%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP547-1 : TPTP v9.3.1. Released v2.6.0.
% 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 07:30:20 AM UTC 2026
% Result : Unsatisfiable 0.16s 10.41s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 45 unt; 0 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 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 : 92 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(identity,divide(VAR_0,VAR_1)),divide(divide(VAR_1,VAR_2),VAR_0)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = 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_57,plain,
multiply(divide(a3,divide(identity,b3)),c3) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_6]) ).
cnf(c_58,plain,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_57]) ).
cnf(c_59,plain,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != multiply(a3,divide(b3,divide(identity,c3))),
inference(paramod,[status(thm)],[c_2,c_58]) ).
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_59]) ).
cnf(c_8,plain,
divide(divide(identity,A),divide(divide(divide(divide(B,A),C),D),divide(identity,divide(C,B)))) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_10,plain,
divide(divide(identity,divide(divide(divide(A,B),C),identity)),B) = divide(C,A),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_60,plain,
divide(divide(identity,identity),divide(divide(A,B),A)) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_11,plain,
divide(identity,divide(divide(A,B),A)) = B,
inference(paramod,[status(thm)],[c_5,c_60]) ).
cnf(c_61,plain,
divide(divide(identity,divide(divide(A,B),A)),identity) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_13,plain,
divide(A,identity) = A,
inference(paramod,[status(thm)],[c_11,c_61]) ).
cnf(c_14,plain,
divide(divide(identity,divide(divide(A,B),C)),B) = divide(C,A),
inference(paramod,[status(thm)],[c_13,c_10]) ).
cnf(c_62,plain,
divide(divide(identity,divide(A,divide(identity,B))),divide(C,A)) = divide(divide(divide(divide(D,B),E),C),divide(identity,divide(E,D))),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_15,plain,
divide(divide(divide(divide(A,B),C),D),divide(identity,divide(C,A))) = divide(divide(identity,divide(E,divide(identity,B))),divide(D,E)),
inference(copy,[status(thm)],[c_62]) ).
cnf(c_20,plain,
divide(divide(identity,A),divide(identity,divide(identity,divide(B,C)))) = divide(divide(C,A),B),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_23,plain,
divide(divide(identity,divide(identity,A)),divide(A,B)) = B,
inference(paramod,[status(thm)],[c_13,c_1]) ).
cnf(c_29,plain,
divide(identity,divide(A,divide(identity,divide(B,C)))) = divide(divide(C,A),B),
inference(paramod,[status(thm)],[c_1,c_11]) ).
cnf(c_30,plain,
divide(identity,divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_5,c_11]) ).
cnf(c_63,plain,
divide(identity,divide(A,divide(identity,B))) = divide(divide(divide(divide(C,B),D),A),divide(identity,divide(D,C))),
inference(paramod,[status(thm)],[c_8,c_11]) ).
cnf(c_34,plain,
divide(divide(divide(divide(A,B),C),D),divide(identity,divide(C,A))) = divide(identity,divide(D,divide(identity,B))),
inference(copy,[status(thm)],[c_63]) ).
cnf(c_64,plain,
divide(identity,divide(A,identity)) = divide(divide(B,A),B),
inference(paramod,[status(thm)],[c_11,c_11]) ).
cnf(c_65,plain,
divide(identity,A) = divide(divide(B,A),B),
inference(paramod,[status(thm)],[c_13,c_64]) ).
cnf(c_35,plain,
divide(divide(A,B),A) = divide(identity,B),
inference(copy,[status(thm)],[c_65]) ).
cnf(c_39,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_30,c_23]) ).
cnf(c_40,plain,
divide(divide(identity,A),divide(B,C)) = divide(divide(C,A),B),
inference(paramod,[status(thm)],[c_39,c_20]) ).
cnf(c_66,plain,
divide(identity,divide(D,divide(identity,B))) = divide(divide(identity,divide(E,divide(identity,B))),divide(D,E)),
inference(paramod,[status(thm)],[c_34,c_15]) ).
cnf(c_67,plain,
divide(identity,divide(D,divide(identity,B))) = divide(divide(E,divide(E,divide(identity,B))),D),
inference(paramod,[status(thm)],[c_40,c_66]) ).
cnf(c_41,plain,
divide(identity,divide(A,divide(identity,B))) = divide(divide(identity,B),A),
inference(paramod,[status(thm)],[c_39,c_67]) ).
cnf(c_47,plain,
divide(divide(identity,divide(A,B)),C) = divide(divide(B,C),A),
inference(paramod,[status(thm)],[c_41,c_29]) ).
cnf(c_48,plain,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(divide(identity,c3),b3)),
inference(paramod,[status(thm)],[c_41,c_7]) ).
cnf(c_49,plain,
divide(divide(A,B),divide(C,B)) = divide(A,C),
inference(paramod,[status(thm)],[c_47,c_14]) ).
cnf(c_68,plain,
divide(A,B) = divide(identity,divide(B,A)),
inference(paramod,[status(thm)],[c_39,c_35]) ).
cnf(c_50,plain,
divide(identity,divide(A,B)) = divide(B,A),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_51,plain,
divide(divide(A,B),C) = divide(divide(A,C),B),
inference(paramod,[status(thm)],[c_50,c_47]) ).
cnf(c_52,plain,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(divide(identity,b3),c3)),
inference(paramod,[status(thm)],[c_51,c_48]) ).
cnf(c_55,plain,
divide(divide(A,B),divide(identity,C)) = divide(A,divide(B,C)),
inference(paramod,[status(thm)],[c_35,c_49]) ).
cnf(c_56,plain,
$false,
inference(resolve,[status(thm)],[c_55,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP547-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/10.39 % Computer : n005.cluster.edu
% 0.12/10.39 % Model : x86_64 x86_64
% 0.12/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.39 % Memory : 8046.5625MB
% 0.12/10.39 % OS : Linux 6.8.0-71-generic
% 0.12/10.39 % CPULimit : 300
% 0.12/10.39 % WCLimit : 300
% 0.12/10.39 % DateTime : Fri Sep 25 14:59:42 UTC 2026
% 0.12/10.39 % CPUTime :
% 0.12/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/10.39 % Process 3772349 was started by sandbox on n005,
% 0.12/10.39 % Fri Sep 25 14:59:42 2026
% 0.12/10.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/10.40
% 0.16/10.40 % From the command line: assign(max_seconds, 300).
% 0.16/10.41
% 0.16/10.41 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.16/10.41
% 0.16/10.41 % SZS status Unsatisfiable for theBenchmark
% 0.16/10.41
% 0.16/10.41 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.16/10.41 % Length of proof is 29.
% 0.16/10.41 % Level of proof is 11.
% 0.16/10.41 % Maximum clause weight is 95.000.
% 0.16/10.41 % Given clauses 12.
% 0.16/10.41
% 0.16/10.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------