%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP683-10 : 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 : n014.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 07:31:11 AM UTC 2026
% Result : Unsatisfiable 0.89s 0.61s
% Output : CNFRefutation 0.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 7
% Syntax : Number of formulae : 75 ( 75 unt; 0 def)
% Number of atoms : 75 ( 74 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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; 3 con; 0-2 aty)
% Number of variables : 187 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [VAR_0] : ld(VAR_0,mult(VAR_0,VAR_0)) = VAR_0,
file('theBenchmark.p',f01) ).
cnf(c_1,plain,
ld(A,mult(A,A)) = A,
inference(clausify,[status(thm)],[f01]) ).
fof(f02,axiom,
! [VAR_0] : rd(mult(VAR_0,VAR_0),VAR_0) = VAR_0,
file('theBenchmark.p',f02) ).
cnf(c_2,plain,
rd(mult(A,A),A) = A,
inference(clausify,[status(thm)],[f02]) ).
fof(f03,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,ld(VAR_0,VAR_1)) = ld(VAR_0,mult(VAR_0,VAR_1)),
file('theBenchmark.p',f03) ).
cnf(c_3,plain,
mult(A,ld(A,B)) = ld(A,mult(A,B)),
inference(clausify,[status(thm)],[f03]) ).
cnf(c_4,plain,
ld(A,mult(A,B)) = mult(A,ld(A,B)),
inference(copy,[status(thm)],[c_3]) ).
fof(f04,axiom,
! [VAR_0,VAR_1] : mult(rd(VAR_0,VAR_1),VAR_1) = rd(mult(VAR_0,VAR_1),VAR_1),
file('theBenchmark.p',f04) ).
cnf(c_5,plain,
mult(rd(A,B),B) = rd(mult(A,B),B),
inference(clausify,[status(thm)],[f04]) ).
cnf(c_6,plain,
rd(mult(A,B),B) = mult(rd(A,B),B),
inference(copy,[status(thm)],[c_5]) ).
fof(f05,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : ld(ld(VAR_0,VAR_1),mult(ld(VAR_0,VAR_1),mult(VAR_2,VAR_3))) = mult(ld(VAR_0,mult(VAR_0,VAR_2)),VAR_3),
file('theBenchmark.p',f05) ).
cnf(c_7,plain,
ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D),
inference(clausify,[status(thm)],[f05]) ).
cnf(c_547,plain,
mult(ld(A,B),ld(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D),
inference(paramod,[status(thm)],[c_4,c_7]) ).
cnf(c_8,plain,
mult(ld(A,B),ld(ld(A,B),mult(C,D))) = mult(mult(A,ld(A,C)),D),
inference(paramod,[status(thm)],[c_4,c_547]) ).
fof(f07,axiom,
! [VAR_0,VAR_1] : ld(VAR_0,mult(VAR_0,ld(VAR_1,VAR_1))) = rd(mult(rd(VAR_0,VAR_0),VAR_1),VAR_1),
file('theBenchmark.p',f07) ).
cnf(c_11,plain,
ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B),
inference(clausify,[status(thm)],[f07]) ).
cnf(c_548,plain,
mult(A,ld(A,ld(B,B))) = rd(mult(rd(A,A),B),B),
inference(paramod,[status(thm)],[c_4,c_11]) ).
cnf(c_549,plain,
mult(A,ld(A,ld(B,B))) = mult(rd(rd(A,A),B),B),
inference(paramod,[status(thm)],[c_6,c_548]) ).
cnf(c_12,plain,
mult(rd(rd(A,A),B),B) = mult(A,ld(A,ld(B,B))),
inference(copy,[status(thm)],[c_549]) ).
fof(goal,axiom,
mult(x3,ld(x4,mult(x4,x5))) != mult(x3,x5),
file('theBenchmark.p',goal) ).
cnf(c_13,plain,
mult(x3,ld(x4,mult(x4,x5))) != mult(x3,x5),
inference(clausify,[status(thm)],[goal]) ).
cnf(c_14,plain,
mult(x3,mult(x4,ld(x4,x5))) != mult(x3,x5),
inference(paramod,[status(thm)],[c_4,c_13]) ).
cnf(c_15,plain,
mult(A,ld(A,A)) = A,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_16,plain,
mult(rd(A,A),A) = A,
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_550,plain,
ld(ld(A,B),mult(mult(A,ld(A,C)),D)) = mult(ld(A,B),ld(ld(A,B),ld(ld(A,B),mult(C,D)))),
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_17,plain,
mult(ld(A,B),ld(ld(A,B),ld(ld(A,B),mult(C,D)))) = ld(ld(A,B),mult(mult(A,ld(A,C)),D)),
inference(copy,[status(thm)],[c_550]) ).
cnf(c_551,plain,
mult(mult(A,ld(A,B)),ld(ld(A,mult(A,B)),mult(C,D))) = mult(mult(A,ld(A,C)),D),
inference(paramod,[status(thm)],[c_4,c_8]) ).
cnf(c_18,plain,
mult(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),mult(C,D))) = mult(mult(A,ld(A,C)),D),
inference(paramod,[status(thm)],[c_4,c_551]) ).
cnf(c_552,plain,
ld(A,A) = mult(A,ld(A,ld(A,A))),
inference(paramod,[status(thm)],[c_15,c_4]) ).
cnf(c_33,plain,
mult(A,ld(A,ld(A,A))) = ld(A,A),
inference(copy,[status(thm)],[c_552]) ).
cnf(c_553,plain,
rd(A,A) = mult(rd(rd(A,A),A),A),
inference(paramod,[status(thm)],[c_16,c_6]) ).
cnf(c_554,plain,
rd(A,A) = mult(A,ld(A,ld(A,A))),
inference(paramod,[status(thm)],[c_12,c_553]) ).
cnf(c_38,plain,
rd(A,A) = ld(A,A),
inference(paramod,[status(thm)],[c_33,c_554]) ).
cnf(c_555,plain,
rd(mult(A,A),A) = A,
inference(paramod,[status(thm)],[c_16,c_6]) ).
cnf(c_556,plain,
mult(rd(A,A),A) = A,
inference(paramod,[status(thm)],[c_6,c_555]) ).
cnf(c_39,plain,
mult(ld(A,A),A) = A,
inference(paramod,[status(thm)],[c_38,c_556]) ).
cnf(c_557,plain,
mult(ld(A,B),ld(ld(A,B),C)) = mult(mult(A,ld(A,rd(C,C))),C),
inference(paramod,[status(thm)],[c_16,c_8]) ).
cnf(c_40,plain,
mult(ld(A,B),ld(ld(A,B),C)) = mult(mult(A,ld(A,ld(C,C))),C),
inference(paramod,[status(thm)],[c_38,c_557]) ).
cnf(c_558,plain,
mult(mult(A,ld(A,B)),ld(ld(A,mult(A,B)),ld(ld(A,mult(A,B)),mult(C,D)))) = ld(ld(A,mult(A,B)),mult(mult(A,ld(A,C)),D)),
inference(paramod,[status(thm)],[c_4,c_17]) ).
cnf(c_559,plain,
mult(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),ld(ld(A,mult(A,B)),mult(C,D)))) = ld(ld(A,mult(A,B)),mult(mult(A,ld(A,C)),D)),
inference(paramod,[status(thm)],[c_4,c_558]) ).
cnf(c_560,plain,
mult(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),mult(C,D)))) = ld(ld(A,mult(A,B)),mult(mult(A,ld(A,C)),D)),
inference(paramod,[status(thm)],[c_4,c_559]) ).
cnf(c_51,plain,
mult(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),mult(C,D)))) = ld(mult(A,ld(A,B)),mult(mult(A,ld(A,C)),D)),
inference(paramod,[status(thm)],[c_4,c_560]) ).
cnf(c_561,plain,
mult(A,ld(mult(A,ld(A,A)),mult(B,C))) = mult(mult(A,ld(A,B)),C),
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_562,plain,
mult(A,ld(A,mult(B,C))) = mult(mult(A,ld(A,B)),C),
inference(paramod,[status(thm)],[c_15,c_561]) ).
cnf(c_81,plain,
mult(mult(A,ld(A,B)),C) = mult(A,ld(A,mult(B,C))),
inference(copy,[status(thm)],[c_562]) ).
cnf(c_563,plain,
mult(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),C)) = mult(mult(A,ld(A,C)),ld(C,C)),
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_564,plain,
mult(A,ld(A,mult(B,ld(mult(A,ld(A,B)),C)))) = mult(mult(A,ld(A,C)),ld(C,C)),
inference(paramod,[status(thm)],[c_81,c_563]) ).
cnf(c_565,plain,
mult(A,ld(A,mult(B,ld(mult(A,ld(A,B)),C)))) = mult(A,ld(A,mult(C,ld(C,C)))),
inference(paramod,[status(thm)],[c_81,c_564]) ).
cnf(c_82,plain,
mult(A,ld(A,mult(B,ld(mult(A,ld(A,B)),C)))) = mult(A,ld(A,C)),
inference(paramod,[status(thm)],[c_15,c_565]) ).
cnf(c_566,plain,
mult(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),mult(A,C))) = mult(A,C),
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_567,plain,
mult(A,ld(A,mult(B,ld(mult(A,ld(A,B)),mult(A,C))))) = mult(A,C),
inference(paramod,[status(thm)],[c_81,c_566]) ).
cnf(c_568,plain,
mult(A,ld(A,mult(A,C))) = mult(A,C),
inference(paramod,[status(thm)],[c_82,c_567]) ).
cnf(c_83,plain,
mult(A,mult(A,ld(A,B))) = mult(A,B),
inference(paramod,[status(thm)],[c_4,c_568]) ).
cnf(c_569,plain,
mult(A,ld(A,mult(B,ld(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),mult(C,D)))))) = ld(mult(A,ld(A,B)),mult(mult(A,ld(A,C)),D)),
inference(paramod,[status(thm)],[c_81,c_51]) ).
cnf(c_570,plain,
mult(A,ld(A,ld(mult(A,ld(A,B)),mult(C,D)))) = ld(mult(A,ld(A,B)),mult(mult(A,ld(A,C)),D)),
inference(paramod,[status(thm)],[c_82,c_569]) ).
cnf(c_571,plain,
mult(A,ld(A,ld(mult(A,ld(A,B)),mult(C,D)))) = ld(mult(A,ld(A,B)),mult(A,ld(A,mult(C,D)))),
inference(paramod,[status(thm)],[c_81,c_570]) ).
cnf(c_103,plain,
ld(mult(A,ld(A,B)),mult(A,ld(A,mult(C,D)))) = mult(A,ld(A,ld(mult(A,ld(A,B)),mult(C,D)))),
inference(copy,[status(thm)],[c_571]) ).
cnf(c_572,plain,
mult(ld(A,B),ld(ld(A,B),C)) = mult(A,ld(A,mult(ld(C,C),C))),
inference(paramod,[status(thm)],[c_81,c_40]) ).
cnf(c_105,plain,
mult(ld(A,B),ld(ld(A,B),C)) = mult(A,ld(A,C)),
inference(paramod,[status(thm)],[c_39,c_572]) ).
cnf(c_573,plain,
ld(mult(A,ld(A,B)),mult(A,ld(A,mult(B,C)))) = mult(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),C)),
inference(paramod,[status(thm)],[c_81,c_4]) ).
cnf(c_574,plain,
mult(A,ld(A,ld(mult(A,ld(A,B)),mult(B,C)))) = mult(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),C)),
inference(paramod,[status(thm)],[c_103,c_573]) ).
cnf(c_575,plain,
mult(A,ld(A,ld(mult(A,ld(A,B)),mult(B,C)))) = mult(A,ld(A,mult(B,ld(mult(A,ld(A,B)),C)))),
inference(paramod,[status(thm)],[c_81,c_574]) ).
cnf(c_121,plain,
mult(A,ld(A,ld(mult(A,ld(A,B)),mult(B,C)))) = mult(A,ld(A,C)),
inference(paramod,[status(thm)],[c_82,c_575]) ).
cnf(c_127,plain,
mult(A,ld(A,ld(A,B))) = ld(A,B),
inference(paramod,[status(thm)],[c_105,c_15]) ).
cnf(c_576,plain,
ld(mult(A,ld(A,B)),C) = mult(A,ld(A,mult(B,ld(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),C))))),
inference(paramod,[status(thm)],[c_127,c_81]) ).
cnf(c_577,plain,
ld(mult(A,ld(A,B)),C) = mult(A,ld(A,ld(mult(A,ld(A,B)),C))),
inference(paramod,[status(thm)],[c_82,c_576]) ).
cnf(c_146,plain,
mult(A,ld(A,ld(mult(A,ld(A,B)),C))) = ld(mult(A,ld(A,B)),C),
inference(copy,[status(thm)],[c_577]) ).
cnf(c_148,plain,
ld(mult(A,ld(A,B)),mult(B,C)) = mult(A,ld(A,C)),
inference(paramod,[status(thm)],[c_146,c_121]) ).
cnf(c_578,plain,
ld(mult(A,ld(A,B)),mult(B,C)) = mult(A,ld(A,mult(B,ld(B,C)))),
inference(paramod,[status(thm)],[c_83,c_148]) ).
cnf(c_579,plain,
mult(A,ld(A,C)) = mult(A,ld(A,mult(B,ld(B,C)))),
inference(paramod,[status(thm)],[c_148,c_578]) ).
cnf(c_156,plain,
mult(A,ld(A,mult(B,ld(B,C)))) = mult(A,ld(A,C)),
inference(copy,[status(thm)],[c_579]) ).
cnf(c_580,plain,
mult(A,mult(A,ld(A,B))) = mult(A,mult(C,ld(C,B))),
inference(paramod,[status(thm)],[c_156,c_83]) ).
cnf(c_581,plain,
mult(A,B) = mult(A,mult(C,ld(C,B))),
inference(paramod,[status(thm)],[c_83,c_580]) ).
cnf(c_545,plain,
mult(A,mult(B,ld(B,C))) = mult(A,C),
inference(copy,[status(thm)],[c_581]) ).
cnf(c_546,plain,
$false,
inference(resolve,[status(thm)],[c_545,c_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP683-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 15:36:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 582345 was started by sandbox2 on n014,
% 0.11/0.37 % Fri Sep 25 15:36:47 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.89/0.61
% 0.89/0.61 % SZS status Unsatisfiable for theBenchmark
% 0.89/0.61
% 0.89/0.61 % Proof 1 at 0.13 (+ 0.05) seconds.
% 0.89/0.61 % Length of proof is 33.
% 0.89/0.61 % Level of proof is 12.
% 0.89/0.61 % Maximum clause weight is 71.000.
% 0.89/0.61 % Given clauses 79.
% 0.89/0.61
% 0.89/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------