%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP660+1 : 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 : n003.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 0.14s 0.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 6
% Syntax : Number of formulae : 98 ( 93 unt; 0 def)
% Number of atoms : 103 ( 102 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 3 |; 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 : 4 ( 4 usr; 0 con; 1-2 aty)
% Number of variables : 186 ( 0 sgn 15 !; 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,
! [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(X0,X1) = X1
& mult(X1,X0) = X1 ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ? [X0] :
! [X1] :
( mult(X0,X1) = X1
& mult(X1,X0) = X1 ),
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(X0,X1) != X1
| mult(X1,X0) != X1 ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
! [X0] :
( mult(X0,sK0(X0)) != sK0(X0)
| mult(sK0(X0),X0) != sK0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[nnf_6]) ).
cnf(c_12,negated_conjecture,
( mult(A,sK0(A)) != sK0(A)
| mult(sK0(A),A) != sK0(A) ),
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_693,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_693]) ).
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_694,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_694]) ).
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_695,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_695]) ).
cnf(c_696,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_696]) ).
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_697,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_697]) ).
cnf(c_84,plain,
rd(ld(A,B),B) = ld(mult(B,A),B),
inference(paramod,[status(thm)],[c_77,c_10]) ).
cnf(c_698,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_698]) ).
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_699,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_699]) ).
cnf(c_700,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_700]) ).
cnf(c_701,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_702,plain,
rd(A,A) = ld(rd(A,A),rd(A,A)),
inference(paramod,[status(thm)],[c_8,c_701]) ).
cnf(c_287,plain,
ld(rd(A,A),rd(A,A)) = rd(A,A),
inference(copy,[status(thm)],[c_702]) ).
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_703,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_703]) ).
cnf(c_704,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_705,plain,
rd(ld(A,A),A) = ld(A,rd(A,A)),
inference(paramod,[status(thm)],[c_9,c_704]) ).
cnf(c_312,plain,
ld(mult(A,A),A) = ld(A,rd(A,A)),
inference(paramod,[status(thm)],[c_84,c_705]) ).
cnf(c_706,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_707,plain,
ld(A,A) = mult(ld(A,rd(A,A)),A),
inference(paramod,[status(thm)],[c_8,c_706]) ).
cnf(c_322,plain,
mult(ld(A,rd(A,A)),A) = ld(A,A),
inference(copy,[status(thm)],[c_707]) ).
cnf(c_708,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_708]) ).
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_709,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_709]) ).
cnf(c_710,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_710]) ).
cnf(c_711,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_712,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_711]) ).
cnf(c_713,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_712]) ).
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_713]) ).
cnf(c_714,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_715,plain,
mult(B,ld(A,A)) = ld(ld(A,A),rd(B,ld(A,A))),
inference(paramod,[status(thm)],[c_10,c_714]) ).
cnf(c_390,plain,
ld(ld(A,A),rd(B,ld(A,A))) = mult(B,ld(A,A)),
inference(copy,[status(thm)],[c_715]) ).
cnf(c_716,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_717,plain,
B = rd(ld(ld(A,A),B),ld(A,A)),
inference(paramod,[status(thm)],[c_9,c_716]) ).
cnf(c_391,plain,
rd(ld(ld(A,A),B),ld(A,A)) = B,
inference(copy,[status(thm)],[c_717]) ).
cnf(c_718,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_719,plain,
ld(mult(rd(A,A),A),mult(rd(A,A),A)) = rd(A,A),
inference(paramod,[status(thm)],[c_299,c_718]) ).
cnf(c_720,plain,
ld(A,mult(rd(A,A),A)) = rd(A,A),
inference(paramod,[status(thm)],[c_9,c_719]) ).
cnf(c_721,plain,
ld(A,A) = rd(A,A),
inference(paramod,[status(thm)],[c_9,c_720]) ).
cnf(c_393,plain,
rd(A,A) = ld(A,A),
inference(copy,[status(thm)],[c_721]) ).
cnf(c_516,plain,
rd(A,ld(B,B)) = mult(ld(B,B),A),
inference(paramod,[status(thm)],[c_8,c_391]) ).
cnf(c_722,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_722]) ).
cnf(c_723,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_724,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_723]) ).
cnf(c_725,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_724]) ).
cnf(c_726,plain,
mult(A,ld(B,B)) = ld(ld(B,B),rd(A,ld(B,B))),
inference(paramod,[status(thm)],[c_337,c_725]) ).
cnf(c_727,plain,
mult(A,ld(B,B)) = ld(ld(B,B),mult(ld(B,B),A)),
inference(paramod,[status(thm)],[c_516,c_726]) ).
cnf(c_527,plain,
mult(A,ld(B,B)) = A,
inference(paramod,[status(thm)],[c_8,c_727]) ).
cnf(c_728,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_729,plain,
rd(mult(B,ld(A,A)),ld(ld(A,A),ld(A,A))) = B,
inference(paramod,[status(thm)],[c_517,c_728]) ).
cnf(c_730,plain,
rd(B,ld(ld(A,A),ld(A,A))) = B,
inference(paramod,[status(thm)],[c_527,c_729]) ).
cnf(c_731,plain,
rd(B,mult(ld(A,A),ld(A,A))) = B,
inference(paramod,[status(thm)],[c_517,c_730]) ).
cnf(c_732,plain,
rd(B,ld(A,A)) = B,
inference(paramod,[status(thm)],[c_527,c_731]) ).
cnf(c_528,plain,
mult(ld(A,A),B) = B,
inference(paramod,[status(thm)],[c_516,c_732]) ).
cnf(c_733,negated_conjecture,
mult(ld(A,A),sK0(ld(A,A))) != sK0(ld(A,A)),
inference(resolve,[status(thm)],[c_12,c_527]) ).
cnf(c_734,negated_conjecture,
sK0(ld(A,A)) != sK0(ld(A,A)),
inference(paramod,[status(thm)],[c_528,c_733]) ).
cnf(c_692,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_734]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP660+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 15:33:52 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 542330 was started by sandbox2 on n003,
% 0.09/0.36 % Fri Sep 25 15:33:52 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.14/0.46
% 0.14/0.46 % Assigning unary symbol f1 kb_weight 0 and highest precedence (5).
% 0.14/0.46
% 0.14/0.46 % SZS status Theorem for theBenchmark
% 0.14/0.46
% 0.14/0.46 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.14/0.46 % Length of proof is 53.
% 0.14/0.46 % Level of proof is 24.
% 0.14/0.46 % Maximum clause weight is 54.000.
% 0.14/0.46 % Given clauses 53.
% 0.14/0.46
% 0.14/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------