%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE013+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 07:44:04 AM UTC 2026
% Result : Theorem 25.68s 8.87s
% Output : CNFRefutation 25.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 13
% Syntax : Number of formulae : 104 ( 76 unt; 0 def)
% Number of atoms : 152 ( 98 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 94 ( 46 ~; 34 |; 8 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 126 ( 5 sgn 25 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(additive_associativity,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('theBenchmark.p',additive_associativity) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A,
file('theBenchmark.p',additive_identity) ).
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',additive_idempotence) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A,
file('theBenchmark.p',multiplicative_right_identity) ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('theBenchmark.p',multiplicative_left_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(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('theBenchmark.p',left_distributivity) ).
fof(right_annihilation,axiom,
! [A] : multiplication(A,zero) = zero,
file('theBenchmark.p',right_annihilation) ).
fof(test_1,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('theBenchmark.p',test_1) ).
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] :
( ( test(X0)
& test(X1) )
=> one = addition(addition(X0,X1),multiplication(c(X0),c(X1))) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> one = addition(addition(X0,X1),multiplication(c(X0),c(X1))) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_20,plain,
( ~ complement(A,B)
| c(A) = B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
fof(nnf_17,plain,
? [X0,X1] :
( addition(addition(X0,X1),multiplication(c(X0),c(X1))) != one
& test(X0)
& test(X1) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( addition(addition(sK1,sK0),multiplication(c(sK1),c(sK0))) != one
& test(sK1)
& test(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK1),skolemize(X1,sK0)],[nnf_17]) ).
cnf(c_22,negated_conjecture,
test(sK0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_23,negated_conjecture,
test(sK1),
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_25,plain,
( ~ complement(B,A)
| test(A) ),
inference(clausify,[status(thm)],[test_1]) ).
cnf(c_31,plain,
( ~ complement(B,C)
| c(B) = C
| ~ complement(A,B) ),
inference(resolve,[status(thm)],[c_25,c_20]) ).
cnf(c_32,plain,
( complement(B,C)
| c(B) != C
| ~ complement(A,B) ),
inference(resolve,[status(thm)],[c_25,c_24]) ).
cnf(c_33,negated_conjecture,
( complement(sK1,A)
| c(sK1) != A ),
inference(resolve,[status(thm)],[c_24,c_23]) ).
cnf(c_34,negated_conjecture,
( complement(sK0,A)
| c(sK0) != A ),
inference(resolve,[status(thm)],[c_24,c_22]) ).
cnf(c_39,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_40,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_41,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_42,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_44,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_45,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_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_48,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_49,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_50,plain,
multiplication(A,zero) = zero,
inference(clausify,[status(thm)],[right_annihilation]) ).
cnf(c_54,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_55,plain,
( addition(B,A) != one
| multiplication(A,B) != zero
| multiplication(B,A) != zero
| complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_56,negated_conjecture,
addition(addition(sK1,sK0),multiplication(c(sK1),c(sK0))) != one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_57,negated_conjecture,
addition(sK1,addition(sK0,multiplication(c(sK1),c(sK0)))) != one,
inference(paramod,[status(thm)],[c_40,c_56]) ).
cnf(c_64,plain,
( complement(B,c(B))
| ~ complement(A,B) ),
inference(xxres,[status(thm)],[c_32]) ).
cnf(c_65,plain,
complement(sK1,c(sK1)),
inference(xxres,[status(thm)],[c_33]) ).
cnf(c_66,plain,
complement(sK0,c(sK0)),
inference(xxres,[status(thm)],[c_34]) ).
cnf(c_4907,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_39,c_40]) ).
cnf(c_73,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_40,c_4907]) ).
cnf(c_4908,plain,
A = addition(zero,A),
inference(paramod,[status(thm)],[c_41,c_39]) ).
cnf(c_78,plain,
addition(zero,A) = A,
inference(copy,[status(thm)],[c_4908]) ).
cnf(c_4909,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_42,c_40]) ).
cnf(c_79,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_4909]) ).
cnf(c_4910,plain,
addition(addition(A,B),B) = addition(A,B),
inference(paramod,[status(thm)],[c_42,c_40]) ).
cnf(c_81,plain,
addition(A,addition(B,A)) = addition(B,A),
inference(paramod,[status(thm)],[c_39,c_4910]) ).
cnf(c_4911,plain,
addition(multiplication(addition(A,B),C),D) = addition(multiplication(A,C),addition(multiplication(B,C),D)),
inference(paramod,[status(thm)],[c_49,c_40]) ).
cnf(c_85,plain,
addition(multiplication(A,B),addition(multiplication(C,B),D)) = addition(multiplication(addition(A,C),B),D),
inference(copy,[status(thm)],[c_4911]) ).
cnf(c_4912,plain,
( addition(one,zero) != one
| multiplication(zero,one) != zero
| complement(zero,one) ),
inference(resolve,[status(thm)],[c_55,c_45]) ).
cnf(c_4913,plain,
( addition(one,zero) != one
| zero != zero
| complement(zero,one) ),
inference(paramod,[status(thm)],[c_44,c_4912]) ).
cnf(c_4914,plain,
( addition(zero,one) != one
| zero != zero
| complement(zero,one) ),
inference(paramod,[status(thm)],[c_39,c_4913]) ).
cnf(c_4915,plain,
( one != one
| zero != zero
| complement(zero,one) ),
inference(paramod,[status(thm)],[c_78,c_4914]) ).
cnf(c_4916,plain,
( one != one
| complement(zero,one) ),
inference(copy,[status(thm)],[c_4915]) ).
cnf(c_101,plain,
complement(zero,one),
inference(copy,[status(thm)],[c_4916]) ).
cnf(c_4917,plain,
( addition(zero,one) != one
| multiplication(one,zero) != zero
| complement(one,zero) ),
inference(resolve,[status(thm)],[c_55,c_44]) ).
cnf(c_4918,plain,
( addition(zero,one) != one
| zero != zero
| complement(one,zero) ),
inference(paramod,[status(thm)],[c_50,c_4917]) ).
cnf(c_4919,plain,
( one != one
| zero != zero
| complement(one,zero) ),
inference(paramod,[status(thm)],[c_78,c_4918]) ).
cnf(c_4920,plain,
( one != one
| complement(one,zero) ),
inference(copy,[status(thm)],[c_4919]) ).
cnf(c_102,plain,
complement(one,zero),
inference(copy,[status(thm)],[c_4920]) ).
cnf(c_112,plain,
( ~ complement(zero,A)
| c(zero) = A ),
inference(resolve,[status(thm)],[c_102,c_31]) ).
cnf(c_4921,plain,
addition(c(sK1),sK1) = one,
inference(resolve,[status(thm)],[c_65,c_54]) ).
cnf(c_116,plain,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_39,c_4921]) ).
cnf(c_4922,plain,
addition(c(sK0),sK0) = one,
inference(resolve,[status(thm)],[c_66,c_54]) ).
cnf(c_122,plain,
addition(sK0,c(sK0)) = one,
inference(paramod,[status(thm)],[c_39,c_4922]) ).
cnf(c_132,plain,
complement(zero,c(zero)),
inference(resolve,[status(thm)],[c_64,c_102]) ).
cnf(c_4923,plain,
addition(c(zero),zero) = one,
inference(resolve,[status(thm)],[c_132,c_54]) ).
cnf(c_4924,plain,
addition(zero,c(zero)) = one,
inference(paramod,[status(thm)],[c_39,c_4923]) ).
cnf(c_136,plain,
c(zero) = one,
inference(paramod,[status(thm)],[c_78,c_4924]) ).
cnf(c_137,plain,
( ~ complement(zero,A)
| one = A ),
inference(paramod,[status(thm)],[c_136,c_112]) ).
cnf(c_4925,negated_conjecture,
one != addition(sK1,addition(sK0,multiplication(c(sK1),c(sK0)))),
inference(copy,[status(thm)],[c_57]) ).
cnf(c_138,negated_conjecture,
~ complement(zero,addition(sK1,addition(sK0,multiplication(c(sK1),c(sK0))))),
inference(resolve,[status(thm)],[c_137,c_4925]) ).
cnf(c_4926,plain,
addition(A,multiplication(B,addition(C,D))) = addition(multiplication(B,C),addition(A,multiplication(B,D))),
inference(paramod,[status(thm)],[c_47,c_73]) ).
cnf(c_190,plain,
addition(multiplication(A,B),addition(C,multiplication(A,D))) = addition(C,multiplication(A,addition(B,D))),
inference(copy,[status(thm)],[c_4926]) ).
cnf(c_4927,plain,
addition(sK0,one) = addition(sK0,c(sK0)),
inference(paramod,[status(thm)],[c_122,c_79]) ).
cnf(c_4928,plain,
addition(one,sK0) = addition(sK0,c(sK0)),
inference(paramod,[status(thm)],[c_39,c_4927]) ).
cnf(c_211,plain,
addition(one,sK0) = one,
inference(paramod,[status(thm)],[c_122,c_4928]) ).
cnf(c_4929,plain,
addition(multiplication(A,one),multiplication(A,sK0)) = multiplication(A,one),
inference(paramod,[status(thm)],[c_211,c_47]) ).
cnf(c_4930,plain,
addition(A,multiplication(A,sK0)) = multiplication(A,one),
inference(paramod,[status(thm)],[c_44,c_4929]) ).
cnf(c_221,plain,
addition(A,multiplication(A,sK0)) = A,
inference(paramod,[status(thm)],[c_44,c_4930]) ).
cnf(c_4931,plain,
addition(A,addition(B,addition(C,A))) = addition(addition(B,C),A),
inference(paramod,[status(thm)],[c_40,c_81]) ).
cnf(c_230,plain,
addition(A,addition(B,addition(C,A))) = addition(B,addition(C,A)),
inference(paramod,[status(thm)],[c_40,c_4931]) ).
cnf(c_4932,plain,
addition(multiplication(A,sK0),addition(B,A)) = addition(B,addition(A,multiplication(A,sK0))),
inference(paramod,[status(thm)],[c_221,c_230]) ).
cnf(c_1545,plain,
addition(multiplication(A,sK0),addition(B,A)) = addition(B,A),
inference(paramod,[status(thm)],[c_221,c_4932]) ).
cnf(c_4933,plain,
addition(multiplication(A,sK0),B) = addition(multiplication(addition(B,A),sK0),B),
inference(paramod,[status(thm)],[c_1545,c_85]) ).
cnf(c_4934,plain,
addition(multiplication(A,sK0),B) = addition(B,multiplication(addition(B,A),sK0)),
inference(paramod,[status(thm)],[c_39,c_4933]) ).
cnf(c_1626,plain,
addition(A,multiplication(addition(A,B),sK0)) = addition(multiplication(B,sK0),A),
inference(copy,[status(thm)],[c_4934]) ).
cnf(c_4935,plain,
addition(sK1,multiplication(one,sK0)) = addition(multiplication(c(sK1),sK0),sK1),
inference(paramod,[status(thm)],[c_116,c_1626]) ).
cnf(c_4936,plain,
addition(sK1,sK0) = addition(multiplication(c(sK1),sK0),sK1),
inference(paramod,[status(thm)],[c_45,c_4935]) ).
cnf(c_4937,plain,
addition(sK1,sK0) = addition(sK1,multiplication(c(sK1),sK0)),
inference(paramod,[status(thm)],[c_39,c_4936]) ).
cnf(c_4845,plain,
addition(sK1,multiplication(c(sK1),sK0)) = addition(sK1,sK0),
inference(copy,[status(thm)],[c_4937]) ).
cnf(c_4938,plain,
addition(multiplication(c(sK1),A),addition(sK1,sK0)) = addition(sK1,multiplication(c(sK1),addition(A,sK0))),
inference(paramod,[status(thm)],[c_4845,c_190]) ).
cnf(c_4939,plain,
addition(addition(sK1,sK0),multiplication(c(sK1),A)) = addition(sK1,multiplication(c(sK1),addition(A,sK0))),
inference(paramod,[status(thm)],[c_39,c_4938]) ).
cnf(c_4900,plain,
addition(sK1,addition(sK0,multiplication(c(sK1),A))) = addition(sK1,multiplication(c(sK1),addition(A,sK0))),
inference(paramod,[status(thm)],[c_40,c_4939]) ).
cnf(c_4940,negated_conjecture,
~ complement(zero,addition(sK1,multiplication(c(sK1),addition(c(sK0),sK0)))),
inference(paramod,[status(thm)],[c_4900,c_138]) ).
cnf(c_4941,negated_conjecture,
~ complement(zero,addition(sK1,multiplication(c(sK1),addition(sK0,c(sK0))))),
inference(paramod,[status(thm)],[c_39,c_4940]) ).
cnf(c_4942,negated_conjecture,
~ complement(zero,addition(sK1,multiplication(c(sK1),one))),
inference(paramod,[status(thm)],[c_122,c_4941]) ).
cnf(c_4943,negated_conjecture,
~ complement(zero,addition(sK1,c(sK1))),
inference(paramod,[status(thm)],[c_44,c_4942]) ).
cnf(c_4944,negated_conjecture,
~ complement(zero,one),
inference(paramod,[status(thm)],[c_116,c_4943]) ).
cnf(c_4906,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_101,c_4944]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE013+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.54 % Computer : n002.cluster.edu
% 0.12/5.54 % Model : x86_64 x86_64
% 0.12/5.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.54 % Memory : 8046.5625MB
% 0.12/5.54 % OS : Linux 6.8.0-71-generic
% 0.12/5.54 % CPULimit : 300
% 0.12/5.54 % WCLimit : 300
% 0.12/5.54 % DateTime : Fri Sep 25 19:15:42 UTC 2026
% 0.12/5.54 % CPUTime :
% 0.12/5.54 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/5.54 % Process 3913466 was started by sandbox on n002,
% 0.12/5.54 % Fri Sep 25 19:15:42 2026
% 0.12/5.54 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/5.55
% 0.12/5.55 % From the command line: assign(max_seconds, 300).
% 25.68/8.87
% 25.68/8.87 % SZS status Theorem for theBenchmark
% 25.68/8.87
% 25.68/8.87 % Proof 1 at 2.51 (+ 0.72) seconds.
% 25.68/8.87 % Length of proof is 63.
% 25.68/8.87 % Level of proof is 11.
% 25.68/8.87 % Maximum clause weight is 44.000.
% 25.68/8.87 % Given clauses 407.
% 25.68/8.87
% 25.68/8.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------