%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE025+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 07:44:07 AM UTC 2026
% Result : Theorem 121.96s 16.91s
% Output : CNFRefutation 121.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 23 unt; 0 def)
% Number of atoms : 53 ( 35 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 8 ~; 4 |; 10 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 17 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A,
file('theBenchmark.p',additive_identity) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A,
file('theBenchmark.p',multiplicative_right_identity) ).
fof(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('theBenchmark.p',right_distributivity) ).
fof(test_2,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('theBenchmark.p',test_2) ).
fof(test_3,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('theBenchmark.p',test_3) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(multiplication(X1,X0),c(X2)) = zero
=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(multiplication(X1,X0),c(X2)) = zero
=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_17,plain,
? [X0,X1,X2] :
( multiplication(multiplication(X1,X0),X2) != multiplication(X1,X0)
& multiplication(multiplication(X1,X0),c(X2)) = zero
& test(X2)
& test(X1) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( multiplication(multiplication(sK1,sK2),sK0) != multiplication(sK1,sK2)
& multiplication(multiplication(sK1,sK2),c(sK0)) = zero
& test(sK0)
& test(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK2]),skolemize(X0,sK2),skolemize(X1,sK1),skolemize(X2,sK0)],[nnf_17]) ).
cnf(c_23,negated_conjecture,
test(sK0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_24,plain,
( complement(A,B)
| c(A) != B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
cnf(c_33,negated_conjecture,
( complement(sK0,A)
| c(sK0) != A ),
inference(resolve,[status(thm)],[c_24,c_23]) ).
cnf(c_39,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_41,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_44,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_46,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_47,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_54,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_56,negated_conjecture,
multiplication(multiplication(sK1,sK2),c(sK0)) = zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_57,negated_conjecture,
multiplication(multiplication(sK1,sK2),sK0) != multiplication(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_64,plain,
complement(sK0,c(sK0)),
inference(xxres,[status(thm)],[c_33]) ).
cnf(c_1132,plain,
A = addition(zero,A),
inference(paramod,[status(thm)],[c_41,c_39]) ).
cnf(c_80,plain,
addition(zero,A) = A,
inference(copy,[status(thm)],[c_1132]) ).
cnf(c_1133,plain,
addition(zero,multiplication(multiplication(sK1,sK2),A)) = multiplication(multiplication(sK1,sK2),addition(c(sK0),A)),
inference(paramod,[status(thm)],[c_56,c_47]) ).
cnf(c_1134,plain,
multiplication(multiplication(sK1,sK2),A) = multiplication(multiplication(sK1,sK2),addition(c(sK0),A)),
inference(paramod,[status(thm)],[c_80,c_1133]) ).
cnf(c_117,plain,
multiplication(multiplication(sK1,sK2),addition(c(sK0),A)) = multiplication(multiplication(sK1,sK2),A),
inference(copy,[status(thm)],[c_1134]) ).
cnf(c_127,plain,
addition(c(sK0),sK0) = one,
inference(resolve,[status(thm)],[c_64,c_54]) ).
cnf(c_1135,plain,
multiplication(multiplication(sK1,sK2),one) = multiplication(multiplication(sK1,sK2),sK0),
inference(paramod,[status(thm)],[c_127,c_117]) ).
cnf(c_1136,plain,
multiplication(sK1,sK2) = multiplication(multiplication(sK1,sK2),sK0),
inference(paramod,[status(thm)],[c_44,c_1135]) ).
cnf(c_1137,plain,
multiplication(multiplication(sK1,sK2),sK0) = multiplication(sK1,sK2),
inference(copy,[status(thm)],[c_1136]) ).
cnf(c_1131,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_57,c_1137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE025+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n003.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 19:16:23 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 854953 was started by sandbox2 on n003,
% 0.16/0.43 % Fri Sep 25 19:16:23 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 121.96/16.91
% 121.96/16.91 % SZS status Theorem for theBenchmark
% 121.96/16.91
% 121.96/16.91 % Proof 1 at 0.27 (+ 0.08) seconds.
% 121.96/16.91 % Length of proof is 23.
% 121.96/16.91 % Level of proof is 5.
% 121.96/16.91 % Maximum clause weight is 38.000.
% 121.96/16.91 % Given clauses 132.
% 121.96/16.91
% 121.96/16.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------