%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP376-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 07:28:44 AM UTC 2026
% Result : Unsatisfiable 111.45s 16.33s
% Output : CNFRefutation 111.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 65
% Number of leaves : 19
% Syntax : Number of formulae : 168 ( 27 unt; 0 def)
% Number of atoms : 501 ( 500 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 570 ( 237 ~; 333 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 60 ( 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_c6,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_4,axiom,
( inverse(sk_c4) = sk_c6
| inverse(sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_13,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_14,axiom,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_19,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_31,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( multiply(VAR_3,sk_c5) != sk_c6
| inverse(VAR_3) != sk_c6
| multiply(VAR_2,sk_c6) != sk_c7
| inverse(VAR_2) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(VAR_1) != sk_c5
| multiply(VAR_1,sk_c5) != sk_c7
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(VAR_0) != sk_c7
| multiply(VAR_0,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c6 ),
file('theBenchmark.p',prove_this_31) ).
cnf(c_34,plain,
( multiply(D,sk_c5) != sk_c6
| inverse(D) != sk_c6
| multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(B) != sk_c5
| multiply(B,sk_c5) != sk_c7
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
cnf(c_14645,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_14646,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_14645]) ).
cnf(c_42,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_14646]) ).
cnf(c_43,plain,
( multiply(sk_c6,sk_c7) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_46,plain,
( multiply(sk_c6,sk_c4) = identity
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_50,plain,
( multiply(sk_c7,sk_c3) = identity
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_53,plain,
( multiply(sk_c6,sk_c4) = identity
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_14647,plain,
( multiply(sk_c6,A) = multiply(sk_c4,multiply(sk_c5,A))
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_23,c_3]) ).
cnf(c_67,plain,
( multiply(sk_c4,multiply(sk_c5,A)) = multiply(sk_c6,A)
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_14647]) ).
cnf(c_371,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_42]) ).
cnf(c_403,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_42,c_42]) ).
cnf(c_404,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_403,c_371]) ).
cnf(c_405,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_404,c_2]) ).
cnf(c_14648,plain,
( multiply(inverse(sk_c6),identity) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_43,c_42]) ).
cnf(c_477,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_404,c_14648]) ).
cnf(c_709,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_403,c_2]) ).
cnf(c_14649,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_403,c_404]) ).
cnf(c_14650,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_404,c_14649]) ).
cnf(c_732,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_14650]) ).
cnf(c_14651,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(C) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c7
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(inverse(sk_c7),sk_c7) != sk_c6
| inverse(sk_c7) != sk_c6 ),
inference(resolve,[status(thm)],[c_732,c_34]) ).
cnf(c_764,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(C) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c7
| multiply(sk_c5,sk_c6) != sk_c7
| identity != sk_c6
| inverse(sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_14651]) ).
cnf(c_768,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_8,c_732]) ).
cnf(c_777,plain,
( inverse(sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_22,c_732]) ).
cnf(c_806,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_46,c_732]) ).
cnf(c_824,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_14,c_709]) ).
cnf(c_825,plain,
( multiply(sk_c1,sk_c7) = identity
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_15,c_709]) ).
cnf(c_826,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_16,c_709]) ).
cnf(c_827,plain,
( multiply(sk_c1,sk_c7) = identity
| inverse(sk_c4) = sk_c6 ),
inference(paramod,[status(thm)],[c_17,c_709]) ).
cnf(c_828,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_18,c_709]) ).
cnf(c_2508,plain,
( multiply(sk_c7,sk_c3) = identity
| multiply(sk_c1,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_825,c_2]) ).
cnf(c_2751,plain,
( multiply(sk_c6,sk_c4) = identity
| multiply(sk_c1,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_827,c_2]) ).
cnf(c_5093,plain,
( multiply(sk_c4,multiply(sk_c5,inverse(sk_c6))) = identity
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_709,c_67]) ).
cnf(c_14652,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| identity = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_824,c_9]) ).
cnf(c_8790,plain,
( identity = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_14652]) ).
cnf(c_8796,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_8790,c_42]) ).
cnf(c_14653,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| identity = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_826,c_11]) ).
cnf(c_8885,plain,
( identity = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_14653]) ).
cnf(c_8890,plain,
( multiply(inverse(sk_c3),sk_c7) = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_8885,c_42]) ).
cnf(c_14654,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| identity = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_828,c_13]) ).
cnf(c_8982,plain,
( identity = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_14654]) ).
cnf(c_10153,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c7
| multiply(sk_c5,sk_c6) != sk_c7
| identity != sk_c6
| inverse(sk_c7) != sk_c6 ),
inference(resolve,[status(thm)],[c_764,c_732]) ).
cnf(c_14655,plain,
( multiply(sk_c7,sk_c3) = identity
| identity = sk_c6
| multiply(sk_c7,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_2508,c_50]) ).
cnf(c_10564,plain,
( identity = sk_c6
| multiply(sk_c7,sk_c3) = identity ),
inference(copy,[status(thm)],[c_14655]) ).
cnf(c_14656,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_10564,c_42]) ).
cnf(c_10567,plain,
( inverse(sk_c7) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_404,c_14656]) ).
cnf(c_10573,plain,
( inverse(sk_c3) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_10567,c_732]) ).
cnf(c_14657,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_10573,c_8890]) ).
cnf(c_10654,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_14657]) ).
cnf(c_14658,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c5
| multiply(identity,sk_c5) != sk_c7
| multiply(sk_c5,sk_c6) != sk_c7
| identity != sk_c6
| inverse(sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_405,c_10153]) ).
cnf(c_10927,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c5
| sk_c5 != sk_c7
| multiply(sk_c5,sk_c6) != sk_c7
| identity != sk_c6
| inverse(sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_14658]) ).
cnf(c_10934,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_10654,c_42]) ).
cnf(c_14659,plain,
( multiply(sk_c6,sk_c4) = identity
| identity = sk_c6
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_2751,c_53]) ).
cnf(c_11012,plain,
( identity = sk_c6
| multiply(sk_c6,sk_c4) = identity ),
inference(copy,[status(thm)],[c_14659]) ).
cnf(c_14660,plain,
( multiply(inverse(sk_c6),identity) = sk_c4
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_11012,c_42]) ).
cnf(c_11015,plain,
( inverse(sk_c6) = sk_c4
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_404,c_14660]) ).
cnf(c_14661,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_11015,c_8796]) ).
cnf(c_11049,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_14661]) ).
cnf(c_14662,plain,
( identity = sk_c6
| sk_c7 = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_11049,c_8982]) ).
cnf(c_14663,plain,
( identity = sk_c6
| sk_c6 = sk_c7
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_14662]) ).
cnf(c_11097,plain,
( sk_c6 = sk_c7
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_14663]) ).
cnf(c_11098,plain,
( multiply(sk_c6,A) = A
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_11097,c_1]) ).
cnf(c_11100,plain,
( inverse(sk_c6) = identity
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_11097,c_405]) ).
cnf(c_14664,plain,
( inverse(sk_c6) = sk_c6
| sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_11097,c_11100]) ).
cnf(c_11223,plain,
( inverse(sk_c6) = sk_c6
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_14664]) ).
cnf(c_14665,plain,
( sk_c6 = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_11223,c_477]) ).
cnf(c_11257,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_14665]) ).
cnf(c_14666,plain,
( sk_c6 = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_11223,c_768]) ).
cnf(c_11259,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_14666]) ).
cnf(c_14667,plain,
( sk_c6 = sk_c7
| multiply(sk_c6,sk_c4) = identity
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_11223,c_806]) ).
cnf(c_11266,plain,
( multiply(sk_c6,sk_c4) = identity
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_14667]) ).
cnf(c_14668,plain,
( sk_c5 = sk_c7
| sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_11257,c_11098]) ).
cnf(c_11364,plain,
( sk_c5 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_14668]) ).
cnf(c_14669,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_11364,c_11259]) ).
cnf(c_11482,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_14669]) ).
cnf(c_14670,plain,
( identity = sk_c4
| sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_11266,c_11098]) ).
cnf(c_11687,plain,
( identity = sk_c4
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_14670]) ).
cnf(c_11688,plain,
( multiply(sk_c4,A) = A
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_11687,c_1]) ).
cnf(c_14671,plain,
( sk_c7 = sk_c6
| sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_11688,c_11482]) ).
cnf(c_14672,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_14671]) ).
cnf(c_14673,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_14672]) ).
cnf(c_11885,plain,
sk_c6 = sk_c7,
inference(copy,[status(thm)],[c_14673]) ).
cnf(c_14674,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_11885,c_10934]) ).
cnf(c_14675,plain,
( multiply(inverse(sk_c7),sk_c7) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_11885,c_14674]) ).
cnf(c_14676,plain,
( identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_2,c_14675]) ).
cnf(c_12032,plain,
identity = sk_c7,
inference(copy,[status(thm)],[c_14676]) ).
cnf(c_14677,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c5
| sk_c5 != sk_c7
| multiply(sk_c5,sk_c6) != sk_c7
| identity != sk_c6
| inverse(sk_c7) != sk_c7 ),
inference(paramod,[status(thm)],[c_11885,c_10927]) ).
cnf(c_14678,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c5
| sk_c5 != sk_c7
| multiply(sk_c5,sk_c6) != sk_c7
| sk_c7 != sk_c6
| inverse(sk_c7) != sk_c7 ),
inference(paramod,[status(thm)],[c_12032,c_14677]) ).
cnf(c_14679,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c5
| sk_c5 != sk_c7
| multiply(sk_c5,sk_c6) != sk_c7
| sk_c7 != sk_c7
| inverse(sk_c7) != sk_c7 ),
inference(paramod,[status(thm)],[c_11885,c_14678]) ).
cnf(c_14680,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c5
| sk_c5 != sk_c7
| multiply(sk_c5,sk_c7) != sk_c7
| sk_c7 != sk_c7
| inverse(sk_c7) != sk_c7 ),
inference(paramod,[status(thm)],[c_11885,c_14679]) ).
cnf(c_14681,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c7 != sk_c5
| sk_c5 != sk_c7
| multiply(sk_c5,sk_c7) != sk_c7
| sk_c7 != sk_c7
| inverse(sk_c7) != sk_c7 ),
inference(paramod,[status(thm)],[c_12032,c_14680]) ).
cnf(c_14682,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5
| sk_c7 != sk_c5
| sk_c5 != sk_c7
| multiply(sk_c5,sk_c7) != sk_c7
| sk_c7 != sk_c7
| inverse(sk_c7) != sk_c7 ),
inference(paramod,[status(thm)],[c_11885,c_14681]) ).
cnf(c_14683,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(A,sk_c7) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5
| sk_c7 != sk_c5
| sk_c5 != sk_c7
| multiply(sk_c5,sk_c7) != sk_c7
| sk_c7 != sk_c7
| inverse(sk_c7) != sk_c7 ),
inference(paramod,[status(thm)],[c_11885,c_14682]) ).
cnf(c_14684,plain,
( multiply(inverse(sk_c7),sk_c5) != sk_c6
| multiply(A,sk_c7) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5
| sk_c7 != sk_c5
| sk_c5 != sk_c7
| multiply(sk_c5,sk_c7) != sk_c7
| sk_c7 != sk_c7
| inverse(sk_c7) != sk_c7 ),
inference(paramod,[status(thm)],[c_11885,c_14683]) ).
cnf(c_14685,plain,
( multiply(inverse(sk_c7),sk_c5) != sk_c7
| multiply(A,sk_c7) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5
| sk_c7 != sk_c5
| sk_c5 != sk_c7
| multiply(sk_c5,sk_c7) != sk_c7
| sk_c7 != sk_c7
| inverse(sk_c7) != sk_c7 ),
inference(paramod,[status(thm)],[c_11885,c_14684]) ).
cnf(c_14686,plain,
( multiply(inverse(sk_c7),sk_c5) != sk_c7
| multiply(A,sk_c7) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5
| sk_c5 != sk_c7
| sk_c5 != sk_c7
| multiply(sk_c5,sk_c7) != sk_c7
| sk_c7 != sk_c7
| inverse(sk_c7) != sk_c7 ),
inference(copy,[status(thm)],[c_14685]) ).
cnf(c_14687,plain,
( multiply(inverse(sk_c7),sk_c5) != sk_c7
| multiply(A,sk_c7) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5
| sk_c5 != sk_c7
| sk_c5 != sk_c7
| multiply(sk_c5,sk_c7) != sk_c7
| inverse(sk_c7) != sk_c7 ),
inference(copy,[status(thm)],[c_14686]) ).
cnf(c_12035,plain,
( multiply(inverse(sk_c7),sk_c5) != sk_c7
| multiply(A,sk_c7) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5
| sk_c5 != sk_c7
| multiply(sk_c5,sk_c7) != sk_c7
| inverse(sk_c7) != sk_c7 ),
inference(copy,[status(thm)],[c_14687]) ).
cnf(c_14688,plain,
( multiply(sk_c4,multiply(sk_c5,inverse(sk_c6))) = identity
| multiply(sk_c5,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_11885,c_5093]) ).
cnf(c_14689,plain,
( multiply(sk_c4,multiply(sk_c5,inverse(sk_c7))) = identity
| multiply(sk_c5,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_11885,c_14688]) ).
cnf(c_13599,plain,
( multiply(sk_c4,multiply(sk_c5,inverse(sk_c7))) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_12032,c_14689]) ).
cnf(c_14690,plain,
( inverse(sk_c6) = sk_c4
| multiply(sk_c5,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_11885,c_777]) ).
cnf(c_14504,plain,
( inverse(sk_c7) = sk_c4
| multiply(sk_c5,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_11885,c_14690]) ).
cnf(c_14691,plain,
inverse(sk_c7) = identity,
inference(paramod,[status(thm)],[c_12032,c_405]) ).
cnf(c_14615,plain,
inverse(sk_c7) = sk_c7,
inference(paramod,[status(thm)],[c_12032,c_14691]) ).
cnf(c_14616,plain,
multiply(A,sk_c7) = A,
inference(paramod,[status(thm)],[c_12032,c_404]) ).
cnf(c_14618,plain,
multiply(sk_c7,A) = A,
inference(paramod,[status(thm)],[c_12032,c_1]) ).
cnf(c_14692,plain,
( multiply(inverse(sk_c7),sk_c5) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5
| sk_c5 != sk_c7
| multiply(sk_c5,sk_c7) != sk_c7
| inverse(sk_c7) != sk_c7 ),
inference(factor,[status(thm)],[c_12035]) ).
cnf(c_14693,plain,
( multiply(inverse(sk_c7),sk_c5) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5
| sk_c5 != sk_c7
| multiply(sk_c5,sk_c7) != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_14615,c_14692]) ).
cnf(c_14694,plain,
( multiply(inverse(sk_c7),sk_c5) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5
| sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_14616,c_14693]) ).
cnf(c_14695,plain,
( multiply(inverse(sk_c7),sk_c5) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c7
| sk_c7 != sk_c5
| sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_14616,c_14694]) ).
cnf(c_14696,plain,
( multiply(inverse(sk_c7),sk_c5) != sk_c7
| sk_c7 != sk_c7
| sk_c7 != sk_c5
| sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_14616,c_14695]) ).
cnf(c_14697,plain,
( multiply(sk_c7,sk_c5) != sk_c7
| sk_c7 != sk_c7
| sk_c7 != sk_c5
| sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_14615,c_14696]) ).
cnf(c_14698,plain,
( sk_c5 != sk_c7
| sk_c7 != sk_c7
| sk_c7 != sk_c5
| sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_14618,c_14697]) ).
cnf(c_14699,plain,
( sk_c5 != sk_c7
| sk_c7 != sk_c7
| sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c7 != sk_c7 ),
inference(copy,[status(thm)],[c_14698]) ).
cnf(c_14700,plain,
( sk_c5 != sk_c7
| sk_c7 != sk_c7
| sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c5 != sk_c7 ),
inference(copy,[status(thm)],[c_14699]) ).
cnf(c_14701,plain,
( sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c5 != sk_c7 ),
inference(copy,[status(thm)],[c_14700]) ).
cnf(c_14702,plain,
( sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c5 != sk_c7 ),
inference(copy,[status(thm)],[c_14701]) ).
cnf(c_14703,plain,
( sk_c5 != sk_c7
| sk_c5 != sk_c7 ),
inference(copy,[status(thm)],[c_14702]) ).
cnf(c_14621,plain,
sk_c5 != sk_c7,
inference(copy,[status(thm)],[c_14703]) ).
cnf(c_14704,plain,
( inverse(sk_c7) = sk_c4
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_14616,c_14504]) ).
cnf(c_14705,plain,
( sk_c7 = sk_c4
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_14615,c_14704]) ).
cnf(c_14706,plain,
( sk_c4 = sk_c7
| sk_c5 = sk_c7 ),
inference(copy,[status(thm)],[c_14705]) ).
cnf(c_14643,plain,
sk_c4 = sk_c7,
inference(resolve,[status(thm)],[c_14621,c_14706]) ).
cnf(c_14707,plain,
( multiply(sk_c4,multiply(sk_c5,inverse(sk_c7))) = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_14616,c_13599]) ).
cnf(c_14708,plain,
( multiply(sk_c7,multiply(sk_c5,inverse(sk_c7))) = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_14643,c_14707]) ).
cnf(c_14709,plain,
( multiply(sk_c7,multiply(sk_c5,sk_c7)) = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_14615,c_14708]) ).
cnf(c_14710,plain,
( multiply(sk_c7,sk_c5) = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_14616,c_14709]) ).
cnf(c_14711,plain,
( sk_c5 = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_14618,c_14710]) ).
cnf(c_14712,plain,
sk_c5 = sk_c7,
inference(copy,[status(thm)],[c_14711]) ).
cnf(c_14644,plain,
$false,
inference(resolve,[status(thm)],[c_14621,c_14712]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP376-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 14:48:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 669394 was started by sandbox2 on n013,
% 0.10/0.37 % Fri Sep 25 14:48:52 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 111.45/16.33
% 111.45/16.33 % given #500 (F,wt=44): 11610 inverse(sk_c7) != sk_c6 | identity != sk_c6 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(inverse(A),sk_c5) != sk_c7 | sk_c5 != A | multiply(sk_c6,sk_c7) != sk_c5 | sk_c7 != B | multiply(inverse(B),sk_c6) != sk_c7 | sk_c6 != C | multiply(inverse(C),sk_c5) != sk_c6. [para(732(a,1),11456(i,1)),flip(i)].
% 111.45/16.33
% 111.45/16.33 % SZS status Unsatisfiable for theBenchmark
% 111.45/16.33
% 111.45/16.33 % Proof 1 at 13.79 (+ 2.05) seconds.
% 111.45/16.33 % Length of proof is 81.
% 111.45/16.33 % Level of proof is 20.
% 111.45/16.33 % Maximum clause weight is 50.000.
% 111.45/16.33 % Given clauses 522.
% 111.45/16.33
% 111.45/16.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------