%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP660-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 07:31:05 AM UTC 2026
% Result : Unsatisfiable 0.89s 0.67s
% Output : CNFRefutation 0.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 6
% Syntax : Number of formulae : 95 ( 95 unt; 0 def)
% Number of atoms : 95 ( 94 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 0 con; 1-2 aty)
% Number of variables : 180 ( 0 sgn 12 !; 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,VAR_1,VAR_2] : mult(mult(mult(VAR_0,VAR_1),VAR_2),VAR_0) = mult(VAR_0,mult(VAR_1,mult(VAR_2,VAR_0))),
file('theBenchmark.p',f05) ).
cnf(c_5,plain,
mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))),
inference(clausify,[status(thm)],[f05]) ).
fof(goal,axiom,
! [VAR_0] : tuple(mult(VAR_0,x1(VAR_0)),mult(x1_2(VAR_0),VAR_0)) != tuple(x1(VAR_0),x1_2(VAR_0)),
file('theBenchmark.p',goal) ).
cnf(c_6,plain,
tuple(mult(A,x1(A)),mult(x1_2(A),A)) != tuple(x1(A),x1_2(A)),
inference(clausify,[status(thm)],[goal]) ).
cnf(c_7,plain,
ld(rd(A,B),A) = B,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_8,plain,
rd(A,ld(B,A)) = B,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_687,plain,
mult(mult(A,B),C) = mult(C,mult(ld(C,A),mult(B,C))),
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_9,plain,
mult(A,mult(ld(A,B),mult(C,A))) = mult(mult(B,C),A),
inference(copy,[status(thm)],[c_687]) ).
cnf(c_11,plain,
ld(mult(mult(A,B),C),mult(A,mult(B,mult(C,A)))) = A,
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_688,plain,
mult(mult(A,B),rd(A,C)) = mult(rd(A,C),mult(C,mult(B,rd(A,C)))),
inference(paramod,[status(thm)],[c_3,c_5]) ).
cnf(c_12,plain,
mult(rd(A,B),mult(B,mult(C,rd(A,B)))) = mult(mult(A,C),rd(A,B)),
inference(copy,[status(thm)],[c_688]) ).
cnf(c_17,plain,
ld(A,mult(mult(B,C),A)) = mult(ld(A,B),mult(C,A)),
inference(paramod,[status(thm)],[c_9,c_2]) ).
cnf(c_689,plain,
ld(A,mult(B,A)) = mult(ld(A,C),mult(ld(C,B),A)),
inference(paramod,[status(thm)],[c_1,c_17]) ).
cnf(c_24,plain,
mult(ld(A,B),mult(ld(B,C),A)) = ld(A,mult(C,A)),
inference(copy,[status(thm)],[c_689]) ).
cnf(c_690,plain,
ld(A,mult(B,A)) = mult(ld(A,rd(B,C)),mult(C,A)),
inference(paramod,[status(thm)],[c_3,c_17]) ).
cnf(c_27,plain,
mult(ld(A,rd(B,C)),mult(C,A)) = ld(A,mult(B,A)),
inference(copy,[status(thm)],[c_690]) ).
cnf(c_34,plain,
rd(ld(A,mult(B,A)),mult(ld(C,B),A)) = ld(A,C),
inference(paramod,[status(thm)],[c_24,c_4]) ).
cnf(c_43,plain,
rd(A,mult(ld(B,A),A)) = ld(A,B),
inference(paramod,[status(thm)],[c_2,c_34]) ).
cnf(c_46,plain,
rd(ld(A,mult(B,A)),mult(C,A)) = ld(A,rd(B,C)),
inference(paramod,[status(thm)],[c_7,c_34]) ).
cnf(c_53,plain,
ld(ld(A,B),A) = mult(ld(B,A),A),
inference(paramod,[status(thm)],[c_43,c_7]) ).
cnf(c_691,plain,
ld(A,B) = mult(ld(mult(B,A),B),B),
inference(paramod,[status(thm)],[c_2,c_53]) ).
cnf(c_71,plain,
mult(ld(mult(A,B),A),A) = ld(B,A),
inference(copy,[status(thm)],[c_691]) ).
cnf(c_78,plain,
rd(ld(A,B),B) = ld(mult(B,A),B),
inference(paramod,[status(thm)],[c_71,c_4]) ).
cnf(c_692,plain,
rd(A,B) = ld(mult(B,rd(B,A)),B),
inference(paramod,[status(thm)],[c_7,c_78]) ).
cnf(c_88,plain,
ld(mult(A,rd(A,B)),A) = rd(B,A),
inference(copy,[status(thm)],[c_692]) ).
cnf(c_92,plain,
mult(mult(A,rd(A,B)),rd(B,A)) = A,
inference(paramod,[status(thm)],[c_88,c_1]) ).
cnf(c_122,plain,
rd(ld(A,B),mult(C,A)) = ld(A,rd(rd(B,A),C)),
inference(paramod,[status(thm)],[c_3,c_46]) ).
cnf(c_123,plain,
rd(ld(A,mult(B,A)),C) = ld(A,rd(B,rd(C,A))),
inference(paramod,[status(thm)],[c_3,c_46]) ).
cnf(c_693,plain,
ld(A,rd(B,B)) = ld(mult(mult(B,A),A),mult(B,A)),
inference(paramod,[status(thm)],[c_46,c_78]) ).
cnf(c_125,plain,
ld(mult(mult(A,B),B),mult(A,B)) = ld(B,rd(A,A)),
inference(copy,[status(thm)],[c_693]) ).
cnf(c_694,plain,
mult(ld(ld(A,B),rd(C,A)),B) = ld(ld(A,B),mult(C,ld(A,B))),
inference(paramod,[status(thm)],[c_1,c_27]) ).
cnf(c_164,plain,
ld(ld(A,B),mult(C,ld(A,B))) = mult(ld(ld(A,B),rd(C,A)),B),
inference(copy,[status(thm)],[c_694]) ).
cnf(c_695,plain,
ld(A,mult(A,rd(A,A))) = ld(rd(A,A),rd(A,A)),
inference(paramod,[status(thm)],[c_92,c_125]) ).
cnf(c_696,plain,
rd(A,A) = ld(rd(A,A),rd(A,A)),
inference(paramod,[status(thm)],[c_2,c_695]) ).
cnf(c_281,plain,
ld(rd(A,A),rd(A,A)) = rd(A,A),
inference(copy,[status(thm)],[c_696]) ).
cnf(c_293,plain,
mult(rd(A,A),rd(A,A)) = rd(A,A),
inference(paramod,[status(thm)],[c_281,c_1]) ).
cnf(c_294,plain,
rd(rd(A,A),rd(A,A)) = rd(A,A),
inference(paramod,[status(thm)],[c_281,c_8]) ).
cnf(c_697,plain,
mult(rd(A,A),mult(A,rd(A,A))) = mult(mult(A,rd(A,A)),rd(A,A)),
inference(paramod,[status(thm)],[c_293,c_12]) ).
cnf(c_302,plain,
mult(rd(A,A),mult(A,rd(A,A))) = A,
inference(paramod,[status(thm)],[c_92,c_697]) ).
cnf(c_698,plain,
rd(ld(A,A),mult(rd(A,A),A)) = ld(A,rd(A,A)),
inference(paramod,[status(thm)],[c_294,c_122]) ).
cnf(c_699,plain,
rd(ld(A,A),A) = ld(A,rd(A,A)),
inference(paramod,[status(thm)],[c_3,c_698]) ).
cnf(c_306,plain,
ld(mult(A,A),A) = ld(A,rd(A,A)),
inference(paramod,[status(thm)],[c_78,c_699]) ).
cnf(c_700,plain,
ld(ld(A,mult(A,A)),A) = mult(ld(A,rd(A,A)),A),
inference(paramod,[status(thm)],[c_306,c_53]) ).
cnf(c_701,plain,
ld(A,A) = mult(ld(A,rd(A,A)),A),
inference(paramod,[status(thm)],[c_2,c_700]) ).
cnf(c_316,plain,
mult(ld(A,rd(A,A)),A) = ld(A,A),
inference(copy,[status(thm)],[c_701]) ).
cnf(c_702,plain,
mult(ld(A,A),ld(A,A)) = ld(A,mult(rd(A,A),A)),
inference(paramod,[status(thm)],[c_316,c_24]) ).
cnf(c_331,plain,
mult(ld(A,A),ld(A,A)) = ld(A,A),
inference(paramod,[status(thm)],[c_3,c_702]) ).
cnf(c_372,plain,
ld(ld(A,A),ld(A,A)) = ld(A,A),
inference(paramod,[status(thm)],[c_331,c_2]) ).
cnf(c_373,plain,
rd(ld(A,A),ld(A,A)) = ld(A,A),
inference(paramod,[status(thm)],[c_331,c_4]) ).
cnf(c_375,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_331,c_9]) ).
cnf(c_703,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_331,c_122]) ).
cnf(c_380,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_703]) ).
cnf(c_704,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_373,c_123]) ).
cnf(c_382,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_164,c_704]) ).
cnf(c_705,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_372,c_24]) ).
cnf(c_706,plain,
mult(mult(B,ld(A,A)),ld(A,A)) = ld(ld(A,A),mult(B,ld(A,A))),
inference(paramod,[status(thm)],[c_375,c_705]) ).
cnf(c_707,plain,
mult(mult(B,ld(A,A)),ld(A,A)) = mult(ld(ld(A,A),rd(B,A)),A),
inference(paramod,[status(thm)],[c_164,c_706]) ).
cnf(c_383,plain,
mult(ld(ld(A,A),rd(B,A)),A) = mult(mult(B,ld(A,A)),ld(A,A)),
inference(copy,[status(thm)],[c_707]) ).
cnf(c_708,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_383,c_382]) ).
cnf(c_709,plain,
mult(B,ld(A,A)) = ld(ld(A,A),rd(B,ld(A,A))),
inference(paramod,[status(thm)],[c_4,c_708]) ).
cnf(c_384,plain,
ld(ld(A,A),rd(B,ld(A,A))) = mult(B,ld(A,A)),
inference(copy,[status(thm)],[c_709]) ).
cnf(c_710,plain,
mult(rd(B,ld(A,A)),ld(A,A)) = rd(ld(ld(A,A),B),ld(A,A)),
inference(paramod,[status(thm)],[c_384,c_380]) ).
cnf(c_711,plain,
B = rd(ld(ld(A,A),B),ld(A,A)),
inference(paramod,[status(thm)],[c_3,c_710]) ).
cnf(c_385,plain,
rd(ld(ld(A,A),B),ld(A,A)) = B,
inference(copy,[status(thm)],[c_711]) ).
cnf(c_712,plain,
ld(mult(mult(rd(A,A),rd(A,A)),A),mult(rd(A,A),A)) = rd(A,A),
inference(paramod,[status(thm)],[c_302,c_11]) ).
cnf(c_713,plain,
ld(mult(rd(A,A),A),mult(rd(A,A),A)) = rd(A,A),
inference(paramod,[status(thm)],[c_293,c_712]) ).
cnf(c_714,plain,
ld(A,mult(rd(A,A),A)) = rd(A,A),
inference(paramod,[status(thm)],[c_3,c_713]) ).
cnf(c_715,plain,
ld(A,A) = rd(A,A),
inference(paramod,[status(thm)],[c_3,c_714]) ).
cnf(c_387,plain,
rd(A,A) = ld(A,A),
inference(copy,[status(thm)],[c_715]) ).
cnf(c_510,plain,
rd(A,ld(B,B)) = mult(ld(B,B),A),
inference(paramod,[status(thm)],[c_2,c_385]) ).
cnf(c_716,plain,
mult(A,ld(B,B)) = ld(ld(B,B),A),
inference(paramod,[status(thm)],[c_385,c_3]) ).
cnf(c_511,plain,
ld(ld(A,A),B) = mult(B,ld(A,A)),
inference(copy,[status(thm)],[c_716]) ).
cnf(c_717,plain,
mult(A,ld(B,B)) = ld(ld(B,B),rd(A,rd(ld(B,B),ld(B,B)))),
inference(paramod,[status(thm)],[c_385,c_123]) ).
cnf(c_718,plain,
mult(A,ld(B,B)) = ld(ld(B,B),rd(A,ld(ld(B,B),ld(B,B)))),
inference(paramod,[status(thm)],[c_387,c_717]) ).
cnf(c_719,plain,
mult(A,ld(B,B)) = ld(ld(B,B),rd(A,mult(ld(B,B),ld(B,B)))),
inference(paramod,[status(thm)],[c_511,c_718]) ).
cnf(c_720,plain,
mult(A,ld(B,B)) = ld(ld(B,B),rd(A,ld(B,B))),
inference(paramod,[status(thm)],[c_331,c_719]) ).
cnf(c_721,plain,
mult(A,ld(B,B)) = ld(ld(B,B),mult(ld(B,B),A)),
inference(paramod,[status(thm)],[c_510,c_720]) ).
cnf(c_521,plain,
mult(A,ld(B,B)) = A,
inference(paramod,[status(thm)],[c_2,c_721]) ).
cnf(c_722,plain,
rd(ld(ld(A,A),B),ld(ld(A,A),ld(A,A))) = B,
inference(paramod,[status(thm)],[c_372,c_385]) ).
cnf(c_723,plain,
rd(mult(B,ld(A,A)),ld(ld(A,A),ld(A,A))) = B,
inference(paramod,[status(thm)],[c_511,c_722]) ).
cnf(c_724,plain,
rd(B,ld(ld(A,A),ld(A,A))) = B,
inference(paramod,[status(thm)],[c_521,c_723]) ).
cnf(c_725,plain,
rd(B,mult(ld(A,A),ld(A,A))) = B,
inference(paramod,[status(thm)],[c_511,c_724]) ).
cnf(c_726,plain,
rd(B,ld(A,A)) = B,
inference(paramod,[status(thm)],[c_521,c_725]) ).
cnf(c_522,plain,
mult(ld(A,A),B) = B,
inference(paramod,[status(thm)],[c_510,c_726]) ).
cnf(c_727,plain,
tuple(mult(ld(A,A),x1(ld(A,A))),x1_2(ld(A,A))) != tuple(x1(ld(A,A)),x1_2(ld(A,A))),
inference(paramod,[status(thm)],[c_521,c_6]) ).
cnf(c_728,plain,
tuple(x1(ld(A,A)),x1_2(ld(A,A))) != tuple(x1(ld(A,A)),x1_2(ld(A,A))),
inference(paramod,[status(thm)],[c_522,c_727]) ).
cnf(c_686,plain,
$false,
inference(copy,[status(thm)],[c_728]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP660-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n013.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 15:31:36 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 734596 was started by sandbox on n013,
% 0.17/0.43 % Fri Sep 25 15:31:36 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.43
% 0.17/0.43 % From the command line: assign(max_seconds, 300).
% 0.89/0.67
% 0.89/0.67 % SZS status Unsatisfiable for theBenchmark
% 0.89/0.67
% 0.89/0.67 % Proof 1 at 0.15 (+ 0.06) seconds.
% 0.89/0.67 % Length of proof is 47.
% 0.89/0.67 % Level of proof is 23.
% 0.89/0.67 % Maximum clause weight is 54.000.
% 0.89/0.67 % Given clauses 53.
% 0.89/0.67
% 0.89/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------