%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP253-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 07:28:28 AM UTC 2026
% Result : Unsatisfiable 10.00s 1.91s
% Output : CNFRefutation 10.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 10
% Syntax : Number of formulae : 147 ( 25 unt; 0 def)
% Number of atoms : 428 ( 427 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 525 ( 244 ~; 281 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 9 !; 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(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(prove_this_1,axiom,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_4,axiom,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_9,axiom,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_12,axiom,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_19,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( inverse(sk_c5) != sk_c6
| inverse(VAR_3) != sk_c7
| multiply(VAR_3,sk_c7) != sk_c6
| multiply(VAR_2,sk_c5) != sk_c6
| inverse(VAR_2) != sk_c6
| inverse(VAR_1) != sk_c6
| multiply(VAR_1,sk_c6) != sk_c5
| inverse(VAR_0) != sk_c7
| multiply(VAR_0,sk_c7) != sk_c6 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( inverse(sk_c5) != sk_c6
| inverse(D) != sk_c7
| multiply(D,sk_c7) != sk_c6
| multiply(C,sk_c5) != sk_c6
| inverse(C) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
cnf(c_3616,plain,
( inverse(sk_c5) != sk_c6
| inverse(A) != sk_c7
| multiply(C,sk_c5) != sk_c6
| inverse(C) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_22]) ).
cnf(c_23,plain,
( inverse(sk_c5) != sk_c6
| multiply(C,sk_c5) != sk_c6
| inverse(C) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_3616]) ).
cnf(c_24,plain,
( inverse(sk_c5) != sk_c6
| multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_23]) ).
cnf(c_27,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_24]) ).
cnf(c_3617,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_3618,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_3617]) ).
cnf(c_28,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_3618]) ).
cnf(c_39,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c4,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_42,plain,
( multiply(sk_c7,sk_c1) = identity
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_53,plain,
( multiply(sk_c6,sk_c5) = identity
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_61,plain,
( multiply(sk_c6,sk_c2) = identity
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_82,plain,
( inverse(sk_c1) = sk_c7
| inverse(sk_c5) != sk_c6
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c4) != sk_c7 ),
inference(resolve,[status(thm)],[c_24,c_7]) ).
cnf(c_83,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c5) != sk_c6
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c1) != sk_c7 ),
inference(resolve,[status(thm)],[c_24,c_5]) ).
cnf(c_123,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c5
| inverse(inverse(sk_c7)) != sk_c7
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_27]) ).
cnf(c_130,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_28]) ).
cnf(c_168,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_28,c_28]) ).
cnf(c_169,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_168,c_130]) ).
cnf(c_226,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_169,c_2]) ).
cnf(c_3619,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_42,c_28]) ).
cnf(c_288,plain,
( inverse(sk_c7) = sk_c1
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_169,c_3619]) ).
cnf(c_291,plain,
( multiply(sk_c7,sk_c4) = identity
| inverse(sk_c7) = sk_c1 ),
inference(paramod,[status(thm)],[c_288,c_2]) ).
cnf(c_292,plain,
( multiply(sk_c1,sk_c7) = identity
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_288,c_2]) ).
cnf(c_3620,plain,
( multiply(inverse(sk_c6),identity) = sk_c2
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_61,c_28]) ).
cnf(c_514,plain,
( inverse(sk_c6) = sk_c2
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_169,c_3620]) ).
cnf(c_536,plain,
( multiply(sk_c6,sk_c5) = identity
| inverse(sk_c6) = sk_c2 ),
inference(paramod,[status(thm)],[c_514,c_2]) ).
cnf(c_3621,plain,
( multiply(inverse(sk_c7),identity) = sk_c4
| inverse(sk_c7) = sk_c1 ),
inference(paramod,[status(thm)],[c_291,c_28]) ).
cnf(c_781,plain,
( inverse(sk_c7) = sk_c4
| inverse(sk_c7) = sk_c1 ),
inference(paramod,[status(thm)],[c_169,c_3621]) ).
cnf(c_818,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c5
| inverse(sk_c1) != sk_c7
| identity != sk_c6
| inverse(sk_c7) = sk_c4 ),
inference(paramod,[status(thm)],[c_781,c_123]) ).
cnf(c_819,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c5
| inverse(sk_c4) != sk_c7
| identity != sk_c6
| inverse(sk_c7) = sk_c1 ),
inference(paramod,[status(thm)],[c_781,c_123]) ).
cnf(c_3622,plain,
( inverse(sk_c4) = sk_c7
| identity = sk_c6
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_292,c_5]) ).
cnf(c_824,plain,
( identity = sk_c6
| inverse(sk_c4) = sk_c7 ),
inference(copy,[status(thm)],[c_3622]) ).
cnf(c_839,plain,
( multiply(sk_c7,sk_c4) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_824,c_2]) ).
cnf(c_3623,plain,
( multiply(inverse(sk_c7),identity) = sk_c4
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_839,c_28]) ).
cnf(c_858,plain,
( inverse(sk_c7) = sk_c4
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_169,c_3623]) ).
cnf(c_876,plain,
( multiply(sk_c4,sk_c7) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_858,c_2]) ).
cnf(c_3624,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_876,c_4]) ).
cnf(c_1003,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_3624]) ).
cnf(c_3625,plain,
( multiply(sk_c7,sk_c1) = identity
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_876,c_39]) ).
cnf(c_1023,plain,
( multiply(sk_c7,sk_c1) = identity
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_3625]) ).
cnf(c_3626,plain,
( multiply(inverse(sk_c6),identity) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_53,c_28]) ).
cnf(c_1128,plain,
( inverse(sk_c6) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_169,c_3626]) ).
cnf(c_3627,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1023,c_28]) ).
cnf(c_1381,plain,
( inverse(sk_c7) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_169,c_3627]) ).
cnf(c_1419,plain,
( multiply(sk_c1,sk_c7) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1381,c_2]) ).
cnf(c_3628,plain,
( inverse(sk_c1) = sk_c7
| inverse(sk_c1) = sk_c7
| inverse(sk_c5) != sk_c6
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5 ),
inference(resolve,[status(thm)],[c_82,c_8]) ).
cnf(c_2316,plain,
( inverse(sk_c1) = sk_c7
| inverse(sk_c5) != sk_c6
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5 ),
inference(copy,[status(thm)],[c_3628]) ).
cnf(c_2346,plain,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c5 ),
inference(factor,[status(thm)],[c_2316]) ).
cnf(c_3629,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c4) = sk_c7
| inverse(sk_c5) != sk_c6
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5 ),
inference(resolve,[status(thm)],[c_83,c_8]) ).
cnf(c_2353,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c5) != sk_c6
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5 ),
inference(copy,[status(thm)],[c_3629]) ).
cnf(c_2379,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c5 ),
inference(factor,[status(thm)],[c_2353]) ).
cnf(c_3630,plain,
( identity = sk_c6
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1419,c_1003]) ).
cnf(c_3631,plain,
( identity = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_3630]) ).
cnf(c_2402,plain,
identity = sk_c6,
inference(copy,[status(thm)],[c_3631]) ).
cnf(c_3632,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c5
| inverse(sk_c4) != sk_c7
| sk_c6 != sk_c6
| inverse(sk_c7) = sk_c1 ),
inference(paramod,[status(thm)],[c_2402,c_819]) ).
cnf(c_2758,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c5
| inverse(sk_c4) != sk_c7
| inverse(sk_c7) = sk_c1 ),
inference(copy,[status(thm)],[c_3632]) ).
cnf(c_3633,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c5
| inverse(sk_c1) != sk_c7
| sk_c6 != sk_c6
| inverse(sk_c7) = sk_c4 ),
inference(paramod,[status(thm)],[c_2402,c_818]) ).
cnf(c_2759,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c5
| inverse(sk_c1) != sk_c7
| inverse(sk_c7) = sk_c4 ),
inference(copy,[status(thm)],[c_3633]) ).
cnf(c_2870,plain,
( multiply(sk_c6,sk_c5) = sk_c6
| inverse(sk_c6) = sk_c2 ),
inference(paramod,[status(thm)],[c_2402,c_536]) ).
cnf(c_3634,plain,
inverse(sk_c6) = identity,
inference(paramod,[status(thm)],[c_2402,c_226]) ).
cnf(c_3070,plain,
inverse(sk_c6) = sk_c6,
inference(paramod,[status(thm)],[c_2402,c_3634]) ).
cnf(c_3071,plain,
multiply(A,sk_c6) = A,
inference(paramod,[status(thm)],[c_2402,c_169]) ).
cnf(c_3635,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c5
| inverse(inverse(sk_c7)) != sk_c7
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_2402,c_123]) ).
cnf(c_3636,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| sk_c5 != sk_c5
| inverse(inverse(sk_c7)) != sk_c7
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_3071,c_3635]) ).
cnf(c_3637,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| sk_c5 != sk_c5
| inverse(inverse(sk_c7)) != sk_c7 ),
inference(copy,[status(thm)],[c_3636]) ).
cnf(c_3072,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| inverse(inverse(sk_c7)) != sk_c7 ),
inference(copy,[status(thm)],[c_3637]) ).
cnf(c_3079,plain,
multiply(sk_c6,A) = A,
inference(paramod,[status(thm)],[c_2402,c_1]) ).
cnf(c_3638,plain,
( multiply(sk_c6,sk_c5) = sk_c6
| sk_c6 = sk_c2 ),
inference(paramod,[status(thm)],[c_3070,c_2870]) ).
cnf(c_3639,plain,
( sk_c5 = sk_c6
| sk_c6 = sk_c2 ),
inference(paramod,[status(thm)],[c_3079,c_3638]) ).
cnf(c_3095,plain,
( sk_c5 = sk_c6
| sk_c2 = sk_c6 ),
inference(copy,[status(thm)],[c_3639]) ).
cnf(c_3640,plain,
( inverse(sk_c6) = sk_c5
| sk_c2 = sk_c5 ),
inference(paramod,[status(thm)],[c_3071,c_1128]) ).
cnf(c_3641,plain,
( sk_c6 = sk_c5
| sk_c2 = sk_c5 ),
inference(paramod,[status(thm)],[c_3070,c_3640]) ).
cnf(c_3117,plain,
( sk_c5 = sk_c6
| sk_c2 = sk_c5 ),
inference(copy,[status(thm)],[c_3641]) ).
cnf(c_3642,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| sk_c5 != sk_c5
| inverse(sk_c1) != sk_c7
| inverse(sk_c7) = sk_c4 ),
inference(paramod,[status(thm)],[c_3071,c_2759]) ).
cnf(c_3200,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| inverse(sk_c1) != sk_c7
| inverse(sk_c7) = sk_c4 ),
inference(copy,[status(thm)],[c_3642]) ).
cnf(c_3643,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| sk_c5 != sk_c5
| inverse(sk_c4) != sk_c7
| inverse(sk_c7) = sk_c1 ),
inference(paramod,[status(thm)],[c_3071,c_2758]) ).
cnf(c_3201,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| inverse(sk_c4) != sk_c7
| inverse(sk_c7) = sk_c1 ),
inference(copy,[status(thm)],[c_3643]) ).
cnf(c_3644,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_3071,c_2379]) ).
cnf(c_3239,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6 ),
inference(copy,[status(thm)],[c_3644]) ).
cnf(c_3645,plain,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_3071,c_2346]) ).
cnf(c_3245,plain,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6 ),
inference(copy,[status(thm)],[c_3645]) ).
cnf(c_3646,plain,
( sk_c5 = sk_c6
| sk_c5 = sk_c6
| sk_c5 = sk_c6 ),
inference(paramod,[status(thm)],[c_3117,c_3095]) ).
cnf(c_3647,plain,
( sk_c5 = sk_c6
| sk_c5 = sk_c6 ),
inference(copy,[status(thm)],[c_3646]) ).
cnf(c_3520,plain,
sk_c5 = sk_c6,
inference(copy,[status(thm)],[c_3647]) ).
cnf(c_3648,plain,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6 ),
inference(paramod,[status(thm)],[c_3520,c_3245]) ).
cnf(c_3649,plain,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c5) != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_3070,c_3648]) ).
cnf(c_3650,plain,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c5) != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_3520,c_3649]) ).
cnf(c_3651,plain,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c6) != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_3520,c_3650]) ).
cnf(c_3652,plain,
( inverse(sk_c1) = sk_c7
| sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_3071,c_3651]) ).
cnf(c_3653,plain,
( inverse(sk_c1) = sk_c7
| sk_c6 != sk_c6 ),
inference(copy,[status(thm)],[c_3652]) ).
cnf(c_3591,plain,
inverse(sk_c1) = sk_c7,
inference(copy,[status(thm)],[c_3653]) ).
cnf(c_3654,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6 ),
inference(paramod,[status(thm)],[c_3520,c_3239]) ).
cnf(c_3655,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c5,sk_c5) != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_3070,c_3654]) ).
cnf(c_3656,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c6,sk_c5) != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_3520,c_3655]) ).
cnf(c_3657,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c6,sk_c6) != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_3520,c_3656]) ).
cnf(c_3658,plain,
( inverse(sk_c4) = sk_c7
| sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_3071,c_3657]) ).
cnf(c_3659,plain,
( inverse(sk_c4) = sk_c7
| sk_c6 != sk_c6 ),
inference(copy,[status(thm)],[c_3658]) ).
cnf(c_3596,plain,
inverse(sk_c4) = sk_c7,
inference(copy,[status(thm)],[c_3659]) ).
cnf(c_3660,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| sk_c7 != sk_c7
| inverse(sk_c7) = sk_c1 ),
inference(paramod,[status(thm)],[c_3596,c_3201]) ).
cnf(c_3661,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6
| sk_c7 != sk_c7
| inverse(sk_c7) = sk_c1 ),
inference(paramod,[status(thm)],[c_3520,c_3660]) ).
cnf(c_3662,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| sk_c6 != sk_c6
| sk_c7 != sk_c7
| inverse(sk_c7) = sk_c1 ),
inference(paramod,[status(thm)],[c_3070,c_3661]) ).
cnf(c_3663,plain,
( multiply(sk_c6,sk_c5) != sk_c6
| sk_c6 != sk_c6
| sk_c7 != sk_c7
| inverse(sk_c7) = sk_c1 ),
inference(paramod,[status(thm)],[c_3520,c_3662]) ).
cnf(c_3664,plain,
( multiply(sk_c6,sk_c6) != sk_c6
| sk_c6 != sk_c6
| sk_c7 != sk_c7
| inverse(sk_c7) = sk_c1 ),
inference(paramod,[status(thm)],[c_3520,c_3663]) ).
cnf(c_3665,plain,
( sk_c6 != sk_c6
| sk_c6 != sk_c6
| sk_c7 != sk_c7
| inverse(sk_c7) = sk_c1 ),
inference(paramod,[status(thm)],[c_3071,c_3664]) ).
cnf(c_3666,plain,
( sk_c6 != sk_c6
| sk_c6 != sk_c6
| inverse(sk_c7) = sk_c1 ),
inference(copy,[status(thm)],[c_3665]) ).
cnf(c_3667,plain,
( sk_c6 != sk_c6
| inverse(sk_c7) = sk_c1 ),
inference(copy,[status(thm)],[c_3666]) ).
cnf(c_3605,plain,
inverse(sk_c7) = sk_c1,
inference(copy,[status(thm)],[c_3667]) ).
cnf(c_3668,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| inverse(sk_c1) != sk_c7
| sk_c1 = sk_c4 ),
inference(paramod,[status(thm)],[c_3605,c_3200]) ).
cnf(c_3669,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| sk_c7 != sk_c7
| sk_c1 = sk_c4 ),
inference(paramod,[status(thm)],[c_3591,c_3668]) ).
cnf(c_3670,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6
| sk_c7 != sk_c7
| sk_c1 = sk_c4 ),
inference(paramod,[status(thm)],[c_3520,c_3669]) ).
cnf(c_3671,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| sk_c6 != sk_c6
| sk_c7 != sk_c7
| sk_c1 = sk_c4 ),
inference(paramod,[status(thm)],[c_3070,c_3670]) ).
cnf(c_3672,plain,
( multiply(sk_c6,sk_c5) != sk_c6
| sk_c6 != sk_c6
| sk_c7 != sk_c7
| sk_c1 = sk_c4 ),
inference(paramod,[status(thm)],[c_3520,c_3671]) ).
cnf(c_3673,plain,
( multiply(sk_c6,sk_c6) != sk_c6
| sk_c6 != sk_c6
| sk_c7 != sk_c7
| sk_c1 = sk_c4 ),
inference(paramod,[status(thm)],[c_3520,c_3672]) ).
cnf(c_3674,plain,
( sk_c6 != sk_c6
| sk_c6 != sk_c6
| sk_c7 != sk_c7
| sk_c1 = sk_c4 ),
inference(paramod,[status(thm)],[c_3071,c_3673]) ).
cnf(c_3675,plain,
( sk_c6 != sk_c6
| sk_c6 != sk_c6
| sk_c1 = sk_c4 ),
inference(copy,[status(thm)],[c_3674]) ).
cnf(c_3676,plain,
( sk_c6 != sk_c6
| sk_c1 = sk_c4 ),
inference(copy,[status(thm)],[c_3675]) ).
cnf(c_3606,plain,
sk_c1 = sk_c4,
inference(copy,[status(thm)],[c_3676]) ).
cnf(c_3677,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| inverse(sk_c1) != sk_c7 ),
inference(paramod,[status(thm)],[c_3605,c_3072]) ).
cnf(c_3678,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| inverse(sk_c4) != sk_c7 ),
inference(paramod,[status(thm)],[c_3606,c_3677]) ).
cnf(c_3679,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_3596,c_3678]) ).
cnf(c_3680,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_3520,c_3679]) ).
cnf(c_3681,plain,
( multiply(sk_c5,sk_c5) != sk_c6
| sk_c6 != sk_c6
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_3070,c_3680]) ).
cnf(c_3682,plain,
( multiply(sk_c6,sk_c5) != sk_c6
| sk_c6 != sk_c6
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_3520,c_3681]) ).
cnf(c_3683,plain,
( multiply(sk_c6,sk_c6) != sk_c6
| sk_c6 != sk_c6
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_3520,c_3682]) ).
cnf(c_3684,plain,
( sk_c6 != sk_c6
| sk_c6 != sk_c6
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_3071,c_3683]) ).
cnf(c_3685,plain,
( sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(copy,[status(thm)],[c_3684]) ).
cnf(c_3686,plain,
sk_c6 != sk_c6,
inference(copy,[status(thm)],[c_3685]) ).
cnf(c_3615,plain,
$false,
inference(copy,[status(thm)],[c_3686]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP253-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n009.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Fri Sep 25 14:41:14 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.46 % Process 1843051 was started by sandbox on n009,
% 0.20/0.46 % Fri Sep 25 14:41:14 2026
% 0.20/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.20/0.47
% 0.20/0.47 % From the command line: assign(max_seconds, 300).
% 10.00/1.91
% 10.00/1.91 % SZS status Unsatisfiable for theBenchmark
% 10.00/1.91
% 10.00/1.91 % Proof 1 at 0.91 (+ 0.34) seconds.
% 10.00/1.91 % Length of proof is 66.
% 10.00/1.91 % Level of proof is 20.
% 10.00/1.91 % Maximum clause weight is 44.000.
% 10.00/1.91 % Given clauses 199.
% 10.00/1.91
% 10.00/1.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------