%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP551-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 07:30:21 AM UTC 2026
% Result : Unsatisfiable 0.15s 5.49s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 55 ( 55 unt; 0 def)
% Number of atoms : 55 ( 54 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 12 ( 12 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(identity,VAR_0),divide(divide(divide(VAR_1,VAR_0),VAR_2),VAR_1)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = divide(VAR_0,divide(identity,VAR_1)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = divide(A,divide(identity,B)),
inference(clausify,[status(thm)],[multiply]) ).
fof(identity,axiom,
! [VAR_0] : identity = divide(VAR_0,VAR_0),
file('theBenchmark.p',identity) ).
cnf(c_4,plain,
identity = divide(A,A),
inference(clausify,[status(thm)],[identity]) ).
cnf(c_5,plain,
divide(A,A) = identity,
inference(copy,[status(thm)],[c_4]) ).
fof(prove_these_axioms_3,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('theBenchmark.p',prove_these_axioms_3) ).
cnf(c_6,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(clausify,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_94,plain,
multiply(divide(a3,divide(identity,b3)),c3) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_6]) ).
cnf(c_95,plain,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_94]) ).
cnf(c_96,plain,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != multiply(a3,divide(b3,divide(identity,c3))),
inference(paramod,[status(thm)],[c_2,c_95]) ).
cnf(c_7,plain,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(paramod,[status(thm)],[c_2,c_96]) ).
cnf(c_8,plain,
divide(divide(identity,divide(divide(divide(A,B),C),A)),divide(divide(C,D),divide(identity,B))) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_97,plain,
divide(divide(identity,A),divide(B,identity)) = divide(divide(divide(C,A),B),C),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_9,plain,
divide(divide(divide(A,B),C),A) = divide(divide(identity,B),divide(C,identity)),
inference(copy,[status(thm)],[c_97]) ).
cnf(c_12,plain,
divide(divide(identity,A),divide(identity,B)) = divide(B,A),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_13,plain,
divide(divide(identity,divide(divide(divide(A,B),C),A)),divide(D,identity)) = divide(divide(C,D),divide(identity,B)),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_19,plain,
divide(divide(identity,divide(divide(divide(A,B),identity),A)),identity) = B,
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_21,plain,
divide(identity,divide(identity,A)) = divide(A,identity),
inference(paramod,[status(thm)],[c_5,c_12]) ).
cnf(c_22,plain,
divide(divide(identity,A),identity) = divide(identity,A),
inference(paramod,[status(thm)],[c_5,c_12]) ).
cnf(c_26,plain,
divide(divide(identity,divide(divide(divide(A,B),identity),A)),divide(B,C)) = C,
inference(paramod,[status(thm)],[c_12,c_8]) ).
cnf(c_30,plain,
divide(identity,divide(divide(divide(A,B),identity),A)) = B,
inference(paramod,[status(thm)],[c_22,c_19]) ).
cnf(c_31,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_30,c_26]) ).
cnf(c_98,plain,
A = divide(A,identity),
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_32,plain,
divide(A,identity) = A,
inference(copy,[status(thm)],[c_98]) ).
cnf(c_33,plain,
divide(identity,divide(divide(A,B),A)) = B,
inference(paramod,[status(thm)],[c_32,c_30]) ).
cnf(c_40,plain,
divide(divide(identity,divide(divide(divide(A,B),C),A)),D) = divide(divide(C,D),divide(identity,B)),
inference(paramod,[status(thm)],[c_32,c_13]) ).
cnf(c_41,plain,
divide(divide(divide(A,B),C),A) = divide(divide(identity,B),C),
inference(paramod,[status(thm)],[c_32,c_9]) ).
cnf(c_45,plain,
divide(divide(identity,divide(divide(identity,A),B)),C) = divide(divide(B,C),divide(identity,A)),
inference(paramod,[status(thm)],[c_41,c_40]) ).
cnf(c_48,plain,
divide(A,divide(identity,B)) = divide(B,divide(identity,A)),
inference(paramod,[status(thm)],[c_31,c_12]) ).
cnf(c_49,plain,
divide(divide(identity,A),B) = divide(divide(identity,B),A),
inference(paramod,[status(thm)],[c_31,c_12]) ).
cnf(c_53,plain,
divide(c3,divide(identity,divide(a3,divide(identity,b3)))) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(paramod,[status(thm)],[c_48,c_7]) ).
cnf(c_59,plain,
divide(identity,divide(A,B)) = divide(B,A),
inference(paramod,[status(thm)],[c_31,c_33]) ).
cnf(c_99,plain,
divide(c3,divide(divide(identity,b3),a3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(paramod,[status(thm)],[c_59,c_53]) ).
cnf(c_100,plain,
divide(c3,divide(divide(identity,a3),b3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(paramod,[status(thm)],[c_49,c_99]) ).
cnf(c_101,plain,
divide(c3,divide(divide(identity,a3),b3)) != divide(a3,divide(divide(identity,c3),b3)),
inference(paramod,[status(thm)],[c_59,c_100]) ).
cnf(c_60,plain,
divide(c3,divide(divide(identity,a3),b3)) != divide(a3,divide(divide(identity,b3),c3)),
inference(paramod,[status(thm)],[c_49,c_101]) ).
cnf(c_63,plain,
divide(divide(A,divide(identity,B)),C) = divide(divide(A,C),divide(identity,B)),
inference(paramod,[status(thm)],[c_59,c_45]) ).
cnf(c_66,plain,
divide(divide(A,B),divide(identity,C)) = divide(C,divide(B,A)),
inference(paramod,[status(thm)],[c_59,c_12]) ).
cnf(c_67,plain,
divide(divide(identity,A),divide(B,C)) = divide(divide(C,B),A),
inference(paramod,[status(thm)],[c_59,c_12]) ).
cnf(c_69,plain,
divide(divide(A,divide(identity,B)),C) = divide(B,divide(C,A)),
inference(paramod,[status(thm)],[c_66,c_63]) ).
cnf(c_102,plain,
divide(divide(identity,A),divide(divide(identity,B),C)) = divide(divide(B,divide(identity,C)),A),
inference(paramod,[status(thm)],[c_48,c_67]) ).
cnf(c_103,plain,
divide(divide(C,divide(identity,B)),A) = divide(divide(B,divide(identity,C)),A),
inference(paramod,[status(thm)],[c_67,c_102]) ).
cnf(c_104,plain,
divide(B,divide(A,C)) = divide(divide(B,divide(identity,C)),A),
inference(paramod,[status(thm)],[c_69,c_103]) ).
cnf(c_75,plain,
divide(A,divide(B,C)) = divide(C,divide(B,A)),
inference(paramod,[status(thm)],[c_69,c_104]) ).
cnf(c_78,plain,
divide(b3,divide(divide(identity,a3),c3)) != divide(a3,divide(divide(identity,b3),c3)),
inference(paramod,[status(thm)],[c_75,c_60]) ).
cnf(c_105,plain,
divide(A,divide(B,divide(identity,C))) = divide(divide(identity,divide(B,A)),C),
inference(paramod,[status(thm)],[c_75,c_49]) ).
cnf(c_81,plain,
divide(A,divide(B,divide(identity,C))) = divide(divide(A,B),C),
inference(paramod,[status(thm)],[c_59,c_105]) ).
cnf(c_106,plain,
divide(divide(identity,divide(A,B)),divide(C,D)) = divide(B,divide(A,divide(D,C))),
inference(paramod,[status(thm)],[c_75,c_67]) ).
cnf(c_91,plain,
divide(divide(A,B),divide(C,D)) = divide(A,divide(B,divide(D,C))),
inference(paramod,[status(thm)],[c_59,c_106]) ).
cnf(c_107,plain,
divide(A,divide(divide(B,C),D)) = divide(divide(C,B),divide(divide(identity,D),A)),
inference(paramod,[status(thm)],[c_67,c_75]) ).
cnf(c_108,plain,
divide(A,divide(divide(B,C),D)) = divide(C,divide(B,divide(A,divide(identity,D)))),
inference(paramod,[status(thm)],[c_91,c_107]) ).
cnf(c_92,plain,
divide(A,divide(divide(B,C),D)) = divide(C,divide(divide(B,A),D)),
inference(paramod,[status(thm)],[c_81,c_108]) ).
cnf(c_93,plain,
$false,
inference(resolve,[status(thm)],[c_92,c_78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP551-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.44 % Computer : n015.cluster.edu
% 0.15/5.44 % Model : x86_64 x86_64
% 0.15/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.44 % Memory : 8046.5625MB
% 0.15/5.44 % OS : Linux 6.8.0-71-generic
% 0.15/5.45 % CPULimit : 300
% 0.15/5.45 % WCLimit : 300
% 0.15/5.45 % DateTime : Fri Sep 25 15:03:04 UTC 2026
% 0.15/5.45 % CPUTime :
% 0.15/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/5.45 % Process 1674238 was started by sandbox2 on n015,
% 0.15/5.45 % Fri Sep 25 15:03:04 2026
% 0.15/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/5.46
% 0.15/5.46 % From the command line: assign(max_seconds, 300).
% 0.15/5.49
% 0.15/5.49 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.15/5.49
% 0.15/5.49 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.49
% 0.15/5.49 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.15/5.49 % Length of proof is 36.
% 0.15/5.49 % Level of proof is 14.
% 0.15/5.49 % Maximum clause weight is 86.000.
% 0.15/5.49 % Given clauses 20.
% 0.15/5.49
% 0.15/5.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------