%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP660+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 07:31:06 AM UTC 2026
% Result : Theorem 1.90s 0.78s
% Output : CNFRefutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 6
% Syntax : Number of formulae : 99 ( 92 unt; 0 def)
% Number of atoms : 106 ( 105 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 12 ~; 5 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 5 ( 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 : 182 ( 0 sgn 15 !; 2 ?)
% 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,
! [C,B,A] : mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))),
file('theBenchmark.p',f05) ).
fof(goals,conjecture,
! [X0,X1] :
( mult(ld(X1,X1),X0) = X0
& mult(X0,ld(X1,X1)) = X0 ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( mult(ld(X1,X1),X0) = X0
& mult(X0,ld(X1,X1)) = X0 ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_7,plain,
mult(A,ld(A,B)) = B,
inference(clausify,[status(thm)],[f01]) ).
cnf(c_8,plain,
ld(A,mult(A,B)) = B,
inference(clausify,[status(thm)],[f02]) ).
cnf(c_9,plain,
mult(rd(A,B),B) = A,
inference(clausify,[status(thm)],[f03]) ).
cnf(c_10,plain,
rd(mult(A,B),B) = A,
inference(clausify,[status(thm)],[f04]) ).
cnf(c_11,plain,
mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))),
inference(clausify,[status(thm)],[f05]) ).
fof(nnf_6,plain,
? [X0,X1] :
( mult(ld(X1,X1),X0) != X0
| mult(X0,ld(X1,X1)) != X0 ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( mult(ld(sK1,sK1),sK0) != sK0
| mult(sK0,ld(sK1,sK1)) != sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[nnf_6]) ).
cnf(c_12,negated_conjecture,
( mult(ld(sK1,sK1),sK0) != sK0
| mult(sK0,ld(sK1,sK1)) != sK0 ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_13,plain,
ld(rd(A,B),A) = B,
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_14,plain,
rd(A,ld(B,A)) = B,
inference(paramod,[status(thm)],[c_7,c_10]) ).
cnf(c_551,plain,
mult(mult(A,B),C) = mult(C,mult(ld(C,A),mult(B,C))),
inference(paramod,[status(thm)],[c_7,c_11]) ).
cnf(c_15,plain,
mult(A,mult(ld(A,B),mult(C,A))) = mult(mult(B,C),A),
inference(copy,[status(thm)],[c_551]) ).
cnf(c_17,plain,
ld(mult(mult(A,B),C),mult(A,mult(B,mult(C,A)))) = A,
inference(paramod,[status(thm)],[c_11,c_8]) ).
cnf(c_552,plain,
mult(mult(A,B),rd(A,C)) = mult(rd(A,C),mult(C,mult(B,rd(A,C)))),
inference(paramod,[status(thm)],[c_9,c_11]) ).
cnf(c_18,plain,
mult(rd(A,B),mult(B,mult(C,rd(A,B)))) = mult(mult(A,C),rd(A,B)),
inference(copy,[status(thm)],[c_552]) ).
cnf(c_23,plain,
ld(A,mult(mult(B,C),A)) = mult(ld(A,B),mult(C,A)),
inference(paramod,[status(thm)],[c_15,c_8]) ).
cnf(c_553,plain,
ld(A,mult(B,A)) = mult(ld(A,C),mult(ld(C,B),A)),
inference(paramod,[status(thm)],[c_7,c_23]) ).
cnf(c_30,plain,
mult(ld(A,B),mult(ld(B,C),A)) = ld(A,mult(C,A)),
inference(copy,[status(thm)],[c_553]) ).
cnf(c_554,plain,
ld(A,mult(B,A)) = mult(ld(A,rd(B,C)),mult(C,A)),
inference(paramod,[status(thm)],[c_9,c_23]) ).
cnf(c_33,plain,
mult(ld(A,rd(B,C)),mult(C,A)) = ld(A,mult(B,A)),
inference(copy,[status(thm)],[c_554]) ).
cnf(c_40,plain,
rd(ld(A,mult(B,A)),mult(ld(C,B),A)) = ld(A,C),
inference(paramod,[status(thm)],[c_30,c_10]) ).
cnf(c_49,plain,
rd(A,mult(ld(B,A),A)) = ld(A,B),
inference(paramod,[status(thm)],[c_8,c_40]) ).
cnf(c_52,plain,
rd(ld(A,mult(B,A)),mult(C,A)) = ld(A,rd(B,C)),
inference(paramod,[status(thm)],[c_13,c_40]) ).
cnf(c_59,plain,
ld(ld(A,B),A) = mult(ld(B,A),A),
inference(paramod,[status(thm)],[c_49,c_13]) ).
cnf(c_555,plain,
ld(A,B) = mult(ld(mult(B,A),B),B),
inference(paramod,[status(thm)],[c_8,c_59]) ).
cnf(c_77,plain,
mult(ld(mult(A,B),A),A) = ld(B,A),
inference(copy,[status(thm)],[c_555]) ).
cnf(c_84,plain,
rd(ld(A,B),B) = ld(mult(B,A),B),
inference(paramod,[status(thm)],[c_77,c_10]) ).
cnf(c_556,plain,
rd(A,B) = ld(mult(B,rd(B,A)),B),
inference(paramod,[status(thm)],[c_13,c_84]) ).
cnf(c_94,plain,
ld(mult(A,rd(A,B)),A) = rd(B,A),
inference(copy,[status(thm)],[c_556]) ).
cnf(c_98,plain,
mult(mult(A,rd(A,B)),rd(B,A)) = A,
inference(paramod,[status(thm)],[c_94,c_7]) ).
cnf(c_128,plain,
rd(ld(A,B),mult(C,A)) = ld(A,rd(rd(B,A),C)),
inference(paramod,[status(thm)],[c_9,c_52]) ).
cnf(c_129,plain,
rd(ld(A,mult(B,A)),C) = ld(A,rd(B,rd(C,A))),
inference(paramod,[status(thm)],[c_9,c_52]) ).
cnf(c_557,plain,
ld(A,rd(B,B)) = ld(mult(mult(B,A),A),mult(B,A)),
inference(paramod,[status(thm)],[c_52,c_84]) ).
cnf(c_131,plain,
ld(mult(mult(A,B),B),mult(A,B)) = ld(B,rd(A,A)),
inference(copy,[status(thm)],[c_557]) ).
cnf(c_558,plain,
mult(ld(ld(A,B),rd(C,A)),B) = ld(ld(A,B),mult(C,ld(A,B))),
inference(paramod,[status(thm)],[c_7,c_33]) ).
cnf(c_170,plain,
ld(ld(A,B),mult(C,ld(A,B))) = mult(ld(ld(A,B),rd(C,A)),B),
inference(copy,[status(thm)],[c_558]) ).
cnf(c_559,plain,
ld(A,mult(A,rd(A,A))) = ld(rd(A,A),rd(A,A)),
inference(paramod,[status(thm)],[c_98,c_131]) ).
cnf(c_560,plain,
rd(A,A) = ld(rd(A,A),rd(A,A)),
inference(paramod,[status(thm)],[c_8,c_559]) ).
cnf(c_287,plain,
ld(rd(A,A),rd(A,A)) = rd(A,A),
inference(copy,[status(thm)],[c_560]) ).
cnf(c_299,plain,
mult(rd(A,A),rd(A,A)) = rd(A,A),
inference(paramod,[status(thm)],[c_287,c_7]) ).
cnf(c_300,plain,
rd(rd(A,A),rd(A,A)) = rd(A,A),
inference(paramod,[status(thm)],[c_287,c_14]) ).
cnf(c_561,plain,
mult(rd(A,A),mult(A,rd(A,A))) = mult(mult(A,rd(A,A)),rd(A,A)),
inference(paramod,[status(thm)],[c_299,c_18]) ).
cnf(c_308,plain,
mult(rd(A,A),mult(A,rd(A,A))) = A,
inference(paramod,[status(thm)],[c_98,c_561]) ).
cnf(c_562,plain,
rd(ld(A,A),mult(rd(A,A),A)) = ld(A,rd(A,A)),
inference(paramod,[status(thm)],[c_300,c_128]) ).
cnf(c_563,plain,
rd(ld(A,A),A) = ld(A,rd(A,A)),
inference(paramod,[status(thm)],[c_9,c_562]) ).
cnf(c_312,plain,
ld(mult(A,A),A) = ld(A,rd(A,A)),
inference(paramod,[status(thm)],[c_84,c_563]) ).
cnf(c_564,plain,
ld(ld(A,mult(A,A)),A) = mult(ld(A,rd(A,A)),A),
inference(paramod,[status(thm)],[c_312,c_59]) ).
cnf(c_565,plain,
ld(A,A) = mult(ld(A,rd(A,A)),A),
inference(paramod,[status(thm)],[c_8,c_564]) ).
cnf(c_322,plain,
mult(ld(A,rd(A,A)),A) = ld(A,A),
inference(copy,[status(thm)],[c_565]) ).
cnf(c_566,plain,
mult(ld(A,A),ld(A,A)) = ld(A,mult(rd(A,A),A)),
inference(paramod,[status(thm)],[c_322,c_30]) ).
cnf(c_337,plain,
mult(ld(A,A),ld(A,A)) = ld(A,A),
inference(paramod,[status(thm)],[c_9,c_566]) ).
cnf(c_378,plain,
ld(ld(A,A),ld(A,A)) = ld(A,A),
inference(paramod,[status(thm)],[c_337,c_8]) ).
cnf(c_379,plain,
rd(ld(A,A),ld(A,A)) = ld(A,A),
inference(paramod,[status(thm)],[c_337,c_10]) ).
cnf(c_381,plain,
mult(ld(A,A),mult(ld(ld(A,A),B),ld(A,A))) = mult(mult(B,ld(A,A)),ld(A,A)),
inference(paramod,[status(thm)],[c_337,c_15]) ).
cnf(c_567,plain,
rd(ld(ld(A,A),B),ld(A,A)) = ld(ld(A,A),rd(rd(B,ld(A,A)),ld(A,A))),
inference(paramod,[status(thm)],[c_337,c_128]) ).
cnf(c_386,plain,
ld(ld(A,A),rd(rd(B,ld(A,A)),ld(A,A))) = rd(ld(ld(A,A),B),ld(A,A)),
inference(copy,[status(thm)],[c_567]) ).
cnf(c_568,plain,
rd(ld(ld(A,A),mult(B,ld(A,A))),ld(A,A)) = ld(ld(A,A),rd(B,ld(A,A))),
inference(paramod,[status(thm)],[c_379,c_129]) ).
cnf(c_388,plain,
rd(mult(ld(ld(A,A),rd(B,A)),A),ld(A,A)) = ld(ld(A,A),rd(B,ld(A,A))),
inference(paramod,[status(thm)],[c_170,c_568]) ).
cnf(c_569,plain,
mult(ld(A,A),mult(ld(ld(A,A),B),ld(A,A))) = ld(ld(A,A),mult(B,ld(A,A))),
inference(paramod,[status(thm)],[c_378,c_30]) ).
cnf(c_570,plain,
mult(mult(B,ld(A,A)),ld(A,A)) = ld(ld(A,A),mult(B,ld(A,A))),
inference(paramod,[status(thm)],[c_381,c_569]) ).
cnf(c_571,plain,
mult(mult(B,ld(A,A)),ld(A,A)) = mult(ld(ld(A,A),rd(B,A)),A),
inference(paramod,[status(thm)],[c_170,c_570]) ).
cnf(c_389,plain,
mult(ld(ld(A,A),rd(B,A)),A) = mult(mult(B,ld(A,A)),ld(A,A)),
inference(copy,[status(thm)],[c_571]) ).
cnf(c_572,plain,
rd(mult(mult(B,ld(A,A)),ld(A,A)),ld(A,A)) = ld(ld(A,A),rd(B,ld(A,A))),
inference(paramod,[status(thm)],[c_389,c_388]) ).
cnf(c_573,plain,
mult(B,ld(A,A)) = ld(ld(A,A),rd(B,ld(A,A))),
inference(paramod,[status(thm)],[c_10,c_572]) ).
cnf(c_390,plain,
ld(ld(A,A),rd(B,ld(A,A))) = mult(B,ld(A,A)),
inference(copy,[status(thm)],[c_573]) ).
cnf(c_574,plain,
mult(rd(B,ld(A,A)),ld(A,A)) = rd(ld(ld(A,A),B),ld(A,A)),
inference(paramod,[status(thm)],[c_390,c_386]) ).
cnf(c_575,plain,
B = rd(ld(ld(A,A),B),ld(A,A)),
inference(paramod,[status(thm)],[c_9,c_574]) ).
cnf(c_391,plain,
rd(ld(ld(A,A),B),ld(A,A)) = B,
inference(copy,[status(thm)],[c_575]) ).
cnf(c_576,plain,
ld(mult(mult(rd(A,A),rd(A,A)),A),mult(rd(A,A),A)) = rd(A,A),
inference(paramod,[status(thm)],[c_308,c_17]) ).
cnf(c_577,plain,
ld(mult(rd(A,A),A),mult(rd(A,A),A)) = rd(A,A),
inference(paramod,[status(thm)],[c_299,c_576]) ).
cnf(c_578,plain,
ld(A,mult(rd(A,A),A)) = rd(A,A),
inference(paramod,[status(thm)],[c_9,c_577]) ).
cnf(c_579,plain,
ld(A,A) = rd(A,A),
inference(paramod,[status(thm)],[c_9,c_578]) ).
cnf(c_393,plain,
rd(A,A) = ld(A,A),
inference(copy,[status(thm)],[c_579]) ).
cnf(c_516,plain,
rd(A,ld(B,B)) = mult(ld(B,B),A),
inference(paramod,[status(thm)],[c_8,c_391]) ).
cnf(c_580,plain,
mult(A,ld(B,B)) = ld(ld(B,B),A),
inference(paramod,[status(thm)],[c_391,c_9]) ).
cnf(c_517,plain,
ld(ld(A,A),B) = mult(B,ld(A,A)),
inference(copy,[status(thm)],[c_580]) ).
cnf(c_581,plain,
mult(A,ld(B,B)) = ld(ld(B,B),rd(A,rd(ld(B,B),ld(B,B)))),
inference(paramod,[status(thm)],[c_391,c_129]) ).
cnf(c_582,plain,
mult(A,ld(B,B)) = ld(ld(B,B),rd(A,ld(ld(B,B),ld(B,B)))),
inference(paramod,[status(thm)],[c_393,c_581]) ).
cnf(c_583,plain,
mult(A,ld(B,B)) = ld(ld(B,B),rd(A,mult(ld(B,B),ld(B,B)))),
inference(paramod,[status(thm)],[c_517,c_582]) ).
cnf(c_584,plain,
mult(A,ld(B,B)) = ld(ld(B,B),rd(A,ld(B,B))),
inference(paramod,[status(thm)],[c_337,c_583]) ).
cnf(c_585,plain,
mult(A,ld(B,B)) = ld(ld(B,B),mult(ld(B,B),A)),
inference(paramod,[status(thm)],[c_516,c_584]) ).
cnf(c_527,plain,
mult(A,ld(B,B)) = A,
inference(paramod,[status(thm)],[c_8,c_585]) ).
cnf(c_586,plain,
rd(ld(ld(A,A),B),ld(ld(A,A),ld(A,A))) = B,
inference(paramod,[status(thm)],[c_378,c_391]) ).
cnf(c_587,plain,
rd(mult(B,ld(A,A)),ld(ld(A,A),ld(A,A))) = B,
inference(paramod,[status(thm)],[c_517,c_586]) ).
cnf(c_588,plain,
rd(B,ld(ld(A,A),ld(A,A))) = B,
inference(paramod,[status(thm)],[c_527,c_587]) ).
cnf(c_589,plain,
rd(B,mult(ld(A,A),ld(A,A))) = B,
inference(paramod,[status(thm)],[c_517,c_588]) ).
cnf(c_590,plain,
rd(B,ld(A,A)) = B,
inference(paramod,[status(thm)],[c_527,c_589]) ).
cnf(c_528,plain,
mult(ld(A,A),B) = B,
inference(paramod,[status(thm)],[c_516,c_590]) ).
cnf(c_591,negated_conjecture,
( mult(ld(sK1,sK1),sK0) != sK0
| sK0 != sK0 ),
inference(paramod,[status(thm)],[c_527,c_12]) ).
cnf(c_592,negated_conjecture,
( sK0 != sK0
| sK0 != sK0 ),
inference(paramod,[status(thm)],[c_528,c_591]) ).
cnf(c_593,negated_conjecture,
sK0 != sK0,
inference(copy,[status(thm)],[c_592]) ).
cnf(c_550,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_593]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP660+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n006.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Fri Sep 25 15:32:11 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 3248793 was started by sandbox2 on n006,
% 0.18/0.44 % Fri Sep 25 15:32:11 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 1.90/0.78
% 1.90/0.78 % SZS status Theorem for theBenchmark
% 1.90/0.78
% 1.90/0.78 % Proof 1 at 0.13 (+ 0.05) seconds.
% 1.90/0.78 % Length of proof is 53.
% 1.90/0.78 % Level of proof is 24.
% 1.90/0.78 % Maximum clause weight is 54.000.
% 1.90/0.78 % Given clauses 51.
% 1.90/0.78
% 1.90/0.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------