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C),
inference(clausify,[status(thm)],[c07]) ).
cnf(c_8,plain,
mult(mult(mult(A,B),A),C) = mult(A,mult(B,mult(A,C))),
inference(copy,[status(thm)],[c_7]) ).
fof(c08,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(VAR_0,mult(VAR_1,mult(VAR_2,VAR_1))) = mult(mult(mult(VAR_0,VAR_1),VAR_2),VAR_1),
file('theBenchmark.p',c08) ).
cnf(c_9,plain,
mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B),
inference(clausify,[status(thm)],[c08]) ).
cnf(c_10,plain,
mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B))),
inference(copy,[status(thm)],[c_9]) ).
fof(c09,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(mult(VAR_0,VAR_1),mult(VAR_2,VAR_0)) = mult(mult(VAR_0,mult(VAR_1,VAR_2)),VAR_0),
file('theBenchmark.p',c09) ).
cnf(c_11,plain,
mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A),
inference(clausify,[status(thm)],[c09]) ).
cnf(c_12,plain,
mult(mult(A,mult(B,C)),A) = mult(mult(A,B),mult(C,A)),
inference(copy,[status(thm)],[c_11]) ).
fof(c10,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(mult(VAR_0,VAR_1),mult(VAR_2,VAR_0)) = mult(VAR_0,mult(mult(VAR_1,VAR_2),VAR_0)),
file('theBenchmark.p',c10) ).
cnf(c_13,plain,
mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)),
inference(clausify,[status(thm)],[c10]) ).
fof(goals,axiom,
mult(mult(a,b),mult(c,mult(a,b))) != mult(mult(mult(a,mult(b,c)),a),b),
file('theBenchmark.p',goals) ).
cnf(c_14,plain,
mult(mult(a,b),mult(c,mult(a,b))) != mult(mult(mult(a,mult(b,c)),a),b),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_422,plain,
mult(mult(a,b),mult(c,mult(a,b))) != mult(mult(mult(a,b),mult(c,a)),b),
inference(paramod,[status(thm)],[c_12,c_14]) ).
cnf(c_423,plain,
mult(mult(a,b),mult(c,mult(a,b))) != mult(mult(a,mult(mult(b,c),a)),b),
inference(paramod,[status(thm)],[c_13,c_422]) ).
cnf(c_15,plain,
mult(mult(a,mult(mult(b,c),a)),b) != mult(mult(a,b),mult(c,mult(a,b))),
inference(copy,[status(thm)],[c_423]) ).
cnf(c_19,plain,
ld(A,A) = unit,
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_424,plain,
mult(mult(A,B),C) = mult(B,mult(ld(B,A),mult(B,C))),
inference(paramod,[status(thm)],[c_1,c_8]) ).
cnf(c_24,plain,
mult(A,mult(ld(A,B),mult(A,C))) = mult(mult(B,A),C),
inference(copy,[status(thm)],[c_424]) ).
cnf(c_27,plain,
rd(mult(A,mult(B,mult(A,C))),C) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_425,plain,
mult(A,mult(B,mult(A,unit))) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_8,c_5]) ).
cnf(c_426,plain,
mult(A,mult(B,A)) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_5,c_425]) ).
cnf(c_28,plain,
mult(mult(A,B),A) = mult(A,mult(B,A)),
inference(copy,[status(thm)],[c_426]) ).
cnf(c_427,plain,
mult(mult(A,A),B) = mult(A,mult(unit,mult(A,B))),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_29,plain,
mult(mult(A,A),B) = mult(A,mult(A,B)),
inference(paramod,[status(thm)],[c_6,c_427]) ).
cnf(c_35,plain,
rd(mult(A,mult(B,mult(A,C))),C) = mult(A,mult(B,A)),
inference(paramod,[status(thm)],[c_28,c_27]) ).
cnf(c_38,plain,
mult(mult(A,mult(B,A)),C) = mult(A,mult(B,mult(A,C))),
inference(paramod,[status(thm)],[c_28,c_8]) ).
cnf(c_428,plain,
mult(a,mult(mult(b,c),mult(a,b))) != mult(mult(a,b),mult(c,mult(a,b))),
inference(paramod,[status(thm)],[c_38,c_15]) ).
cnf(c_429,plain,
mult(a,mult(b,mult(mult(c,a),b))) != mult(mult(a,b),mult(c,mult(a,b))),
inference(paramod,[status(thm)],[c_13,c_428]) ).
cnf(c_42,plain,
mult(mult(a,b),mult(c,mult(a,b))) != mult(a,mult(b,mult(mult(c,a),b))),
inference(copy,[status(thm)],[c_429]) ).
cnf(c_430,plain,
mult(mult(A,B),B) = mult(A,mult(B,mult(unit,B))),
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_48,plain,
mult(mult(A,B),B) = mult(A,mult(B,B)),
inference(paramod,[status(thm)],[c_6,c_430]) ).
cnf(c_60,plain,
mult(mult(A,B),mult(C,mult(A,mult(D,A)))) = mult(A,mult(mult(B,mult(mult(C,A),D)),A)),
inference(paramod,[status(thm)],[c_10,c_13]) ).
cnf(c_431,plain,
mult(A,B) = mult(B,mult(ld(B,A),B)),
inference(paramod,[status(thm)],[c_1,c_28]) ).
cnf(c_64,plain,
mult(A,mult(ld(A,B),A)) = mult(B,A),
inference(copy,[status(thm)],[c_431]) ).
cnf(c_191,plain,
ld(A,mult(B,A)) = mult(ld(A,B),A),
inference(paramod,[status(thm)],[c_64,c_2]) ).
cnf(c_432,plain,
ld(A,A) = mult(ld(A,unit),A),
inference(paramod,[status(thm)],[c_6,c_191]) ).
cnf(c_433,plain,
unit = mult(ld(A,unit),A),
inference(paramod,[status(thm)],[c_19,c_432]) ).
cnf(c_216,plain,
mult(ld(A,unit),A) = unit,
inference(copy,[status(thm)],[c_433]) ).
cnf(c_434,plain,
mult(unit,mult(A,ld(B,unit))) = mult(ld(B,unit),mult(mult(B,A),ld(B,unit))),
inference(paramod,[status(thm)],[c_216,c_13]) ).
cnf(c_435,plain,
mult(A,ld(B,unit)) = mult(ld(B,unit),mult(mult(B,A),ld(B,unit))),
inference(paramod,[status(thm)],[c_6,c_434]) ).
cnf(c_231,plain,
mult(ld(A,unit),mult(mult(A,B),ld(A,unit))) = mult(B,ld(A,unit)),
inference(copy,[status(thm)],[c_435]) ).
cnf(c_436,plain,
mult(ld(A,unit),mult(ld(ld(A,unit),B),unit)) = mult(mult(B,ld(A,unit)),A),
inference(paramod,[status(thm)],[c_216,c_24]) ).
cnf(c_437,plain,
mult(ld(A,unit),ld(ld(A,unit),B)) = mult(mult(B,ld(A,unit)),A),
inference(paramod,[status(thm)],[c_5,c_436]) ).
cnf(c_438,plain,
B = mult(mult(B,ld(A,unit)),A),
inference(paramod,[status(thm)],[c_1,c_437]) ).
cnf(c_233,plain,
mult(mult(A,ld(B,unit)),B) = A,
inference(copy,[status(thm)],[c_438]) ).
cnf(c_439,plain,
mult(unit,A) = mult(ld(A,unit),mult(A,A)),
inference(paramod,[status(thm)],[c_216,c_48]) ).
cnf(c_440,plain,
A = mult(ld(A,unit),mult(A,A)),
inference(paramod,[status(thm)],[c_6,c_439]) ).
cnf(c_235,plain,
mult(ld(A,unit),mult(A,A)) = A,
inference(copy,[status(thm)],[c_440]) ).
cnf(c_441,plain,
mult(A,mult(B,ld(A,unit))) = mult(ld(A,unit),mult(mult(mult(A,A),B),ld(A,unit))),
inference(paramod,[status(thm)],[c_235,c_13]) ).
cnf(c_442,plain,
mult(A,mult(B,ld(A,unit))) = mult(ld(A,unit),mult(mult(A,mult(A,B)),ld(A,unit))),
inference(paramod,[status(thm)],[c_29,c_441]) ).
cnf(c_443,plain,
mult(A,mult(B,ld(A,unit))) = mult(mult(A,B),ld(A,unit)),
inference(paramod,[status(thm)],[c_231,c_442]) ).
cnf(c_248,plain,
mult(mult(A,B),ld(A,unit)) = mult(A,mult(B,ld(A,unit))),
inference(copy,[status(thm)],[c_443]) ).
cnf(c_444,plain,
rd(mult(mult(A,B),mult(C,mult(A,mult(B,A)))),A) = mult(mult(A,B),mult(C,mult(A,B))),
inference(paramod,[status(thm)],[c_28,c_35]) ).
cnf(c_445,plain,
rd(mult(A,mult(mult(B,mult(mult(C,A),B)),A)),A) = mult(mult(A,B),mult(C,mult(A,B))),
inference(paramod,[status(thm)],[c_60,c_444]) ).
cnf(c_262,plain,
rd(mult(A,mult(B,mult(mult(C,A),mult(B,A)))),A) = mult(mult(A,B),mult(C,mult(A,B))),
inference(paramod,[status(thm)],[c_38,c_445]) ).
cnf(c_446,plain,
rd(A,B) = mult(A,ld(B,unit)),
inference(paramod,[status(thm)],[c_233,c_4]) ).
cnf(c_395,plain,
mult(A,ld(B,unit)) = rd(A,B),
inference(copy,[status(thm)],[c_446]) ).
cnf(c_447,plain,
rd(mult(A,B),A) = mult(A,mult(B,ld(A,unit))),
inference(paramod,[status(thm)],[c_395,c_248]) ).
cnf(c_411,plain,
rd(mult(A,B),A) = mult(A,rd(B,A)),
inference(paramod,[status(thm)],[c_395,c_447]) ).
cnf(c_448,plain,
mult(A,rd(mult(B,mult(mult(C,A),mult(B,A))),A)) = mult(mult(A,B),mult(C,mult(A,B))),
inference(paramod,[status(thm)],[c_411,c_262]) ).
cnf(c_449,plain,
mult(A,mult(B,mult(mult(C,A),B))) = mult(mult(A,B),mult(C,mult(A,B))),
inference(paramod,[status(thm)],[c_35,c_448]) ).
cnf(c_420,plain,
mult(mult(A,B),mult(C,mult(A,B))) = mult(A,mult(B,mult(mult(C,A),B))),
inference(copy,[status(thm)],[c_449]) ).
cnf(c_421,plain,
$false,
inference(resolve,[status(thm)],[c_420,c_42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP669-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 15:34:59 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 1949197 was started by sandbox on n009,
% 0.09/0.35 % Fri Sep 25 15:34:59 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.67/0.50
% 0.67/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.67/0.50
% 0.67/0.50 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.67/0.50 % Length of proof is 36.
% 0.67/0.50 % Level of proof is 10.
% 0.67/0.50 % Maximum clause weight is 69.000.
% 0.67/0.50 % Given clauses 49.
% 0.67/0.50
% 0.67/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------