%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP092-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 07:27:18 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.48s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 5
% Syntax : Number of formulae : 65 ( 37 unt; 0 def)
% Number of atoms : 131 ( 130 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 161 ( 95 ~; 66 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(VAR_0,VAR_1),divide(divide(VAR_0,VAR_2),VAR_1)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(A,B),divide(divide(A,C),B)) = C,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,VAR_1) = divide(VAR_0,divide(divide(VAR_2,VAR_2),VAR_1)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
inference(clausify,[status(thm)],[multiply]) ).
cnf(c_3,plain,
divide(A,divide(divide(B,B),C)) = multiply(A,C),
inference(copy,[status(thm)],[c_2]) ).
fof(inverse,axiom,
! [VAR_0,VAR_1] : inverse(VAR_0) = divide(divide(VAR_1,VAR_1),VAR_0),
file('theBenchmark.p',inverse) ).
cnf(c_4,plain,
inverse(A) = divide(divide(B,B),A),
inference(clausify,[status(thm)],[inverse]) ).
cnf(c_5,plain,
divide(divide(A,A),B) = inverse(B),
inference(copy,[status(thm)],[c_4]) ).
fof(identity,axiom,
! [VAR_0] : identity = divide(VAR_0,VAR_0),
file('theBenchmark.p',identity) ).
cnf(c_6,plain,
identity = divide(A,A),
inference(clausify,[status(thm)],[identity]) ).
cnf(c_7,plain,
divide(A,A) = identity,
inference(copy,[status(thm)],[c_6]) ).
fof(prove_these_axioms,axiom,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('theBenchmark.p',prove_these_axioms) ).
cnf(c_8,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(clausify,[status(thm)],[prove_these_axioms]) ).
cnf(c_77,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ),
inference(copy,[status(thm)],[c_8]) ).
cnf(c_9,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ),
inference(copy,[status(thm)],[c_77]) ).
cnf(c_10,plain,
divide(A,divide(identity,B)) = multiply(A,B),
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_11,plain,
divide(identity,A) = inverse(A),
inference(paramod,[status(thm)],[c_7,c_5]) ).
cnf(c_78,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(paramod,[status(thm)],[c_11,c_10]) ).
cnf(c_12,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(copy,[status(thm)],[c_78]) ).
cnf(c_79,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| divide(inverse(b1),inverse(b1)) != multiply(inverse(a1),a1) ),
inference(paramod,[status(thm)],[c_12,c_9]) ).
cnf(c_80,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| identity != multiply(inverse(a1),a1) ),
inference(paramod,[status(thm)],[c_7,c_79]) ).
cnf(c_81,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| identity != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_12,c_80]) ).
cnf(c_82,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_7,c_81]) ).
cnf(c_83,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(divide(inverse(b2),inverse(b2)),a2) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_12,c_82]) ).
cnf(c_84,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_7,c_83]) ).
cnf(c_85,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| divide(identity,inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_12,c_84]) ).
cnf(c_86,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_11,c_85]) ).
cnf(c_87,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(divide(a3,inverse(b3)),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_12,c_86]) ).
cnf(c_88,plain,
( multiply(b4,a4) != multiply(a4,b4)
| divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_12,c_87]) ).
cnf(c_89,plain,
( multiply(b4,a4) != multiply(a4,b4)
| divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,divide(b3,inverse(c3)))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_12,c_88]) ).
cnf(c_90,plain,
( multiply(b4,a4) != multiply(a4,b4)
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_12,c_89]) ).
cnf(c_91,plain,
( divide(b4,inverse(a4)) != multiply(a4,b4)
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_12,c_90]) ).
cnf(c_92,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_12,c_91]) ).
cnf(c_13,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| inverse(inverse(a2)) != a2 ),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_14,plain,
divide(A,divide(divide(divide(B,C),D),divide(divide(B,A),C))) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_93,plain,
divide(divide(A,B),divide(identity,B)) = A,
inference(paramod,[status(thm)],[c_7,c_1]) ).
cnf(c_18,plain,
divide(divide(A,B),inverse(B)) = A,
inference(paramod,[status(thm)],[c_11,c_93]) ).
cnf(c_19,plain,
divide(divide(A,divide(A,B)),identity) = B,
inference(paramod,[status(thm)],[c_7,c_1]) ).
cnf(c_25,plain,
divide(A,divide(B,divide(divide(C,A),D))) = divide(divide(C,B),D),
inference(paramod,[status(thm)],[c_1,c_14]) ).
cnf(c_32,plain,
divide(A,identity) = A,
inference(paramod,[status(thm)],[c_7,c_14]) ).
cnf(c_39,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_32,c_19]) ).
cnf(c_94,plain,
A = inverse(divide(identity,A)),
inference(paramod,[status(thm)],[c_39,c_11]) ).
cnf(c_95,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_11,c_94]) ).
cnf(c_44,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_95]) ).
cnf(c_96,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_44,c_13]) ).
cnf(c_46,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) ),
inference(copy,[status(thm)],[c_96]) ).
cnf(c_49,plain,
divide(divide(A,B),A) = inverse(B),
inference(paramod,[status(thm)],[c_18,c_39]) ).
cnf(c_97,plain,
divide(A,B) = inverse(divide(B,A)),
inference(paramod,[status(thm)],[c_39,c_49]) ).
cnf(c_51,plain,
inverse(divide(A,B)) = divide(B,A),
inference(copy,[status(thm)],[c_97]) ).
cnf(c_52,plain,
divide(inverse(A),inverse(B)) = divide(B,A),
inference(paramod,[status(thm)],[c_49,c_18]) ).
cnf(c_54,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(c3),b3)) ),
inference(paramod,[status(thm)],[c_51,c_46]) ).
cnf(c_98,plain,
divide(A,divide(B,divide(identity,C))) = divide(divide(A,B),C),
inference(paramod,[status(thm)],[c_7,c_25]) ).
cnf(c_99,plain,
divide(A,divide(B,inverse(C))) = divide(divide(A,B),C),
inference(paramod,[status(thm)],[c_11,c_98]) ).
cnf(c_56,plain,
divide(divide(A,B),C) = divide(A,divide(B,inverse(C))),
inference(copy,[status(thm)],[c_99]) ).
cnf(c_100,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(a3,divide(inverse(b3),inverse(inverse(c3)))) != divide(a3,divide(inverse(c3),b3)) ),
inference(paramod,[status(thm)],[c_56,c_54]) ).
cnf(c_101,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(a3,divide(inverse(b3),c3)) != divide(a3,divide(inverse(c3),b3)) ),
inference(paramod,[status(thm)],[c_44,c_100]) ).
cnf(c_72,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(a3,divide(inverse(c3),b3)) != divide(a3,divide(inverse(b3),c3)) ),
inference(copy,[status(thm)],[c_101]) ).
cnf(c_102,plain,
multiply(A,B) = divide(inverse(inverse(B)),inverse(A)),
inference(paramod,[status(thm)],[c_52,c_12]) ).
cnf(c_103,plain,
divide(A,inverse(B)) = divide(inverse(inverse(B)),inverse(A)),
inference(paramod,[status(thm)],[c_12,c_102]) ).
cnf(c_74,plain,
divide(A,inverse(B)) = divide(B,inverse(A)),
inference(paramod,[status(thm)],[c_44,c_103]) ).
cnf(c_104,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(a3,divide(inverse(b3),inverse(inverse(c3)))) != divide(a3,divide(inverse(b3),c3)) ),
inference(paramod,[status(thm)],[c_52,c_72]) ).
cnf(c_105,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(a3,divide(inverse(b3),c3)) != divide(a3,divide(inverse(b3),c3)) ),
inference(paramod,[status(thm)],[c_44,c_104]) ).
cnf(c_106,plain,
( divide(a4,inverse(b4)) != divide(a4,inverse(b4))
| divide(a3,divide(inverse(b3),c3)) != divide(a3,divide(inverse(b3),c3)) ),
inference(paramod,[status(thm)],[c_74,c_105]) ).
cnf(c_107,plain,
divide(a4,inverse(b4)) != divide(a4,inverse(b4)),
inference(copy,[status(thm)],[c_106]) ).
cnf(c_76,plain,
$false,
inference(copy,[status(thm)],[c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP092-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.40 % Computer : n011.cluster.edu
% 0.08/0.40 % Model : x86_64 x86_64
% 0.08/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.40 % Memory : 8046.5625MB
% 0.08/0.40 % OS : Linux 6.8.0-71-generic
% 0.08/0.40 % CPULimit : 300
% 0.08/0.40 % WCLimit : 300
% 0.08/0.40 % DateTime : Fri Sep 25 14:21:58 UTC 2026
% 0.08/0.40 % CPUTime :
% 0.08/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.40 % Process 2205180 was started by sandbox on n011,
% 0.08/0.40 % Fri Sep 25 14:21:58 2026
% 0.08/0.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.41
% 0.08/0.41 % From the command line: assign(max_seconds, 300).
% 0.08/0.48
% 0.08/0.48 % Assigning unary symbol inverse kb_weight 0 and highest precedence (14).
% 0.08/0.48
% 0.08/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.48
% 0.08/0.48 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.08/0.48 % Length of proof is 29.
% 0.08/0.48 % Level of proof is 8.
% 0.08/0.48 % Maximum clause weight is 70.000.
% 0.08/0.48 % Given clauses 16.
% 0.08/0.48
% 0.08/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------