%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP048-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 07:26:23 AM UTC 2026
% Result : Unsatisfiable 1.10s 0.61s
% Output : CNFRefutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 22 unt; 0 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 125 ( 67 ~; 58 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 123 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(product_substitution3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( product(VAR_2,VAR_3,VAR_1)
| ~ product(VAR_2,VAR_3,VAR_0)
| ~ equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',product_substitution3) ).
cnf(c_1,plain,
( product(C,D,B)
| ~ product(C,D,A)
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[product_substitution3]) ).
fof(total_function2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_2,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',total_function2) ).
cnf(c_2,plain,
( equalish(C,D)
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[total_function2]) ).
fof(a_equals_b,axiom,
equalish(a,b),
file('theBenchmark.p',a_equals_b) ).
cnf(c_3,plain,
equalish(a,b),
inference(clausify,[status(thm)],[a_equals_b]) ).
fof(prove_inverse_substitution,axiom,
~ equalish(inverse(a),inverse(b)),
file('theBenchmark.p',prove_inverse_substitution) ).
cnf(c_4,plain,
~ equalish(inverse(a),inverse(b)),
inference(clausify,[status(thm)],[prove_inverse_substitution]) ).
cnf(c_5,plain,
( ~ product(A,B,inverse(b))
| ~ product(A,B,inverse(a)) ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_6,plain,
( product(A,B,b)
| ~ product(A,B,a) ),
inference(resolve,[status(thm)],[c_3,c_1]) ).
cnf(c_7,plain,
( ~ product(E,F,D)
| ~ product(E,F,C)
| product(A,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(associativity2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( product(VAR_2,VAR_3,VAR_5)
| ~ product(VAR_0,VAR_4,VAR_5)
| ~ product(VAR_1,VAR_3,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity2) ).
cnf(c_8,plain,
( product(C,D,F)
| ~ product(A,E,F)
| ~ product(B,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[associativity2]) ).
fof(associativity1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( product(VAR_0,VAR_4,VAR_5)
| ~ product(VAR_2,VAR_3,VAR_5)
| ~ product(VAR_1,VAR_3,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity1) ).
cnf(c_9,plain,
( product(A,E,F)
| ~ product(C,D,F)
| ~ product(B,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[associativity1]) ).
fof(left_inverse,axiom,
! [VAR_0] : product(inverse(VAR_0),VAR_0,identity),
file('theBenchmark.p',left_inverse) ).
cnf(c_11,plain,
product(inverse(A),A,identity),
inference(clausify,[status(thm)],[left_inverse]) ).
fof(left_identity,axiom,
! [VAR_0] : product(identity,VAR_0,VAR_0),
file('theBenchmark.p',left_identity) ).
cnf(c_12,plain,
product(identity,A,A),
inference(clausify,[status(thm)],[left_identity]) ).
cnf(c_27,plain,
~ product(identity,inverse(b),inverse(a)),
inference(resolve,[status(thm)],[c_12,c_5]) ).
cnf(c_1149,plain,
( product(inverse(A),C,D)
| ~ product(identity,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_9,c_11]) ).
cnf(c_1150,plain,
( product(inverse(identity),A,B)
| ~ product(identity,A,B) ),
inference(resolve,[status(thm)],[c_1149,c_12]) ).
cnf(c_30,plain,
product(inverse(identity),A,A),
inference(resolve,[status(thm)],[c_1150,c_12]) ).
cnf(c_1151,plain,
( product(inverse(A),C,D)
| ~ product(identity,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_9,c_11]) ).
cnf(c_1152,plain,
( product(inverse(inverse(A)),identity,B)
| ~ product(identity,A,B) ),
inference(resolve,[status(thm)],[c_1151,c_11]) ).
cnf(c_31,plain,
product(inverse(inverse(A)),identity,A),
inference(resolve,[status(thm)],[c_1152,c_12]) ).
cnf(c_45,plain,
product(identity,a,b),
inference(resolve,[status(thm)],[c_6,c_12]) ).
cnf(c_1153,plain,
( product(identity,B,D)
| ~ product(inverse(A),C,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_11]) ).
cnf(c_1154,plain,
( product(identity,A,B)
| ~ product(inverse(inverse(A)),identity,B) ),
inference(resolve,[status(thm)],[c_1153,c_11]) ).
cnf(c_69,plain,
~ product(inverse(inverse(inverse(b))),identity,inverse(a)),
inference(resolve,[status(thm)],[c_1154,c_27]) ).
cnf(c_1155,plain,
( product(inverse(A),C,D)
| ~ product(identity,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_9,c_11]) ).
cnf(c_1156,plain,
( product(inverse(identity),A,B)
| ~ product(identity,A,B) ),
inference(resolve,[status(thm)],[c_1155,c_12]) ).
cnf(c_94,plain,
product(inverse(identity),a,b),
inference(resolve,[status(thm)],[c_1156,c_45]) ).
cnf(c_1157,plain,
( product(inverse(A),C,D)
| ~ product(identity,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_9,c_11]) ).
cnf(c_1158,plain,
( product(inverse(A),C,B)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_1157,c_12]) ).
cnf(c_443,plain,
~ product(inverse(inverse(b)),inverse(a),identity),
inference(resolve,[status(thm)],[c_1158,c_69]) ).
cnf(c_1159,plain,
( product(inverse(A),C,D)
| ~ product(identity,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_9,c_11]) ).
cnf(c_1160,plain,
( product(inverse(A),C,B)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_1159,c_12]) ).
cnf(c_468,plain,
~ product(inverse(b),identity,inverse(a)),
inference(resolve,[status(thm)],[c_1160,c_443]) ).
cnf(c_1161,plain,
( product(inverse(A),C,D)
| ~ product(identity,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_9,c_11]) ).
cnf(c_1162,plain,
( product(inverse(A),C,B)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_1161,c_12]) ).
cnf(c_502,plain,
~ product(b,inverse(a),identity),
inference(resolve,[status(thm)],[c_1162,c_468]) ).
cnf(c_1163,plain,
( product(C,A,D)
| ~ product(inverse(inverse(C)),B,D)
| ~ product(identity,A,B) ),
inference(resolve,[status(thm)],[c_8,c_31]) ).
cnf(c_1164,plain,
( product(A,B,C)
| ~ product(inverse(inverse(A)),B,C) ),
inference(resolve,[status(thm)],[c_1163,c_12]) ).
cnf(c_568,plain,
product(A,identity,A),
inference(resolve,[status(thm)],[c_1164,c_31]) ).
cnf(c_1165,plain,
( product(b,A,C)
| ~ product(inverse(identity),B,C)
| ~ product(a,A,B) ),
inference(resolve,[status(thm)],[c_8,c_94]) ).
cnf(c_1166,plain,
( product(b,identity,A)
| ~ product(inverse(identity),a,A) ),
inference(resolve,[status(thm)],[c_1165,c_568]) ).
cnf(c_780,plain,
product(b,identity,a),
inference(resolve,[status(thm)],[c_1166,c_30]) ).
cnf(c_1167,plain,
( ~ product(B,C,A)
| ~ product(B,C,a)
| product(b,identity,A) ),
inference(resolve,[status(thm)],[c_7,c_780]) ).
cnf(c_1168,plain,
( ~ product(inverse(inverse(a)),identity,A)
| product(b,identity,A) ),
inference(resolve,[status(thm)],[c_1167,c_31]) ).
cnf(c_934,plain,
product(b,identity,inverse(inverse(a))),
inference(resolve,[status(thm)],[c_1168,c_568]) ).
cnf(c_1169,plain,
( product(A,C,D)
| ~ product(B,C,D)
| ~ product(A,identity,B) ),
inference(resolve,[status(thm)],[c_9,c_12]) ).
cnf(c_1170,plain,
( product(A,B,identity)
| ~ product(A,identity,inverse(B)) ),
inference(resolve,[status(thm)],[c_1169,c_11]) ).
cnf(c_1171,plain,
~ product(b,identity,inverse(inverse(a))),
inference(resolve,[status(thm)],[c_1170,c_502]) ).
cnf(c_1148,plain,
$false,
inference(resolve,[status(thm)],[c_934,c_1171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP048-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n005.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:19:32 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3676687 was started by sandbox on n005,
% 0.08/0.35 % Fri Sep 25 14:19:32 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 1.10/0.61
% 1.10/0.61 % SZS status Unsatisfiable for theBenchmark
% 1.10/0.61
% 1.10/0.61 % Proof 1 at 0.15 (+ 0.08) seconds.
% 1.10/0.61 % Length of proof is 24.
% 1.10/0.61 % Level of proof is 7.
% 1.10/0.61 % Maximum clause weight is 16.000.
% 1.10/0.61 % Given clauses 37.
% 1.10/0.61
% 1.10/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------