%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP200-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 07:28:21 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.67s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 81 ( 81 unt; 0 def)
% Number of atoms : 81 ( 80 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 156 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(right_identity,axiom,
! [VAR_0] : multiply(VAR_0,identity) = VAR_0,
file('theBenchmark.p',right_identity) ).
cnf(c_2,plain,
multiply(A,identity) = A,
inference(clausify,[status(thm)],[right_identity]) ).
fof(multiply_left_division,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,left_division(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',multiply_left_division) ).
cnf(c_3,plain,
multiply(A,left_division(A,B)) = B,
inference(clausify,[status(thm)],[multiply_left_division]) ).
fof(left_division_multiply,axiom,
! [VAR_0,VAR_1] : left_division(VAR_0,multiply(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',left_division_multiply) ).
cnf(c_4,plain,
left_division(A,multiply(A,B)) = B,
inference(clausify,[status(thm)],[left_division_multiply]) ).
fof(multiply_right_division,axiom,
! [VAR_0,VAR_1] : multiply(right_division(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',multiply_right_division) ).
cnf(c_5,plain,
multiply(right_division(A,B),B) = A,
inference(clausify,[status(thm)],[multiply_right_division]) ).
fof(right_division_multiply,axiom,
! [VAR_0,VAR_1] : right_division(multiply(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',right_division_multiply) ).
cnf(c_6,plain,
right_division(multiply(A,B),B) = A,
inference(clausify,[status(thm)],[right_division_multiply]) ).
fof(right_inverse,axiom,
! [VAR_0] : multiply(VAR_0,right_inverse(VAR_0)) = identity,
file('theBenchmark.p',right_inverse) ).
cnf(c_7,plain,
multiply(A,right_inverse(A)) = identity,
inference(clausify,[status(thm)],[right_inverse]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(left_inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_8,plain,
multiply(left_inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(moufang1,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,multiply(VAR_1,VAR_2)),VAR_0) = multiply(multiply(VAR_0,VAR_1),multiply(VAR_2,VAR_0)),
file('theBenchmark.p',moufang1) ).
cnf(c_9,plain,
multiply(multiply(A,multiply(B,C)),A) = multiply(multiply(A,B),multiply(C,A)),
inference(clausify,[status(thm)],[moufang1]) ).
fof(prove_moufang2,axiom,
multiply(multiply(multiply(a,b),c),b) != multiply(a,multiply(b,multiply(c,b))),
file('theBenchmark.p',prove_moufang2) ).
cnf(c_10,plain,
multiply(multiply(multiply(a,b),c),b) != multiply(a,multiply(b,multiply(c,b))),
inference(clausify,[status(thm)],[prove_moufang2]) ).
cnf(c_12,plain,
left_division(A,A) = identity,
inference(paramod,[status(thm)],[c_2,c_4]) ).
cnf(c_14,plain,
left_division(right_division(A,B),A) = B,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_18,plain,
left_division(A,identity) = right_inverse(A),
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_22,plain,
right_division(identity,A) = left_inverse(A),
inference(paramod,[status(thm)],[c_8,c_6]) ).
cnf(c_664,plain,
multiply(multiply(A,B),A) = multiply(multiply(A,identity),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_9]) ).
cnf(c_24,plain,
multiply(multiply(A,B),A) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_664]) ).
cnf(c_665,plain,
multiply(multiply(A,multiply(left_division(A,B),C)),A) = multiply(B,multiply(C,A)),
inference(paramod,[status(thm)],[c_3,c_9]) ).
cnf(c_26,plain,
multiply(A,multiply(multiply(left_division(A,B),C),A)) = multiply(B,multiply(C,A)),
inference(paramod,[status(thm)],[c_24,c_665]) ).
cnf(c_666,plain,
multiply(multiply(left_division(A,B),multiply(C,A)),left_division(A,B)) = multiply(multiply(left_division(A,B),C),B),
inference(paramod,[status(thm)],[c_3,c_9]) ).
cnf(c_27,plain,
multiply(left_division(A,B),multiply(multiply(C,A),left_division(A,B))) = multiply(multiply(left_division(A,B),C),B),
inference(paramod,[status(thm)],[c_24,c_666]) ).
cnf(c_667,plain,
multiply(multiply(A,multiply(B,left_inverse(A))),A) = multiply(multiply(A,B),identity),
inference(paramod,[status(thm)],[c_8,c_9]) ).
cnf(c_668,plain,
multiply(A,multiply(multiply(B,left_inverse(A)),A)) = multiply(multiply(A,B),identity),
inference(paramod,[status(thm)],[c_24,c_667]) ).
cnf(c_40,plain,
multiply(A,multiply(multiply(B,left_inverse(A)),A)) = multiply(A,B),
inference(paramod,[status(thm)],[c_2,c_668]) ).
cnf(c_669,plain,
multiply(A,multiply(multiply(B,C),A)) = multiply(multiply(A,B),multiply(C,A)),
inference(paramod,[status(thm)],[c_24,c_9]) ).
cnf(c_43,plain,
multiply(multiply(A,B),multiply(C,A)) = multiply(A,multiply(multiply(B,C),A)),
inference(copy,[status(thm)],[c_669]) ).
cnf(c_670,plain,
multiply(A,B) = multiply(B,multiply(left_division(B,A),B)),
inference(paramod,[status(thm)],[c_3,c_24]) ).
cnf(c_49,plain,
multiply(A,multiply(left_division(A,B),A)) = multiply(B,A),
inference(copy,[status(thm)],[c_670]) ).
cnf(c_671,plain,
multiply(identity,A) = multiply(A,multiply(right_inverse(A),A)),
inference(paramod,[status(thm)],[c_7,c_24]) ).
cnf(c_672,plain,
A = multiply(A,multiply(right_inverse(A),A)),
inference(paramod,[status(thm)],[c_1,c_671]) ).
cnf(c_53,plain,
multiply(A,multiply(right_inverse(A),A)) = A,
inference(copy,[status(thm)],[c_672]) ).
cnf(c_673,plain,
left_division(A,A) = multiply(right_inverse(A),A),
inference(paramod,[status(thm)],[c_53,c_4]) ).
cnf(c_674,plain,
identity = multiply(right_inverse(A),A),
inference(paramod,[status(thm)],[c_12,c_673]) ).
cnf(c_56,plain,
multiply(right_inverse(A),A) = identity,
inference(copy,[status(thm)],[c_674]) ).
cnf(c_675,plain,
multiply(A,multiply(B,A)) = multiply(C,multiply(left_division(left_division(A,C),B),A)),
inference(paramod,[status(thm)],[c_3,c_26]) ).
cnf(c_57,plain,
multiply(A,multiply(left_division(left_division(B,A),C),B)) = multiply(B,multiply(C,B)),
inference(copy,[status(thm)],[c_675]) ).
cnf(c_676,plain,
right_division(identity,A) = right_inverse(A),
inference(paramod,[status(thm)],[c_56,c_6]) ).
cnf(c_677,plain,
left_inverse(A) = right_inverse(A),
inference(paramod,[status(thm)],[c_22,c_676]) ).
cnf(c_64,plain,
right_inverse(A) = left_inverse(A),
inference(copy,[status(thm)],[c_677]) ).
cnf(c_70,plain,
left_division(A,identity) = left_inverse(A),
inference(paramod,[status(thm)],[c_64,c_18]) ).
cnf(c_71,plain,
left_division(A,multiply(B,A)) = multiply(left_division(A,B),A),
inference(paramod,[status(thm)],[c_49,c_4]) ).
cnf(c_678,plain,
left_division(A,B) = multiply(left_division(A,right_division(B,A)),A),
inference(paramod,[status(thm)],[c_5,c_71]) ).
cnf(c_89,plain,
multiply(left_division(A,right_division(B,A)),A) = left_division(A,B),
inference(copy,[status(thm)],[c_678]) ).
cnf(c_679,plain,
left_division(A,multiply(A,B)) = multiply(multiply(B,left_inverse(A)),A),
inference(paramod,[status(thm)],[c_40,c_4]) ).
cnf(c_680,plain,
B = multiply(multiply(B,left_inverse(A)),A),
inference(paramod,[status(thm)],[c_4,c_679]) ).
cnf(c_191,plain,
multiply(multiply(A,left_inverse(B)),B) = A,
inference(copy,[status(thm)],[c_680]) ).
cnf(c_681,plain,
multiply(A,B) = right_division(A,left_inverse(B)),
inference(paramod,[status(thm)],[c_5,c_191]) ).
cnf(c_383,plain,
right_division(A,left_inverse(B)) = multiply(A,B),
inference(copy,[status(thm)],[c_681]) ).
cnf(c_682,plain,
right_division(A,B) = multiply(A,left_inverse(B)),
inference(paramod,[status(thm)],[c_191,c_6]) ).
cnf(c_384,plain,
multiply(A,left_inverse(B)) = right_division(A,B),
inference(copy,[status(thm)],[c_682]) ).
cnf(c_683,plain,
multiply(left_division(left_inverse(A),B),A) = left_division(left_inverse(A),right_division(B,left_inverse(A))),
inference(paramod,[status(thm)],[c_89,c_191]) ).
cnf(c_684,plain,
multiply(left_division(left_inverse(A),B),A) = left_division(left_inverse(A),multiply(B,A)),
inference(paramod,[status(thm)],[c_383,c_683]) ).
cnf(c_386,plain,
left_division(left_inverse(A),multiply(B,A)) = multiply(left_division(left_inverse(A),B),A),
inference(copy,[status(thm)],[c_684]) ).
cnf(c_417,plain,
left_division(multiply(A,B),A) = left_inverse(B),
inference(paramod,[status(thm)],[c_383,c_14]) ).
cnf(c_433,plain,
multiply(left_division(left_inverse(A),B),multiply(right_division(C,A),left_division(left_inverse(A),B))) = multiply(multiply(left_division(left_inverse(A),B),C),B),
inference(paramod,[status(thm)],[c_384,c_27]) ).
cnf(c_685,plain,
multiply(A,multiply(B,A)) = multiply(left_division(left_division(A,identity),B),A),
inference(paramod,[status(thm)],[c_57,c_1]) ).
cnf(c_686,plain,
multiply(A,multiply(B,A)) = multiply(left_division(left_inverse(A),B),A),
inference(paramod,[status(thm)],[c_70,c_685]) ).
cnf(c_561,plain,
multiply(left_division(left_inverse(A),B),A) = multiply(A,multiply(B,A)),
inference(copy,[status(thm)],[c_686]) ).
cnf(c_579,plain,
multiply(A,multiply(left_division(left_inverse(B),C),multiply(A,B))) = multiply(multiply(A,B),multiply(C,multiply(A,B))),
inference(paramod,[status(thm)],[c_417,c_57]) ).
cnf(c_586,plain,
left_division(left_inverse(A),multiply(B,A)) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_561,c_386]) ).
cnf(c_687,plain,
left_division(left_inverse(A),B) = multiply(A,multiply(right_division(B,A),A)),
inference(paramod,[status(thm)],[c_5,c_586]) ).
cnf(c_631,plain,
left_division(left_inverse(A),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_5,c_687]) ).
cnf(c_688,plain,
multiply(A,multiply(multiply(B,C),multiply(A,B))) = multiply(multiply(A,B),multiply(C,multiply(A,B))),
inference(paramod,[status(thm)],[c_631,c_579]) ).
cnf(c_689,plain,
multiply(A,multiply(B,multiply(multiply(C,A),B))) = multiply(multiply(A,B),multiply(C,multiply(A,B))),
inference(paramod,[status(thm)],[c_43,c_688]) ).
cnf(c_659,plain,
multiply(multiply(A,B),multiply(C,multiply(A,B))) = multiply(A,multiply(B,multiply(multiply(C,A),B))),
inference(copy,[status(thm)],[c_689]) ).
cnf(c_690,plain,
multiply(multiply(A,B),multiply(right_division(C,A),left_division(left_inverse(A),B))) = multiply(multiply(left_division(left_inverse(A),B),C),B),
inference(paramod,[status(thm)],[c_631,c_433]) ).
cnf(c_691,plain,
multiply(multiply(A,B),multiply(right_division(C,A),multiply(A,B))) = multiply(multiply(left_division(left_inverse(A),B),C),B),
inference(paramod,[status(thm)],[c_631,c_690]) ).
cnf(c_692,plain,
multiply(A,multiply(B,multiply(multiply(right_division(C,A),A),B))) = multiply(multiply(left_division(left_inverse(A),B),C),B),
inference(paramod,[status(thm)],[c_659,c_691]) ).
cnf(c_693,plain,
multiply(A,multiply(B,multiply(C,B))) = multiply(multiply(left_division(left_inverse(A),B),C),B),
inference(paramod,[status(thm)],[c_5,c_692]) ).
cnf(c_694,plain,
multiply(A,multiply(B,multiply(C,B))) = multiply(multiply(multiply(A,B),C),B),
inference(paramod,[status(thm)],[c_631,c_693]) ).
cnf(c_662,plain,
multiply(multiply(multiply(A,B),C),B) = multiply(A,multiply(B,multiply(C,B))),
inference(copy,[status(thm)],[c_694]) ).
cnf(c_663,plain,
$false,
inference(resolve,[status(thm)],[c_662,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP200-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n020.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Fri Sep 25 14:38:05 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 3144993 was started by sandbox2 on n020,
% 0.18/0.45 % Fri Sep 25 14:38:05 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 0.23/0.67
% 0.23/0.67 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.67
% 0.23/0.67 % Proof 1 at 0.14 (+ 0.07) seconds.
% 0.23/0.67 % Length of proof is 40.
% 0.23/0.67 % Level of proof is 11.
% 0.23/0.67 % Maximum clause weight is 74.000.
% 0.23/0.67 % Given clauses 84.
% 0.23/0.67
% 0.23/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------