%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP700+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 : n019.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 : Theorem 0.25s 0.60s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 9
% Syntax : Number of formulae : 83 ( 78 unt; 0 def)
% Number of atoms : 88 ( 87 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 3 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 119 ( 0 sgn 20 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [B,A] : mult(A,ld(A,B)) = B,
file('theBenchmark.p',f01) ).
fof(f02,axiom,
! [B,A] : ld(A,mult(A,B)) = B,
file('theBenchmark.p',f02) ).
fof(f03,axiom,
! [B,A] : mult(rd(A,B),B) = A,
file('theBenchmark.p',f03) ).
fof(f04,axiom,
! [B,A] : rd(mult(A,B),B) = A,
file('theBenchmark.p',f04) ).
fof(f05,axiom,
! [A] : mult(A,unit) = A,
file('theBenchmark.p',f05) ).
fof(f06,axiom,
! [A] : mult(unit,A) = A,
file('theBenchmark.p',f06) ).
fof(f07,axiom,
! [C,B,A] : mult(mult(mult(A,B),A),mult(A,C)) = mult(A,mult(mult(mult(B,A),A),C)),
file('theBenchmark.p',f07) ).
fof(f08,axiom,
! [C,B,A] : mult(mult(A,B),mult(B,mult(C,B))) = mult(mult(A,mult(B,mult(B,C))),B),
file('theBenchmark.p',f08) ).
fof(goals,conjecture,
! [X0] :
? [X1] :
( mult(X0,X1) = unit
& mult(X1,X0) = unit ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
? [X1] :
( mult(X0,X1) = unit
& mult(X1,X0) = unit ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_10,plain,
mult(A,ld(A,B)) = B,
inference(clausify,[status(thm)],[f01]) ).
cnf(c_11,plain,
ld(A,mult(A,B)) = B,
inference(clausify,[status(thm)],[f02]) ).
cnf(c_12,plain,
mult(rd(A,B),B) = A,
inference(clausify,[status(thm)],[f03]) ).
cnf(c_13,plain,
rd(mult(A,B),B) = A,
inference(clausify,[status(thm)],[f04]) ).
cnf(c_14,plain,
mult(A,unit) = A,
inference(clausify,[status(thm)],[f05]) ).
cnf(c_15,plain,
mult(unit,A) = A,
inference(clausify,[status(thm)],[f06]) ).
cnf(c_16,plain,
mult(mult(mult(A,B),A),mult(A,C)) = mult(A,mult(mult(mult(B,A),A),C)),
inference(clausify,[status(thm)],[f07]) ).
cnf(c_17,plain,
mult(mult(A,mult(B,mult(B,C))),B) = mult(mult(A,B),mult(B,mult(C,B))),
inference(clausify,[status(thm)],[f08]) ).
fof(nnf_9,plain,
? [X0] :
! [X1] :
( mult(X0,X1) != unit
| mult(X1,X0) != unit ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
! [X1] :
( mult(sK0,X1) != unit
| mult(X1,sK0) != unit ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_9]) ).
cnf(c_18,negated_conjecture,
( mult(sK0,A) != unit
| mult(A,sK0) != unit ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_20,plain,
ld(rd(A,B),A) = B,
inference(paramod,[status(thm)],[c_12,c_11]) ).
cnf(c_21,plain,
rd(A,ld(B,A)) = B,
inference(paramod,[status(thm)],[c_10,c_13]) ).
cnf(c_22,plain,
ld(A,A) = unit,
inference(paramod,[status(thm)],[c_14,c_11]) ).
cnf(c_25,plain,
rd(A,A) = unit,
inference(paramod,[status(thm)],[c_15,c_13]) ).
cnf(c_31,plain,
rd(mult(A,mult(mult(mult(B,A),A),C)),mult(A,C)) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_16,c_13]) ).
cnf(c_433,plain,
mult(mult(A,A),mult(A,B)) = mult(A,mult(mult(mult(unit,A),A),B)),
inference(paramod,[status(thm)],[c_14,c_16]) ).
cnf(c_32,plain,
mult(mult(A,A),mult(A,B)) = mult(A,mult(mult(A,A),B)),
inference(paramod,[status(thm)],[c_15,c_433]) ).
cnf(c_434,plain,
mult(mult(A,mult(B,B)),B) = mult(mult(A,B),mult(B,mult(unit,B))),
inference(paramod,[status(thm)],[c_14,c_17]) ).
cnf(c_40,plain,
mult(mult(A,mult(B,B)),B) = mult(mult(A,B),mult(B,B)),
inference(paramod,[status(thm)],[c_15,c_434]) ).
cnf(c_44,negated_conjecture,
mult(ld(sK0,unit),sK0) != unit,
inference(resolve,[status(thm)],[c_18,c_10]) ).
cnf(c_435,plain,
mult(mult(A,A),B) = mult(A,mult(mult(A,A),ld(A,B))),
inference(paramod,[status(thm)],[c_10,c_32]) ).
cnf(c_46,plain,
mult(A,mult(mult(A,A),ld(A,B))) = mult(mult(A,A),B),
inference(copy,[status(thm)],[c_435]) ).
cnf(c_80,plain,
ld(A,mult(mult(A,A),B)) = mult(mult(A,A),ld(A,B)),
inference(paramod,[status(thm)],[c_46,c_11]) ).
cnf(c_436,plain,
ld(A,mult(A,A)) = mult(mult(A,A),ld(A,unit)),
inference(paramod,[status(thm)],[c_14,c_80]) ).
cnf(c_437,plain,
A = mult(mult(A,A),ld(A,unit)),
inference(paramod,[status(thm)],[c_11,c_436]) ).
cnf(c_89,plain,
mult(mult(A,A),ld(A,unit)) = A,
inference(copy,[status(thm)],[c_437]) ).
cnf(c_96,plain,
rd(A,ld(A,unit)) = mult(A,A),
inference(paramod,[status(thm)],[c_89,c_13]) ).
cnf(c_438,plain,
ld(A,A) = mult(mult(A,A),ld(A,ld(A,unit))),
inference(paramod,[status(thm)],[c_89,c_80]) ).
cnf(c_439,plain,
unit = mult(mult(A,A),ld(A,ld(A,unit))),
inference(paramod,[status(thm)],[c_22,c_438]) ).
cnf(c_103,plain,
mult(mult(A,A),ld(A,ld(A,unit))) = unit,
inference(copy,[status(thm)],[c_439]) ).
cnf(c_440,plain,
rd(rd(unit,A),A) = mult(rd(unit,A),rd(unit,A)),
inference(paramod,[status(thm)],[c_20,c_96]) ).
cnf(c_122,plain,
mult(rd(unit,A),rd(unit,A)) = rd(rd(unit,A),A),
inference(copy,[status(thm)],[c_440]) ).
cnf(c_140,plain,
ld(mult(A,A),unit) = ld(A,ld(A,unit)),
inference(paramod,[status(thm)],[c_103,c_11]) ).
cnf(c_141,plain,
rd(unit,ld(A,ld(A,unit))) = mult(A,A),
inference(paramod,[status(thm)],[c_103,c_13]) ).
cnf(c_441,plain,
rd(unit,ld(rd(unit,A),A)) = mult(rd(unit,A),rd(unit,A)),
inference(paramod,[status(thm)],[c_20,c_141]) ).
cnf(c_156,plain,
rd(unit,ld(rd(unit,A),A)) = rd(rd(unit,A),A),
inference(paramod,[status(thm)],[c_122,c_441]) ).
cnf(c_208,plain,
ld(mult(A,mult(B,B)),mult(mult(A,B),mult(B,B))) = B,
inference(paramod,[status(thm)],[c_40,c_11]) ).
cnf(c_219,plain,
ld(mult(rd(A,B),mult(B,B)),mult(A,mult(B,B))) = B,
inference(paramod,[status(thm)],[c_12,c_208]) ).
cnf(c_239,plain,
ld(mult(rd(unit,A),mult(A,A)),mult(A,A)) = A,
inference(paramod,[status(thm)],[c_15,c_219]) ).
cnf(c_442,plain,
rd(mult(A,A),A) = mult(rd(unit,A),mult(A,A)),
inference(paramod,[status(thm)],[c_239,c_21]) ).
cnf(c_443,plain,
A = mult(rd(unit,A),mult(A,A)),
inference(paramod,[status(thm)],[c_13,c_442]) ).
cnf(c_248,plain,
mult(rd(unit,A),mult(A,A)) = A,
inference(copy,[status(thm)],[c_443]) ).
cnf(c_252,plain,
ld(rd(unit,A),A) = mult(A,A),
inference(paramod,[status(thm)],[c_248,c_11]) ).
cnf(c_253,plain,
rd(A,mult(A,A)) = rd(unit,A),
inference(paramod,[status(thm)],[c_248,c_13]) ).
cnf(c_444,plain,
rd(unit,mult(A,A)) = rd(rd(unit,A),A),
inference(paramod,[status(thm)],[c_252,c_156]) ).
cnf(c_275,plain,
rd(rd(unit,A),A) = rd(unit,mult(A,A)),
inference(copy,[status(thm)],[c_444]) ).
cnf(c_300,plain,
mult(rd(unit,A),rd(unit,A)) = rd(unit,mult(A,A)),
inference(paramod,[status(thm)],[c_275,c_122]) ).
cnf(c_445,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_252,c_46]) ).
cnf(c_446,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_300,c_445]) ).
cnf(c_447,plain,
mult(rd(unit,A),unit) = mult(mult(rd(unit,A),rd(unit,A)),A),
inference(paramod,[status(thm)],[c_12,c_446]) ).
cnf(c_448,plain,
rd(unit,A) = mult(mult(rd(unit,A),rd(unit,A)),A),
inference(paramod,[status(thm)],[c_14,c_447]) ).
cnf(c_449,plain,
rd(unit,A) = mult(rd(unit,mult(A,A)),A),
inference(paramod,[status(thm)],[c_300,c_448]) ).
cnf(c_308,plain,
mult(rd(unit,mult(A,A)),A) = rd(unit,A),
inference(copy,[status(thm)],[c_449]) ).
cnf(c_450,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_89,c_31]) ).
cnf(c_451,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_10,c_450]) ).
cnf(c_452,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_15,c_451]) ).
cnf(c_453,plain,
unit = mult(mult(ld(A,unit),mult(A,A)),ld(A,unit)),
inference(paramod,[status(thm)],[c_25,c_452]) ).
cnf(c_361,plain,
mult(mult(ld(A,unit),mult(A,A)),ld(A,unit)) = unit,
inference(copy,[status(thm)],[c_453]) ).
cnf(c_454,plain,
rd(mult(A,mult(mult(rd(unit,A),A),B)),mult(A,B)) = mult(mult(A,rd(unit,mult(A,A))),A),
inference(paramod,[status(thm)],[c_308,c_31]) ).
cnf(c_455,plain,
rd(mult(A,mult(unit,B)),mult(A,B)) = mult(mult(A,rd(unit,mult(A,A))),A),
inference(paramod,[status(thm)],[c_12,c_454]) ).
cnf(c_456,plain,
rd(mult(A,B),mult(A,B)) = mult(mult(A,rd(unit,mult(A,A))),A),
inference(paramod,[status(thm)],[c_15,c_455]) ).
cnf(c_457,plain,
unit = mult(mult(A,rd(unit,mult(A,A))),A),
inference(paramod,[status(thm)],[c_25,c_456]) ).
cnf(c_368,plain,
mult(mult(A,rd(unit,mult(A,A))),A) = unit,
inference(copy,[status(thm)],[c_457]) ).
cnf(c_458,plain,
rd(unit,ld(A,unit)) = mult(ld(A,unit),mult(A,A)),
inference(paramod,[status(thm)],[c_361,c_13]) ).
cnf(c_459,plain,
A = mult(ld(A,unit),mult(A,A)),
inference(paramod,[status(thm)],[c_21,c_458]) ).
cnf(c_391,plain,
mult(ld(A,unit),mult(A,A)) = A,
inference(copy,[status(thm)],[c_459]) ).
cnf(c_460,plain,
rd(A,mult(A,A)) = ld(A,unit),
inference(paramod,[status(thm)],[c_391,c_13]) ).
cnf(c_407,plain,
rd(unit,A) = ld(A,unit),
inference(paramod,[status(thm)],[c_253,c_460]) ).
cnf(c_461,plain,
mult(mult(A,ld(mult(A,A),unit)),A) = unit,
inference(paramod,[status(thm)],[c_407,c_368]) ).
cnf(c_462,plain,
mult(mult(A,ld(A,ld(A,unit))),A) = unit,
inference(paramod,[status(thm)],[c_140,c_461]) ).
cnf(c_431,plain,
mult(ld(A,unit),A) = unit,
inference(paramod,[status(thm)],[c_10,c_462]) ).
cnf(c_432,plain,
$false,
inference(resolve,[status(thm)],[c_431,c_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP700+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.39 % Computer : n019.cluster.edu
% 0.06/0.39 % Model : x86_64 x86_64
% 0.06/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.39 % Memory : 8046.5625MB
% 0.06/0.39 % OS : Linux 6.8.0-71-generic
% 0.06/0.39 % CPULimit : 300
% 0.06/0.39 % WCLimit : 300
% 0.06/0.39 % DateTime : Fri Sep 25 15:38:20 UTC 2026
% 0.06/0.39 % CPUTime :
% 0.06/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/0.40 % Process 3138353 was started by sandbox on n019,
% 0.06/0.40 % Fri Sep 25 15:38:20 2026
% 0.06/0.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.06/0.40
% 0.06/0.40 % From the command line: assign(max_seconds, 300).
% 0.25/0.60
% 0.25/0.60 % SZS status Theorem for theBenchmark
% 0.25/0.60
% 0.25/0.60 % Proof 1 at 0.06 (+ 0.01) seconds.
% 0.25/0.60 % Length of proof is 50.
% 0.25/0.60 % Level of proof is 14.
% 0.25/0.60 % Maximum clause weight is 57.000.
% 0.25/0.60 % Given clauses 63.
% 0.25/0.60
% 0.25/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------