%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP700-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 07:31:14 AM UTC 2026
% Result : Unsatisfiable 0.68s 0.58s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 9
% Syntax : Number of formulae : 85 ( 85 unt; 0 def)
% Number of atoms : 85 ( 84 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 15 ( 15 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,ld(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',f01) ).
cnf(c_1,plain,
mult(A,ld(A,B)) = B,
inference(clausify,[status(thm)],[f01]) ).
fof(f02,axiom,
! [VAR_0,VAR_1] : ld(VAR_0,mult(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',f02) ).
cnf(c_2,plain,
ld(A,mult(A,B)) = B,
inference(clausify,[status(thm)],[f02]) ).
fof(f03,axiom,
! [VAR_0,VAR_1] : mult(rd(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',f03) ).
cnf(c_3,plain,
mult(rd(A,B),B) = A,
inference(clausify,[status(thm)],[f03]) ).
fof(f04,axiom,
! [VAR_0,VAR_1] : rd(mult(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',f04) ).
cnf(c_4,plain,
rd(mult(A,B),B) = A,
inference(clausify,[status(thm)],[f04]) ).
fof(f05,axiom,
! [VAR_0] : mult(VAR_0,unit) = VAR_0,
file('theBenchmark.p',f05) ).
cnf(c_5,plain,
mult(A,unit) = A,
inference(clausify,[status(thm)],[f05]) ).
fof(f06,axiom,
! [VAR_0] : mult(unit,VAR_0) = VAR_0,
file('theBenchmark.p',f06) ).
cnf(c_6,plain,
mult(unit,A) = A,
inference(clausify,[status(thm)],[f06]) ).
fof(f07,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(mult(mult(VAR_0,VAR_1),VAR_0),mult(VAR_0,VAR_2)) = mult(VAR_0,mult(mult(mult(VAR_1,VAR_0),VAR_0),VAR_2)),
file('theBenchmark.p',f07) ).
cnf(c_7,plain,
mult(mult(mult(A,B),A),mult(A,C)) = mult(A,mult(mult(mult(B,A),A),C)),
inference(clausify,[status(thm)],[f07]) ).
fof(f08,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(mult(VAR_0,VAR_1),mult(VAR_1,mult(VAR_2,VAR_1))) = mult(mult(VAR_0,mult(VAR_1,mult(VAR_1,VAR_2))),VAR_1),
file('theBenchmark.p',f08) ).
cnf(c_8,plain,
mult(mult(A,B),mult(B,mult(C,B))) = mult(mult(A,mult(B,mult(B,C))),B),
inference(clausify,[status(thm)],[f08]) ).
cnf(c_9,plain,
mult(mult(A,mult(B,mult(B,C))),B) = mult(mult(A,B),mult(B,mult(C,B))),
inference(copy,[status(thm)],[c_8]) ).
fof(goal,axiom,
! [VAR_0] : tuple(mult(VAR_0,x0),mult(x0,VAR_0)) != tuple(unit,unit),
file('theBenchmark.p',goal) ).
cnf(c_10,plain,
tuple(mult(A,x0),mult(x0,A)) != tuple(unit,unit),
inference(clausify,[status(thm)],[goal]) ).
cnf(c_11,plain,
ld(rd(A,B),A) = B,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_12,plain,
rd(A,ld(B,A)) = B,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_13,plain,
ld(A,A) = unit,
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_16,plain,
rd(A,A) = unit,
inference(paramod,[status(thm)],[c_6,c_4]) ).
cnf(c_22,plain,
rd(mult(A,mult(mult(mult(B,A),A),C)),mult(A,C)) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_551,plain,
mult(mult(A,A),mult(A,B)) = mult(A,mult(mult(mult(unit,A),A),B)),
inference(paramod,[status(thm)],[c_5,c_7]) ).
cnf(c_23,plain,
mult(mult(A,A),mult(A,B)) = mult(A,mult(mult(A,A),B)),
inference(paramod,[status(thm)],[c_6,c_551]) ).
cnf(c_552,plain,
mult(mult(A,mult(B,B)),B) = mult(mult(A,B),mult(B,mult(unit,B))),
inference(paramod,[status(thm)],[c_5,c_9]) ).
cnf(c_31,plain,
mult(mult(A,mult(B,B)),B) = mult(mult(A,B),mult(B,B)),
inference(paramod,[status(thm)],[c_6,c_552]) ).
cnf(c_38,plain,
tuple(mult(mult(A,x0),mult(x0,mult(B,x0))),mult(x0,mult(A,mult(x0,mult(x0,B))))) != tuple(unit,unit),
inference(paramod,[status(thm)],[c_9,c_10]) ).
cnf(c_39,plain,
tuple(mult(A,mult(x0,mult(B,x0))),mult(x0,mult(rd(A,x0),mult(x0,mult(x0,B))))) != tuple(unit,unit),
inference(paramod,[status(thm)],[c_3,c_38]) ).
cnf(c_553,plain,
mult(mult(A,A),B) = mult(A,mult(mult(A,A),ld(A,B))),
inference(paramod,[status(thm)],[c_1,c_23]) ).
cnf(c_46,plain,
mult(A,mult(mult(A,A),ld(A,B))) = mult(mult(A,A),B),
inference(copy,[status(thm)],[c_553]) ).
cnf(c_97,plain,
ld(A,mult(mult(A,A),B)) = mult(mult(A,A),ld(A,B)),
inference(paramod,[status(thm)],[c_46,c_2]) ).
cnf(c_554,plain,
ld(A,mult(A,A)) = mult(mult(A,A),ld(A,unit)),
inference(paramod,[status(thm)],[c_5,c_97]) ).
cnf(c_555,plain,
A = mult(mult(A,A),ld(A,unit)),
inference(paramod,[status(thm)],[c_2,c_554]) ).
cnf(c_107,plain,
mult(mult(A,A),ld(A,unit)) = A,
inference(copy,[status(thm)],[c_555]) ).
cnf(c_114,plain,
rd(A,ld(A,unit)) = mult(A,A),
inference(paramod,[status(thm)],[c_107,c_4]) ).
cnf(c_556,plain,
ld(A,A) = mult(mult(A,A),ld(A,ld(A,unit))),
inference(paramod,[status(thm)],[c_107,c_97]) ).
cnf(c_557,plain,
unit = mult(mult(A,A),ld(A,ld(A,unit))),
inference(paramod,[status(thm)],[c_13,c_556]) ).
cnf(c_121,plain,
mult(mult(A,A),ld(A,ld(A,unit))) = unit,
inference(copy,[status(thm)],[c_557]) ).
cnf(c_558,plain,
rd(rd(unit,A),A) = mult(rd(unit,A),rd(unit,A)),
inference(paramod,[status(thm)],[c_11,c_114]) ).
cnf(c_154,plain,
mult(rd(unit,A),rd(unit,A)) = rd(rd(unit,A),A),
inference(copy,[status(thm)],[c_558]) ).
cnf(c_172,plain,
ld(mult(A,A),unit) = ld(A,ld(A,unit)),
inference(paramod,[status(thm)],[c_121,c_2]) ).
cnf(c_173,plain,
rd(unit,ld(A,ld(A,unit))) = mult(A,A),
inference(paramod,[status(thm)],[c_121,c_4]) ).
cnf(c_559,plain,
rd(unit,ld(rd(unit,A),A)) = mult(rd(unit,A),rd(unit,A)),
inference(paramod,[status(thm)],[c_11,c_173]) ).
cnf(c_188,plain,
rd(unit,ld(rd(unit,A),A)) = rd(rd(unit,A),A),
inference(paramod,[status(thm)],[c_154,c_559]) ).
cnf(c_261,plain,
ld(mult(A,mult(B,B)),mult(mult(A,B),mult(B,B))) = B,
inference(paramod,[status(thm)],[c_31,c_2]) ).
cnf(c_278,plain,
ld(mult(rd(A,B),mult(B,B)),mult(A,mult(B,B))) = B,
inference(paramod,[status(thm)],[c_3,c_261]) ).
cnf(c_298,plain,
ld(mult(rd(unit,A),mult(A,A)),mult(A,A)) = A,
inference(paramod,[status(thm)],[c_6,c_278]) ).
cnf(c_560,plain,
rd(mult(A,A),A) = mult(rd(unit,A),mult(A,A)),
inference(paramod,[status(thm)],[c_298,c_12]) ).
cnf(c_561,plain,
A = mult(rd(unit,A),mult(A,A)),
inference(paramod,[status(thm)],[c_4,c_560]) ).
cnf(c_308,plain,
mult(rd(unit,A),mult(A,A)) = A,
inference(copy,[status(thm)],[c_561]) ).
cnf(c_312,plain,
ld(rd(unit,A),A) = mult(A,A),
inference(paramod,[status(thm)],[c_308,c_2]) ).
cnf(c_313,plain,
rd(A,mult(A,A)) = rd(unit,A),
inference(paramod,[status(thm)],[c_308,c_4]) ).
cnf(c_562,plain,
rd(unit,mult(A,A)) = rd(rd(unit,A),A),
inference(paramod,[status(thm)],[c_312,c_188]) ).
cnf(c_336,plain,
rd(rd(unit,A),A) = rd(unit,mult(A,A)),
inference(copy,[status(thm)],[c_562]) ).
cnf(c_361,plain,
mult(rd(unit,A),rd(unit,A)) = rd(unit,mult(A,A)),
inference(paramod,[status(thm)],[c_336,c_154]) ).
cnf(c_563,plain,
mult(rd(unit,A),mult(mult(rd(unit,A),rd(unit,A)),mult(A,A))) = mult(mult(rd(unit,A),rd(unit,A)),A),
inference(paramod,[status(thm)],[c_312,c_46]) ).
cnf(c_564,plain,
mult(rd(unit,A),mult(rd(unit,mult(A,A)),mult(A,A))) = mult(mult(rd(unit,A),rd(unit,A)),A),
inference(paramod,[status(thm)],[c_361,c_563]) ).
cnf(c_565,plain,
mult(rd(unit,A),unit) = mult(mult(rd(unit,A),rd(unit,A)),A),
inference(paramod,[status(thm)],[c_3,c_564]) ).
cnf(c_566,plain,
rd(unit,A) = mult(mult(rd(unit,A),rd(unit,A)),A),
inference(paramod,[status(thm)],[c_5,c_565]) ).
cnf(c_567,plain,
rd(unit,A) = mult(rd(unit,mult(A,A)),A),
inference(paramod,[status(thm)],[c_361,c_566]) ).
cnf(c_383,plain,
mult(rd(unit,mult(A,A)),A) = rd(unit,A),
inference(copy,[status(thm)],[c_567]) ).
cnf(c_568,plain,
rd(mult(ld(A,unit),mult(mult(A,ld(A,unit)),B)),mult(ld(A,unit),B)) = mult(mult(ld(A,unit),mult(A,A)),ld(A,unit)),
inference(paramod,[status(thm)],[c_107,c_22]) ).
cnf(c_569,plain,
rd(mult(ld(A,unit),mult(unit,B)),mult(ld(A,unit),B)) = mult(mult(ld(A,unit),mult(A,A)),ld(A,unit)),
inference(paramod,[status(thm)],[c_1,c_568]) ).
cnf(c_570,plain,
rd(mult(ld(A,unit),B),mult(ld(A,unit),B)) = mult(mult(ld(A,unit),mult(A,A)),ld(A,unit)),
inference(paramod,[status(thm)],[c_6,c_569]) ).
cnf(c_571,plain,
unit = mult(mult(ld(A,unit),mult(A,A)),ld(A,unit)),
inference(paramod,[status(thm)],[c_16,c_570]) ).
cnf(c_444,plain,
mult(mult(ld(A,unit),mult(A,A)),ld(A,unit)) = unit,
inference(copy,[status(thm)],[c_571]) ).
cnf(c_460,plain,
tuple(mult(x0,mult(A,x0)),mult(x0,mult(rd(unit,x0),mult(x0,mult(x0,A))))) != tuple(unit,unit),
inference(paramod,[status(thm)],[c_6,c_39]) ).
cnf(c_572,plain,
rd(unit,ld(A,unit)) = mult(ld(A,unit),mult(A,A)),
inference(paramod,[status(thm)],[c_444,c_4]) ).
cnf(c_573,plain,
A = mult(ld(A,unit),mult(A,A)),
inference(paramod,[status(thm)],[c_12,c_572]) ).
cnf(c_491,plain,
mult(ld(A,unit),mult(A,A)) = A,
inference(copy,[status(thm)],[c_573]) ).
cnf(c_516,plain,
tuple(mult(x0,rd(unit,x0)),mult(x0,mult(rd(unit,x0),mult(x0,mult(x0,rd(unit,mult(x0,x0))))))) != tuple(unit,unit),
inference(paramod,[status(thm)],[c_383,c_460]) ).
cnf(c_574,plain,
rd(A,mult(A,A)) = ld(A,unit),
inference(paramod,[status(thm)],[c_491,c_4]) ).
cnf(c_529,plain,
rd(unit,A) = ld(A,unit),
inference(paramod,[status(thm)],[c_313,c_574]) ).
cnf(c_575,plain,
tuple(mult(x0,ld(x0,unit)),mult(x0,mult(rd(unit,x0),mult(x0,mult(x0,rd(unit,mult(x0,x0))))))) != tuple(unit,unit),
inference(paramod,[status(thm)],[c_529,c_516]) ).
cnf(c_576,plain,
tuple(unit,mult(x0,mult(rd(unit,x0),mult(x0,mult(x0,rd(unit,mult(x0,x0))))))) != tuple(unit,unit),
inference(paramod,[status(thm)],[c_1,c_575]) ).
cnf(c_577,plain,
tuple(unit,mult(x0,mult(ld(x0,unit),mult(x0,mult(x0,rd(unit,mult(x0,x0))))))) != tuple(unit,unit),
inference(paramod,[status(thm)],[c_529,c_576]) ).
cnf(c_578,plain,
tuple(unit,mult(x0,mult(ld(x0,unit),mult(x0,mult(x0,ld(mult(x0,x0),unit)))))) != tuple(unit,unit),
inference(paramod,[status(thm)],[c_529,c_577]) ).
cnf(c_579,plain,
tuple(unit,mult(x0,mult(ld(x0,unit),mult(x0,mult(x0,ld(x0,ld(x0,unit))))))) != tuple(unit,unit),
inference(paramod,[status(thm)],[c_172,c_578]) ).
cnf(c_580,plain,
tuple(unit,mult(x0,mult(ld(x0,unit),mult(x0,ld(x0,unit))))) != tuple(unit,unit),
inference(paramod,[status(thm)],[c_1,c_579]) ).
cnf(c_581,plain,
tuple(unit,mult(x0,mult(ld(x0,unit),unit))) != tuple(unit,unit),
inference(paramod,[status(thm)],[c_1,c_580]) ).
cnf(c_582,plain,
tuple(unit,mult(x0,ld(x0,unit))) != tuple(unit,unit),
inference(paramod,[status(thm)],[c_5,c_581]) ).
cnf(c_583,plain,
tuple(unit,unit) != tuple(unit,unit),
inference(paramod,[status(thm)],[c_1,c_582]) ).
cnf(c_550,plain,
$false,
inference(copy,[status(thm)],[c_583]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP700-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 15:40:54 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 3673212 was started by sandbox2 on n002,
% 0.13/0.36 % Fri Sep 25 15:40:54 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.68/0.58
% 0.68/0.58 % SZS status Unsatisfiable for theBenchmark
% 0.68/0.58
% 0.68/0.58 % Proof 1 at 0.15 (+ 0.04) seconds.
% 0.68/0.58 % Length of proof is 43.
% 0.68/0.58 % Level of proof is 12.
% 0.68/0.58 % Maximum clause weight is 71.000.
% 0.68/0.58 % Given clauses 92.
% 0.68/0.58
% 0.68/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------