%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP202-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 4.26s 1.00s
% Output : CNFRefutation 4.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 71 ( 71 unt; 0 def)
% Number of atoms : 71 ( 70 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 : 7 ( 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 : 119 ( 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(moufang3,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(multiply(VAR_0,VAR_1),VAR_0),VAR_2) = multiply(VAR_0,multiply(VAR_1,multiply(VAR_0,VAR_2))),
file('theBenchmark.p',moufang3) ).
cnf(c_9,plain,
multiply(multiply(multiply(A,B),A),C) = multiply(A,multiply(B,multiply(A,C))),
inference(clausify,[status(thm)],[moufang3]) ).
fof(prove_moufang1,axiom,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
file('theBenchmark.p',prove_moufang1) ).
cnf(c_10,plain,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
inference(clausify,[status(thm)],[prove_moufang1]) ).
cnf(c_12,plain,
left_division(A,A) = identity,
inference(paramod,[status(thm)],[c_2,c_4]) ).
cnf(c_18,plain,
left_division(A,identity) = right_inverse(A),
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_1312,plain,
left_division(left_inverse(A),identity) = A,
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_21,plain,
right_inverse(left_inverse(A)) = A,
inference(paramod,[status(thm)],[c_18,c_1312]) ).
cnf(c_22,plain,
right_division(identity,A) = left_inverse(A),
inference(paramod,[status(thm)],[c_8,c_6]) ).
cnf(c_1313,plain,
multiply(A,multiply(B,multiply(A,identity))) = multiply(multiply(A,B),A),
inference(paramod,[status(thm)],[c_9,c_2]) ).
cnf(c_1314,plain,
multiply(A,multiply(B,A)) = multiply(multiply(A,B),A),
inference(paramod,[status(thm)],[c_2,c_1313]) ).
cnf(c_25,plain,
multiply(multiply(A,B),A) = multiply(A,multiply(B,A)),
inference(copy,[status(thm)],[c_1314]) ).
cnf(c_1315,plain,
multiply(A,multiply(B,multiply(A,left_division(multiply(multiply(A,B),A),C)))) = C,
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_26,plain,
multiply(A,multiply(B,multiply(A,left_division(multiply(A,multiply(B,A)),C)))) = C,
inference(paramod,[status(thm)],[c_25,c_1315]) ).
cnf(c_1316,plain,
multiply(multiply(A,B),C) = multiply(B,multiply(left_division(B,A),multiply(B,C))),
inference(paramod,[status(thm)],[c_3,c_9]) ).
cnf(c_27,plain,
multiply(A,multiply(left_division(A,B),multiply(A,C))) = multiply(multiply(B,A),C),
inference(copy,[status(thm)],[c_1316]) ).
cnf(c_1317,plain,
right_division(multiply(A,multiply(B,multiply(A,C))),C) = multiply(multiply(A,B),A),
inference(paramod,[status(thm)],[c_9,c_6]) ).
cnf(c_33,plain,
right_division(multiply(A,multiply(B,multiply(A,C))),C) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_25,c_1317]) ).
cnf(c_42,plain,
multiply(a,multiply(multiply(b,c),a)) != multiply(multiply(a,b),multiply(c,a)),
inference(paramod,[status(thm)],[c_25,c_10]) ).
cnf(c_1318,plain,
multiply(identity,A) = multiply(A,multiply(right_inverse(A),A)),
inference(paramod,[status(thm)],[c_7,c_25]) ).
cnf(c_1319,plain,
A = multiply(A,multiply(right_inverse(A),A)),
inference(paramod,[status(thm)],[c_1,c_1318]) ).
cnf(c_54,plain,
multiply(A,multiply(right_inverse(A),A)) = A,
inference(copy,[status(thm)],[c_1319]) ).
cnf(c_1320,plain,
left_division(A,A) = multiply(right_inverse(A),A),
inference(paramod,[status(thm)],[c_54,c_4]) ).
cnf(c_1321,plain,
identity = multiply(right_inverse(A),A),
inference(paramod,[status(thm)],[c_12,c_1320]) ).
cnf(c_58,plain,
multiply(right_inverse(A),A) = identity,
inference(copy,[status(thm)],[c_1321]) ).
cnf(c_1322,plain,
left_division(right_inverse(A),identity) = A,
inference(paramod,[status(thm)],[c_58,c_4]) ).
cnf(c_59,plain,
right_inverse(right_inverse(A)) = A,
inference(paramod,[status(thm)],[c_18,c_1322]) ).
cnf(c_1323,plain,
right_division(identity,A) = right_inverse(A),
inference(paramod,[status(thm)],[c_58,c_6]) ).
cnf(c_1324,plain,
left_inverse(A) = right_inverse(A),
inference(paramod,[status(thm)],[c_22,c_1323]) ).
cnf(c_60,plain,
right_inverse(A) = left_inverse(A),
inference(copy,[status(thm)],[c_1324]) ).
cnf(c_61,plain,
multiply(A,left_inverse(A)) = identity,
inference(paramod,[status(thm)],[c_21,c_58]) ).
cnf(c_1325,plain,
right_inverse(left_inverse(A)) = A,
inference(paramod,[status(thm)],[c_60,c_59]) ).
cnf(c_62,plain,
left_inverse(left_inverse(A)) = A,
inference(paramod,[status(thm)],[c_60,c_1325]) ).
cnf(c_1326,plain,
multiply(A,multiply(left_inverse(A),multiply(A,left_division(multiply(A,identity),B)))) = B,
inference(paramod,[status(thm)],[c_8,c_26]) ).
cnf(c_1327,plain,
multiply(A,multiply(left_inverse(A),multiply(A,left_division(A,B)))) = B,
inference(paramod,[status(thm)],[c_2,c_1326]) ).
cnf(c_70,plain,
multiply(A,multiply(left_inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_3,c_1327]) ).
cnf(c_1328,plain,
multiply(A,multiply(left_division(A,B),identity)) = multiply(multiply(B,A),left_inverse(A)),
inference(paramod,[status(thm)],[c_61,c_27]) ).
cnf(c_1329,plain,
multiply(A,left_division(A,B)) = multiply(multiply(B,A),left_inverse(A)),
inference(paramod,[status(thm)],[c_2,c_1328]) ).
cnf(c_1330,plain,
B = multiply(multiply(B,A),left_inverse(A)),
inference(paramod,[status(thm)],[c_3,c_1329]) ).
cnf(c_93,plain,
multiply(multiply(A,B),left_inverse(B)) = A,
inference(copy,[status(thm)],[c_1330]) ).
cnf(c_95,plain,
left_division(multiply(A,B),A) = left_inverse(B),
inference(paramod,[status(thm)],[c_93,c_4]) ).
cnf(c_1331,plain,
multiply(A,left_inverse(B)) = right_division(A,B),
inference(paramod,[status(thm)],[c_5,c_93]) ).
cnf(c_96,plain,
right_division(A,B) = multiply(A,left_inverse(B)),
inference(copy,[status(thm)],[c_1331]) ).
cnf(c_106,plain,
multiply(multiply(A,multiply(B,multiply(A,C))),left_inverse(C)) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_96,c_33]) ).
cnf(c_168,plain,
left_division(A,B) = multiply(left_inverse(A),B),
inference(paramod,[status(thm)],[c_70,c_4]) ).
cnf(c_200,plain,
multiply(left_inverse(multiply(A,B)),A) = left_inverse(B),
inference(paramod,[status(thm)],[c_168,c_95]) ).
cnf(c_1332,plain,
multiply(left_inverse(A),left_inverse(B)) = left_inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_200,c_93]) ).
cnf(c_234,plain,
left_inverse(multiply(A,B)) = multiply(left_inverse(B),left_inverse(A)),
inference(copy,[status(thm)],[c_1332]) ).
cnf(c_1333,plain,
multiply(multiply(A,multiply(B,C)),left_inverse(multiply(left_inverse(A),C))) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_70,c_106]) ).
cnf(c_1334,plain,
multiply(multiply(A,multiply(B,C)),multiply(left_inverse(C),left_inverse(left_inverse(A)))) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_234,c_1333]) ).
cnf(c_432,plain,
multiply(multiply(A,multiply(B,C)),multiply(left_inverse(C),A)) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_62,c_1334]) ).
cnf(c_1335,plain,
multiply(multiply(A,B),multiply(left_inverse(left_inverse(C)),A)) = multiply(A,multiply(multiply(B,C),A)),
inference(paramod,[status(thm)],[c_93,c_432]) ).
cnf(c_1310,plain,
multiply(multiply(A,B),multiply(C,A)) = multiply(A,multiply(multiply(B,C),A)),
inference(paramod,[status(thm)],[c_62,c_1335]) ).
cnf(c_1336,plain,
multiply(multiply(a,b),multiply(c,a)) != multiply(a,multiply(multiply(b,c),a)),
inference(copy,[status(thm)],[c_42]) ).
cnf(c_1311,plain,
$false,
inference(resolve,[status(thm)],[c_1310,c_1336]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP202-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n016.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:42:30 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 2629214 was started by sandbox on n016,
% 0.09/0.36 % Fri Sep 25 14:42:30 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 4.26/1.00
% 4.26/1.00 % SZS status Unsatisfiable for theBenchmark
% 4.26/1.00
% 4.26/1.00 % Proof 1 at 0.49 (+ 0.14) seconds.
% 4.26/1.00 % Length of proof is 36.
% 4.26/1.00 % Level of proof is 11.
% 4.26/1.00 % Maximum clause weight is 65.000.
% 4.26/1.00 % Given clauses 109.
% 4.26/1.00
% 4.26/1.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------