%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP306-1 : 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 : n012.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 07:28:36 AM UTC 2026
% Result : Unsatisfiable 42.11s 5.68s
% Output : CNFRefutation 42.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 18
% Syntax : Number of formulae : 159 ( 30 unt; 0 def)
% Number of atoms : 428 ( 427 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 442 ( 173 ~; 269 |; 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 : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 10 !; 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_c8,sk_c7) = sk_c6,
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(clausify,[status(thm)],[prove_this_1]) ).
cnf(c_5,plain,
sk_c6 = multiply(sk_c8,sk_c7),
inference(copy,[status(thm)],[c_4]) ).
fof(prove_this_4,axiom,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_10,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
cnf(c_11,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c8) = multiply(sk_c8,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_10]) ).
fof(prove_this_5,axiom,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_12,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
cnf(c_13,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = multiply(sk_c8,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_12]) ).
fof(prove_this_6,axiom,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_14,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
cnf(c_15,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = multiply(sk_c8,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_14]) ).
fof(prove_this_7,axiom,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_16,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_17,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_18,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_19,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_20,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c2 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_21,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_13,axiom,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_22,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_14,axiom,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c2 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_23,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c2 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_24,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_25,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_22,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( inverse(VAR_4) != sk_c8
| multiply(VAR_4,sk_c8) != VAR_3
| multiply(sk_c8,VAR_3) != sk_c7
| inverse(VAR_2) != sk_c8
| multiply(VAR_2,sk_c8) != sk_c7
| multiply(VAR_1,sk_c7) != sk_c8
| inverse(VAR_0) != VAR_1
| multiply(VAR_0,VAR_1) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c7) != sk_c6 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_31,plain,
( inverse(E) != sk_c8
| multiply(E,sk_c8) != D
| multiply(sk_c8,D) != sk_c7
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
cnf(c_19036,plain,
( inverse(E) != sk_c8
| multiply(E,sk_c8) != D
| multiply(sk_c8,D) != sk_c7
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c7) != multiply(sk_c8,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_31]) ).
cnf(c_19037,plain,
( inverse(E) != sk_c8
| multiply(E,sk_c8) != D
| multiply(sk_c8,D) != sk_c7
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8
| inverse(sk_c8) != multiply(sk_c8,sk_c7)
| multiply(sk_c8,sk_c7) != multiply(sk_c8,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_19036]) ).
cnf(c_32,plain,
( inverse(E) != sk_c8
| multiply(E,sk_c8) != D
| multiply(sk_c8,D) != sk_c7
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8
| inverse(sk_c8) != multiply(sk_c8,sk_c7) ),
inference(copy,[status(thm)],[c_19037]) ).
cnf(c_19038,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_19039,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_19038]) ).
cnf(c_55,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_19039]) ).
cnf(c_19040,plain,
( multiply(multiply(sk_c8,sk_c7),sk_c8) = identity
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_58,plain,
( multiply(sk_c8,multiply(sk_c7,sk_c8)) = identity
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_3,c_19040]) ).
cnf(c_68,plain,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_20,c_2]) ).
cnf(c_69,plain,
( multiply(sk_c2,sk_c1) = identity
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_21,c_2]) ).
cnf(c_72,plain,
( multiply(sk_c2,sk_c1) = identity
| multiply(sk_c4,sk_c8) = sk_c5 ),
inference(paramod,[status(thm)],[c_24,c_2]) ).
cnf(c_73,plain,
( multiply(sk_c8,sk_c4) = identity
| inverse(sk_c1) = sk_c2 ),
inference(paramod,[status(thm)],[c_25,c_2]) ).
cnf(c_124,plain,
( inverse(F) != sk_c8
| multiply(F,sk_c8) != E
| multiply(sk_c8,E) != sk_c7
| inverse(D) != sk_c8
| multiply(D,sk_c8) != sk_c7
| multiply(B,multiply(C,sk_c7)) != sk_c8
| inverse(A) != multiply(B,C)
| multiply(A,multiply(B,C)) != sk_c8
| inverse(sk_c8) != multiply(sk_c8,sk_c7) ),
inference(paramod,[status(thm)],[c_3,c_32]) ).
cnf(c_817,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_55]) ).
cnf(c_844,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_55,c_55]) ).
cnf(c_845,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_844,c_817]) ).
cnf(c_868,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_845,c_2]) ).
cnf(c_1037,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_844,c_2]) ).
cnf(c_19041,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_844,c_845]) ).
cnf(c_19042,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_845,c_19041]) ).
cnf(c_1072,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_19042]) ).
cnf(c_1195,plain,
( multiply(sk_c4,sk_c8) = identity
| inverse(sk_c8) = multiply(sk_c8,sk_c7) ),
inference(paramod,[status(thm)],[c_15,c_1037]) ).
cnf(c_1196,plain,
( multiply(sk_c3,sk_c8) = identity
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_17,c_1037]) ).
cnf(c_1197,plain,
( multiply(sk_c4,sk_c8) = identity
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_20,c_1037]) ).
cnf(c_1199,plain,
( multiply(sk_c3,sk_c8) = identity
| inverse(sk_c1) = sk_c2 ),
inference(paramod,[status(thm)],[c_22,c_1037]) ).
cnf(c_1200,plain,
( multiply(sk_c1,sk_c2) = identity
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_23,c_1037]) ).
cnf(c_1202,plain,
( multiply(sk_c4,sk_c8) = identity
| inverse(sk_c1) = sk_c2 ),
inference(paramod,[status(thm)],[c_25,c_1037]) ).
cnf(c_1215,plain,
( multiply(sk_c1,sk_c2) = identity
| multiply(sk_c8,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_73,c_1037]) ).
cnf(c_19043,plain,
( multiply(inverse(sk_c8),identity) = multiply(sk_c7,sk_c8)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_58,c_55]) ).
cnf(c_1491,plain,
( inverse(sk_c8) = multiply(sk_c7,sk_c8)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_845,c_19043]) ).
cnf(c_2225,plain,
( multiply(sk_c2,sk_c1) = identity
| multiply(sk_c3,sk_c8) = identity ),
inference(paramod,[status(thm)],[c_1199,c_2]) ).
cnf(c_2359,plain,
( multiply(sk_c2,sk_c1) = identity
| multiply(sk_c4,sk_c8) = identity ),
inference(paramod,[status(thm)],[c_1202,c_2]) ).
cnf(c_19044,plain,
( identity = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_1196,c_16]) ).
cnf(c_5907,plain,
( identity = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(copy,[status(thm)],[c_19044]) ).
cnf(c_19045,plain,
( identity = sk_c5
| multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_1197,c_19]) ).
cnf(c_5960,plain,
( identity = sk_c5
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(copy,[status(thm)],[c_19045]) ).
cnf(c_19046,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| identity = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_1200,c_18]) ).
cnf(c_6162,plain,
( identity = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(copy,[status(thm)],[c_19046]) ).
cnf(c_7063,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c5
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_6162,c_55]) ).
cnf(c_19047,plain,
( multiply(sk_c8,sk_c4) = identity
| identity = sk_c8
| multiply(sk_c8,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_1215,c_68]) ).
cnf(c_9480,plain,
( identity = sk_c8
| multiply(sk_c8,sk_c4) = identity ),
inference(copy,[status(thm)],[c_19047]) ).
cnf(c_19048,plain,
( multiply(inverse(sk_c8),identity) = sk_c4
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_9480,c_55]) ).
cnf(c_9491,plain,
( inverse(sk_c8) = sk_c4
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_845,c_19048]) ).
cnf(c_19049,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_9491,c_7063]) ).
cnf(c_9577,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_19049]) ).
cnf(c_19050,plain,
( multiply(sk_c2,sk_c1) = identity
| identity = sk_c7
| multiply(sk_c2,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_2225,c_69]) ).
cnf(c_9709,plain,
( identity = sk_c7
| multiply(sk_c2,sk_c1) = identity ),
inference(copy,[status(thm)],[c_19050]) ).
cnf(c_19051,plain,
( multiply(inverse(sk_c2),identity) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_9709,c_55]) ).
cnf(c_9957,plain,
( inverse(sk_c2) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_845,c_19051]) ).
cnf(c_9962,plain,
( multiply(sk_c1,sk_c2) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_9957,c_2]) ).
cnf(c_19052,plain,
( identity = sk_c7
| identity = sk_c8
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_9962,c_5907]) ).
cnf(c_10019,plain,
( identity = sk_c8
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_19052]) ).
cnf(c_10218,plain,
( multiply(A,sk_c7) = A
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_10019,c_845]) ).
cnf(c_19053,plain,
( inverse(sk_c8) = sk_c5
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_10218,c_7063]) ).
cnf(c_10665,plain,
( inverse(sk_c8) = sk_c5
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_19053]) ).
cnf(c_19054,plain,
( sk_c4 = sk_c5
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_10218,c_9577]) ).
cnf(c_19055,plain,
( sk_c5 = sk_c4
| identity = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_19054]) ).
cnf(c_10677,plain,
( sk_c5 = sk_c4
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_19055]) ).
cnf(c_10872,plain,
( multiply(sk_c8,A) = A
| sk_c5 = sk_c4 ),
inference(paramod,[status(thm)],[c_10677,c_1]) ).
cnf(c_10916,plain,
( inverse(sk_c5) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_10665,c_1072]) ).
cnf(c_12348,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c7
| sk_c5 = sk_c4 ),
inference(paramod,[status(thm)],[c_10872,c_13]) ).
cnf(c_19056,plain,
( inverse(E) != sk_c8
| multiply(E,sk_c8) != D
| multiply(sk_c8,D) != sk_c7
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c7
| multiply(A,multiply(B,sk_c7)) != sk_c8
| inverse(identity) != multiply(A,B)
| multiply(A,B) != sk_c8
| inverse(sk_c8) != multiply(sk_c8,sk_c7) ),
inference(paramod,[status(thm)],[c_1,c_124]) ).
cnf(c_19057,plain,
( inverse(E) != sk_c8
| multiply(E,sk_c8) != D
| multiply(sk_c8,D) != sk_c7
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c7
| multiply(A,multiply(B,sk_c7)) != sk_c8
| identity != multiply(A,B)
| multiply(A,B) != sk_c8
| inverse(sk_c8) != multiply(sk_c8,sk_c7) ),
inference(paramod,[status(thm)],[c_868,c_19056]) ).
cnf(c_14883,plain,
( inverse(E) != sk_c8
| multiply(E,sk_c8) != D
| multiply(sk_c8,D) != sk_c7
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c7
| multiply(A,multiply(B,sk_c7)) != sk_c8
| multiply(A,B) != identity
| multiply(A,B) != sk_c8
| inverse(sk_c8) != multiply(sk_c8,sk_c7) ),
inference(copy,[status(thm)],[c_19057]) ).
cnf(c_14901,plain,
( inverse(A) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| multiply(A,multiply(sk_c8,sk_c7)) != sk_c8
| multiply(A,sk_c8) != identity
| multiply(A,sk_c8) != sk_c8
| inverse(sk_c8) != multiply(sk_c8,sk_c7) ),
inference(factor,[status(thm)],[c_14883]) ).
cnf(c_14934,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(A,multiply(sk_c8,sk_c7)) != sk_c8
| multiply(A,sk_c8) != identity
| multiply(A,sk_c8) != sk_c8
| inverse(sk_c8) != multiply(sk_c8,sk_c7) ),
inference(factor,[status(thm)],[c_14901]) ).
cnf(c_19058,plain,
( multiply(sk_c2,sk_c1) = identity
| identity = sk_c5
| multiply(sk_c2,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_2359,c_72]) ).
cnf(c_15315,plain,
( identity = sk_c5
| multiply(sk_c2,sk_c1) = identity ),
inference(copy,[status(thm)],[c_19058]) ).
cnf(c_19059,plain,
( multiply(inverse(sk_c2),identity) = sk_c1
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_15315,c_55]) ).
cnf(c_15321,plain,
( inverse(sk_c2) = sk_c1
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_845,c_19059]) ).
cnf(c_15331,plain,
( multiply(sk_c1,sk_c2) = identity
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_15321,c_2]) ).
cnf(c_19060,plain,
( identity = sk_c5
| identity = sk_c8
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_15331,c_5960]) ).
cnf(c_15515,plain,
( identity = sk_c8
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_19060]) ).
cnf(c_15519,plain,
( inverse(sk_c5) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_15515,c_868]) ).
cnf(c_19061,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_15519,c_10916]) ).
cnf(c_19062,plain,
( identity = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_19061]) ).
cnf(c_15846,plain,
identity = sk_c8,
inference(copy,[status(thm)],[c_19062]) ).
cnf(c_19063,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(A,multiply(sk_c8,sk_c7)) != sk_c8
| multiply(A,sk_c8) != sk_c8
| multiply(A,sk_c8) != sk_c8
| inverse(sk_c8) != multiply(sk_c8,sk_c7) ),
inference(paramod,[status(thm)],[c_15846,c_14934]) ).
cnf(c_16598,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(A,multiply(sk_c8,sk_c7)) != sk_c8
| multiply(A,sk_c8) != sk_c8
| inverse(sk_c8) != multiply(sk_c8,sk_c7) ),
inference(copy,[status(thm)],[c_19063]) ).
cnf(c_18901,plain,
( multiply(sk_c4,sk_c8) = sk_c8
| inverse(sk_c8) = multiply(sk_c8,sk_c7) ),
inference(paramod,[status(thm)],[c_15846,c_1195]) ).
cnf(c_19064,plain,
inverse(sk_c8) = identity,
inference(paramod,[status(thm)],[c_15846,c_868]) ).
cnf(c_18960,plain,
inverse(sk_c8) = sk_c8,
inference(paramod,[status(thm)],[c_15846,c_19064]) ).
cnf(c_18966,plain,
multiply(A,sk_c8) = A,
inference(paramod,[status(thm)],[c_15846,c_845]) ).
cnf(c_18979,plain,
multiply(sk_c8,A) = A,
inference(paramod,[status(thm)],[c_15846,c_1]) ).
cnf(c_19065,plain,
( inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c8,multiply(sk_c8,sk_c7)) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c8
| inverse(sk_c8) != multiply(sk_c8,sk_c7) ),
inference(factor,[status(thm)],[c_16598]) ).
cnf(c_19066,plain,
( inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c8,multiply(sk_c8,sk_c7)) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c8
| sk_c8 != multiply(sk_c8,sk_c7) ),
inference(paramod,[status(thm)],[c_18960,c_19065]) ).
cnf(c_19067,plain,
( inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c8,multiply(sk_c8,sk_c7)) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c8
| sk_c8 != sk_c7 ),
inference(paramod,[status(thm)],[c_18979,c_19066]) ).
cnf(c_19068,plain,
( inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c8,multiply(sk_c8,sk_c7)) != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c7 ),
inference(paramod,[status(thm)],[c_18966,c_19067]) ).
cnf(c_19069,plain,
( inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c7 ),
inference(paramod,[status(thm)],[c_18979,c_19068]) ).
cnf(c_19070,plain,
( inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c7 != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c7 ),
inference(paramod,[status(thm)],[c_18979,c_19069]) ).
cnf(c_19071,plain,
( inverse(sk_c8) != sk_c8
| sk_c8 != sk_c7
| sk_c7 != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c7 ),
inference(paramod,[status(thm)],[c_18966,c_19070]) ).
cnf(c_19072,plain,
( sk_c8 != sk_c8
| sk_c8 != sk_c7
| sk_c7 != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c7 ),
inference(paramod,[status(thm)],[c_18960,c_19071]) ).
cnf(c_19073,plain,
( sk_c8 != sk_c8
| sk_c8 != sk_c7
| sk_c7 != sk_c8
| sk_c8 != sk_c8
| sk_c7 != sk_c8 ),
inference(copy,[status(thm)],[c_19072]) ).
cnf(c_19074,plain,
( sk_c8 != sk_c8
| sk_c7 != sk_c8
| sk_c7 != sk_c8
| sk_c8 != sk_c8
| sk_c7 != sk_c8 ),
inference(copy,[status(thm)],[c_19073]) ).
cnf(c_19075,plain,
( sk_c8 != sk_c8
| sk_c7 != sk_c8
| sk_c7 != sk_c8
| sk_c7 != sk_c8 ),
inference(copy,[status(thm)],[c_19074]) ).
cnf(c_19076,plain,
( sk_c7 != sk_c8
| sk_c7 != sk_c8
| sk_c7 != sk_c8 ),
inference(copy,[status(thm)],[c_19075]) ).
cnf(c_19077,plain,
( sk_c7 != sk_c8
| sk_c7 != sk_c8 ),
inference(copy,[status(thm)],[c_19076]) ).
cnf(c_19004,plain,
sk_c7 != sk_c8,
inference(copy,[status(thm)],[c_19077]) ).
cnf(c_19078,plain,
( multiply(sk_c4,sk_c8) = sk_c8
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(paramod,[status(thm)],[c_18960,c_18901]) ).
cnf(c_19079,plain,
( multiply(sk_c4,sk_c8) = sk_c8
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_18979,c_19078]) ).
cnf(c_19080,plain,
( sk_c4 = sk_c8
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_18966,c_19079]) ).
cnf(c_19081,plain,
( sk_c4 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_19080]) ).
cnf(c_19016,plain,
sk_c4 = sk_c8,
inference(resolve,[status(thm)],[c_19004,c_19081]) ).
cnf(c_19082,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c7
| sk_c5 = sk_c8 ),
inference(paramod,[status(thm)],[c_19016,c_12348]) ).
cnf(c_19083,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| sk_c8 = sk_c7
| sk_c5 = sk_c8 ),
inference(paramod,[status(thm)],[c_18960,c_19082]) ).
cnf(c_19084,plain,
( multiply(sk_c8,sk_c8) = sk_c5
| sk_c8 = sk_c7
| sk_c5 = sk_c8 ),
inference(paramod,[status(thm)],[c_19016,c_19083]) ).
cnf(c_19085,plain,
( sk_c8 = sk_c5
| sk_c8 = sk_c7
| sk_c5 = sk_c8 ),
inference(paramod,[status(thm)],[c_18966,c_19084]) ).
cnf(c_19086,plain,
( sk_c8 = sk_c5
| sk_c7 = sk_c8
| sk_c5 = sk_c8 ),
inference(copy,[status(thm)],[c_19085]) ).
cnf(c_19087,plain,
( sk_c5 = sk_c8
| sk_c7 = sk_c8
| sk_c5 = sk_c8 ),
inference(copy,[status(thm)],[c_19086]) ).
cnf(c_19088,plain,
( sk_c7 = sk_c8
| sk_c5 = sk_c8 ),
inference(copy,[status(thm)],[c_19087]) ).
cnf(c_19022,plain,
sk_c5 = sk_c8,
inference(resolve,[status(thm)],[c_19004,c_19088]) ).
cnf(c_19089,plain,
( inverse(sk_c8) = multiply(sk_c7,sk_c8)
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_19022,c_1491]) ).
cnf(c_19090,plain,
( inverse(sk_c8) = multiply(sk_c7,sk_c8)
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_18966,c_19089]) ).
cnf(c_19091,plain,
( sk_c8 = multiply(sk_c7,sk_c8)
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_18960,c_19090]) ).
cnf(c_19092,plain,
( sk_c8 = sk_c7
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_18966,c_19091]) ).
cnf(c_19093,plain,
( sk_c8 = sk_c7
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_19092]) ).
cnf(c_19094,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_19093]) ).
cnf(c_19095,plain,
sk_c7 = sk_c8,
inference(copy,[status(thm)],[c_19094]) ).
cnf(c_19035,plain,
$false,
inference(resolve,[status(thm)],[c_19004,c_19095]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP306-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Fri Sep 25 14:44:05 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.30 % Process 2343303 was started by sandbox on n012,
% 0.02/0.30 % Fri Sep 25 14:44:05 2026
% 0.02/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.30
% 0.02/0.30 % From the command line: assign(max_seconds, 300).
% 42.11/5.68
% 42.11/5.68 % SZS status Unsatisfiable for theBenchmark
% 42.11/5.68
% 42.11/5.68 % Proof 1 at 4.62 (+ 0.66) seconds.
% 42.11/5.68 % Length of proof is 81.
% 42.11/5.68 % Level of proof is 18.
% 42.11/5.68 % Maximum clause weight is 49.000.
% 42.11/5.68 % Given clauses 494.
% 42.11/5.68
% 42.11/5.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------