%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP201-1 : 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 : n018.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 11.18s 7.02s
% Output : CNFRefutation 11.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 10
% Syntax : Number of formulae : 103 ( 103 unt; 0 def)
% Number of atoms : 103 ( 102 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 205 ( 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(moufang2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(multiply(VAR_0,VAR_1),VAR_2),VAR_1) = multiply(VAR_0,multiply(VAR_1,multiply(VAR_2,VAR_1))),
file('theBenchmark.p',moufang2) ).
cnf(c_9,plain,
multiply(multiply(multiply(A,B),C),B) = multiply(A,multiply(B,multiply(C,B))),
inference(clausify,[status(thm)],[moufang2]) ).
fof(prove_moufang3,axiom,
multiply(multiply(multiply(a,b),a),c) != multiply(a,multiply(b,multiply(a,c))),
file('theBenchmark.p',prove_moufang3) ).
cnf(c_10,plain,
multiply(multiply(multiply(a,b),a),c) != multiply(a,multiply(b,multiply(a,c))),
inference(clausify,[status(thm)],[prove_moufang3]) ).
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_2319,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_2319]) ).
cnf(c_22,plain,
right_division(identity,A) = left_inverse(A),
inference(paramod,[status(thm)],[c_8,c_6]) ).
cnf(c_2320,plain,
multiply(multiply(A,B),A) = multiply(identity,multiply(A,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_1,c_2320]) ).
cnf(c_2321,plain,
multiply(multiply(A,B),C) = multiply(right_division(A,C),multiply(C,multiply(B,C))),
inference(paramod,[status(thm)],[c_5,c_9]) ).
cnf(c_29,plain,
multiply(right_division(A,B),multiply(B,multiply(C,B))) = multiply(multiply(A,C),B),
inference(copy,[status(thm)],[c_2321]) ).
cnf(c_2322,plain,
multiply(multiply(identity,A),B) = multiply(left_inverse(B),multiply(B,multiply(A,B))),
inference(paramod,[status(thm)],[c_8,c_9]) ).
cnf(c_2323,plain,
multiply(A,B) = multiply(left_inverse(B),multiply(B,multiply(A,B))),
inference(paramod,[status(thm)],[c_1,c_2322]) ).
cnf(c_33,plain,
multiply(left_inverse(A),multiply(A,multiply(B,A))) = multiply(B,A),
inference(copy,[status(thm)],[c_2323]) ).
cnf(c_34,plain,
multiply(multiply(multiply(A,multiply(B,multiply(C,B))),D),B) = multiply(multiply(multiply(A,B),C),multiply(B,multiply(D,B))),
inference(paramod,[status(thm)],[c_9,c_9]) ).
cnf(c_36,plain,
multiply(multiply(a,multiply(b,a)),c) != multiply(a,multiply(b,multiply(a,c))),
inference(paramod,[status(thm)],[c_24,c_10]) ).
cnf(c_2324,plain,
multiply(identity,A) = multiply(A,multiply(right_inverse(A),A)),
inference(paramod,[status(thm)],[c_7,c_24]) ).
cnf(c_2325,plain,
A = multiply(A,multiply(right_inverse(A),A)),
inference(paramod,[status(thm)],[c_1,c_2324]) ).
cnf(c_41,plain,
multiply(A,multiply(right_inverse(A),A)) = A,
inference(copy,[status(thm)],[c_2325]) ).
cnf(c_2326,plain,
left_division(A,A) = multiply(right_inverse(A),A),
inference(paramod,[status(thm)],[c_41,c_4]) ).
cnf(c_2327,plain,
identity = multiply(right_inverse(A),A),
inference(paramod,[status(thm)],[c_12,c_2326]) ).
cnf(c_46,plain,
multiply(right_inverse(A),A) = identity,
inference(copy,[status(thm)],[c_2327]) ).
cnf(c_2328,plain,
left_division(right_inverse(A),identity) = A,
inference(paramod,[status(thm)],[c_46,c_4]) ).
cnf(c_47,plain,
right_inverse(right_inverse(A)) = A,
inference(paramod,[status(thm)],[c_18,c_2328]) ).
cnf(c_2329,plain,
right_division(identity,A) = right_inverse(A),
inference(paramod,[status(thm)],[c_46,c_6]) ).
cnf(c_2330,plain,
left_inverse(A) = right_inverse(A),
inference(paramod,[status(thm)],[c_22,c_2329]) ).
cnf(c_48,plain,
right_inverse(A) = left_inverse(A),
inference(copy,[status(thm)],[c_2330]) ).
cnf(c_49,plain,
multiply(A,left_inverse(A)) = identity,
inference(paramod,[status(thm)],[c_21,c_46]) ).
cnf(c_2331,plain,
right_inverse(left_inverse(A)) = A,
inference(paramod,[status(thm)],[c_48,c_47]) ).
cnf(c_50,plain,
left_inverse(left_inverse(A)) = A,
inference(paramod,[status(thm)],[c_48,c_2331]) ).
cnf(c_137,plain,
left_division(right_division(A,B),multiply(multiply(A,C),B)) = multiply(B,multiply(C,B)),
inference(paramod,[status(thm)],[c_29,c_4]) ).
cnf(c_138,plain,
multiply(right_division(A,B),multiply(B,C)) = multiply(multiply(A,right_division(C,B)),B),
inference(paramod,[status(thm)],[c_5,c_29]) ).
cnf(c_2332,plain,
multiply(right_division(A,B),multiply(B,identity)) = multiply(multiply(A,left_inverse(B)),B),
inference(paramod,[status(thm)],[c_8,c_29]) ).
cnf(c_2333,plain,
multiply(right_division(A,B),B) = multiply(multiply(A,left_inverse(B)),B),
inference(paramod,[status(thm)],[c_2,c_2332]) ).
cnf(c_2334,plain,
A = multiply(multiply(A,left_inverse(B)),B),
inference(paramod,[status(thm)],[c_5,c_2333]) ).
cnf(c_141,plain,
multiply(multiply(A,left_inverse(B)),B) = A,
inference(copy,[status(thm)],[c_2334]) ).
cnf(c_152,plain,
multiply(right_division(multiply(A,B),C),multiply(C,multiply(A,C))) = multiply(multiply(A,multiply(B,A)),C),
inference(paramod,[status(thm)],[c_24,c_29]) ).
cnf(c_2335,plain,
multiply(right_division(A,left_inverse(B)),multiply(left_inverse(B),identity)) = multiply(multiply(A,B),left_inverse(B)),
inference(paramod,[status(thm)],[c_49,c_29]) ).
cnf(c_2336,plain,
multiply(right_division(A,left_inverse(B)),left_inverse(B)) = multiply(multiply(A,B),left_inverse(B)),
inference(paramod,[status(thm)],[c_2,c_2335]) ).
cnf(c_2337,plain,
A = multiply(multiply(A,B),left_inverse(B)),
inference(paramod,[status(thm)],[c_5,c_2336]) ).
cnf(c_154,plain,
multiply(multiply(A,B),left_inverse(B)) = A,
inference(copy,[status(thm)],[c_2337]) ).
cnf(c_225,plain,
left_division(multiply(A,B),A) = left_inverse(B),
inference(paramod,[status(thm)],[c_154,c_4]) ).
cnf(c_2338,plain,
multiply(A,left_inverse(B)) = right_division(A,B),
inference(paramod,[status(thm)],[c_5,c_154]) ).
cnf(c_226,plain,
right_division(A,B) = multiply(A,left_inverse(B)),
inference(copy,[status(thm)],[c_2338]) ).
cnf(c_227,plain,
multiply(multiply(A,B),left_inverse(C)) = multiply(multiply(A,C),multiply(left_inverse(C),multiply(B,left_inverse(C)))),
inference(paramod,[status(thm)],[c_154,c_9]) ).
cnf(c_230,plain,
multiply(multiply(A,multiply(B,A)),left_inverse(A)) = multiply(A,B),
inference(paramod,[status(thm)],[c_24,c_154]) ).
cnf(c_289,plain,
multiply(multiply(multiply(A,B),left_inverse(C)),multiply(C,multiply(A,C))) = multiply(multiply(A,multiply(B,A)),C),
inference(paramod,[status(thm)],[c_226,c_152]) ).
cnf(c_2339,plain,
multiply(multiply(A,left_inverse(B)),multiply(B,C)) = multiply(multiply(A,right_division(C,B)),B),
inference(paramod,[status(thm)],[c_226,c_138]) ).
cnf(c_2340,plain,
multiply(multiply(A,left_inverse(B)),multiply(B,C)) = multiply(multiply(A,multiply(C,left_inverse(B))),B),
inference(paramod,[status(thm)],[c_226,c_2339]) ).
cnf(c_300,plain,
multiply(multiply(A,multiply(B,left_inverse(C))),C) = multiply(multiply(A,left_inverse(C)),multiply(C,B)),
inference(copy,[status(thm)],[c_2340]) ).
cnf(c_301,plain,
left_division(multiply(A,left_inverse(B)),multiply(multiply(A,C),B)) = multiply(B,multiply(C,B)),
inference(paramod,[status(thm)],[c_226,c_137]) ).
cnf(c_2341,plain,
multiply(multiply(A,B),left_inverse(B)) = multiply(left_inverse(B),multiply(multiply(B,multiply(A,B)),left_inverse(B))),
inference(paramod,[status(thm)],[c_33,c_24]) ).
cnf(c_2342,plain,
A = multiply(left_inverse(B),multiply(multiply(B,multiply(A,B)),left_inverse(B))),
inference(paramod,[status(thm)],[c_154,c_2341]) ).
cnf(c_2343,plain,
A = multiply(left_inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_230,c_2342]) ).
cnf(c_330,plain,
multiply(left_inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_2343]) ).
cnf(c_2344,plain,
multiply(left_inverse(left_inverse(A)),multiply(left_inverse(A),B)) = multiply(multiply(B,A),left_inverse(A)),
inference(paramod,[status(thm)],[c_154,c_33]) ).
cnf(c_2345,plain,
multiply(A,multiply(left_inverse(A),B)) = multiply(multiply(B,A),left_inverse(A)),
inference(paramod,[status(thm)],[c_50,c_2344]) ).
cnf(c_336,plain,
multiply(A,multiply(left_inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_154,c_2345]) ).
cnf(c_2346,plain,
multiply(multiply(A,multiply(multiply(B,multiply(C,B)),A)),B) = multiply(multiply(multiply(A,B),C),multiply(B,multiply(A,B))),
inference(paramod,[status(thm)],[c_24,c_34]) ).
cnf(c_340,plain,
multiply(multiply(multiply(A,B),C),multiply(B,multiply(A,B))) = multiply(multiply(A,multiply(multiply(B,multiply(C,B)),A)),B),
inference(copy,[status(thm)],[c_2346]) ).
cnf(c_2347,plain,
multiply(left_inverse(A),B) = left_division(A,B),
inference(paramod,[status(thm)],[c_3,c_330]) ).
cnf(c_387,plain,
left_division(A,B) = multiply(left_inverse(A),B),
inference(copy,[status(thm)],[c_2347]) ).
cnf(c_2348,plain,
left_division(A,left_inverse(B)) = left_inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_330,c_225]) ).
cnf(c_2349,plain,
multiply(left_inverse(A),left_inverse(B)) = left_inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_387,c_2348]) ).
cnf(c_402,plain,
left_inverse(multiply(A,B)) = multiply(left_inverse(B),left_inverse(A)),
inference(copy,[status(thm)],[c_2349]) ).
cnf(c_2350,plain,
multiply(left_inverse(multiply(A,left_inverse(B))),multiply(multiply(A,C),B)) = multiply(B,multiply(C,B)),
inference(paramod,[status(thm)],[c_387,c_301]) ).
cnf(c_2351,plain,
multiply(multiply(left_inverse(left_inverse(B)),left_inverse(A)),multiply(multiply(A,C),B)) = multiply(B,multiply(C,B)),
inference(paramod,[status(thm)],[c_402,c_2350]) ).
cnf(c_431,plain,
multiply(multiply(A,left_inverse(B)),multiply(multiply(B,C),A)) = multiply(A,multiply(C,A)),
inference(paramod,[status(thm)],[c_50,c_2351]) ).
cnf(c_2352,plain,
multiply(multiply(left_inverse(A),B),left_inverse(left_inverse(A))) = multiply(left_inverse(A),multiply(B,A)),
inference(paramod,[status(thm)],[c_154,c_230]) ).
cnf(c_568,plain,
multiply(multiply(left_inverse(A),B),A) = multiply(left_inverse(A),multiply(B,A)),
inference(paramod,[status(thm)],[c_50,c_2352]) ).
cnf(c_2353,plain,
multiply(multiply(A,left_inverse(left_inverse(B))),multiply(C,A)) = multiply(A,multiply(multiply(B,C),A)),
inference(paramod,[status(thm)],[c_330,c_431]) ).
cnf(c_1841,plain,
multiply(multiply(A,B),multiply(C,A)) = multiply(A,multiply(multiply(B,C),A)),
inference(paramod,[status(thm)],[c_50,c_2353]) ).
cnf(c_1941,plain,
multiply(multiply(A,multiply(multiply(B,C),A)),B) = multiply(A,multiply(B,multiply(multiply(C,A),B))),
inference(paramod,[status(thm)],[c_1841,c_9]) ).
cnf(c_2354,plain,
multiply(multiply(multiply(left_inverse(A),B),multiply(C,left_inverse(A))),A) = multiply(left_inverse(A),multiply(multiply(multiply(B,C),left_inverse(A)),A)),
inference(paramod,[status(thm)],[c_1841,c_568]) ).
cnf(c_2355,plain,
multiply(multiply(multiply(left_inverse(A),B),left_inverse(A)),multiply(A,C)) = multiply(left_inverse(A),multiply(multiply(multiply(B,C),left_inverse(A)),A)),
inference(paramod,[status(thm)],[c_300,c_2354]) ).
cnf(c_2356,plain,
multiply(multiply(left_inverse(A),multiply(B,left_inverse(A))),multiply(A,C)) = multiply(left_inverse(A),multiply(multiply(multiply(B,C),left_inverse(A)),A)),
inference(paramod,[status(thm)],[c_24,c_2355]) ).
cnf(c_2012,plain,
multiply(multiply(left_inverse(A),multiply(B,left_inverse(A))),multiply(A,C)) = multiply(left_inverse(A),multiply(B,C)),
inference(paramod,[status(thm)],[c_141,c_2356]) ).
cnf(c_2357,plain,
multiply(multiply(multiply(A,B),C),multiply(B,multiply(A,B))) = multiply(A,multiply(B,multiply(multiply(multiply(C,B),A),B))),
inference(paramod,[status(thm)],[c_1941,c_340]) ).
cnf(c_2129,plain,
multiply(multiply(multiply(A,B),C),multiply(B,multiply(A,B))) = multiply(A,multiply(B,multiply(C,multiply(B,multiply(A,B))))),
inference(paramod,[status(thm)],[c_9,c_2357]) ).
cnf(c_2358,plain,
multiply(multiply(multiply(A,B),multiply(left_inverse(B),multiply(C,left_inverse(B)))),multiply(B,multiply(A,B))) = multiply(multiply(A,multiply(C,A)),B),
inference(paramod,[status(thm)],[c_227,c_289]) ).
cnf(c_2359,plain,
multiply(A,multiply(B,multiply(multiply(left_inverse(B),multiply(C,left_inverse(B))),multiply(B,multiply(A,B))))) = multiply(multiply(A,multiply(C,A)),B),
inference(paramod,[status(thm)],[c_2129,c_2358]) ).
cnf(c_2360,plain,
multiply(A,multiply(B,multiply(left_inverse(B),multiply(C,multiply(A,B))))) = multiply(multiply(A,multiply(C,A)),B),
inference(paramod,[status(thm)],[c_2012,c_2359]) ).
cnf(c_2361,plain,
multiply(A,multiply(C,multiply(A,B))) = multiply(multiply(A,multiply(C,A)),B),
inference(paramod,[status(thm)],[c_336,c_2360]) ).
cnf(c_2317,plain,
multiply(multiply(A,multiply(B,A)),C) = multiply(A,multiply(B,multiply(A,C))),
inference(copy,[status(thm)],[c_2361]) ).
cnf(c_2318,plain,
$false,
inference(resolve,[status(thm)],[c_2317,c_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP201-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.39 % Computer : n018.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Fri Sep 25 14:39:55 UTC 2026
% 0.11/5.40 % CPUTime :
% 0.11/5.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.40 % Process 2190185 was started by sandbox on n018,
% 0.11/5.40 % Fri Sep 25 14:39:55 2026
% 0.11/5.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/5.41
% 0.15/5.41 % From the command line: assign(max_seconds, 300).
% 11.18/7.02
% 11.18/7.02 % SZS status Unsatisfiable for theBenchmark
% 11.18/7.02
% 11.18/7.02 % Proof 1 at 1.26 (+ 0.33) seconds.
% 11.18/7.02 % Length of proof is 50.
% 11.18/7.02 % Level of proof is 15.
% 11.18/7.02 % Maximum clause weight is 93.000.
% 11.18/7.02 % Given clauses 132.
% 11.18/7.02
% 11.18/7.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------