%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE015+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 : n010.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 07:44:05 AM UTC 2026
% Result : Theorem 1.75s 0.67s
% Output : CNFRefutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 12
% Syntax : Number of formulae : 101 ( 70 unt; 0 def)
% Number of atoms : 157 ( 99 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 101 ( 45 ~; 39 |; 11 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn 33 !; 4 ?)
% 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_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('theBenchmark.p',multiplicative_associativity) ).
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(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('theBenchmark.p',left_distributivity) ).
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) )
=> multiplication(multiplication(addition(X0,X1),c(X0)),c(X1)) = zero ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> multiplication(multiplication(addition(X0,X1),c(X0)),c(X1)) = zero ),
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] :
( multiplication(multiplication(addition(X0,X1),c(X0)),c(X1)) != zero
& test(X0)
& test(X1) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( multiplication(multiplication(addition(sK1,sK0),c(sK1)),c(sK0)) != zero
& 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]) ).
fof(nnf_13,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( ? [X2] : complement(X2,X0)
| ~ test(X0) ) ),
inference(fof_nnf,[status(thm)],[test_1]) ).
fof(sk_test_1_sk,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( complement(sK2(X0),X0)
| ~ test(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0))],[nnf_13]) ).
fof(sk_test_1,plain,
( ! [VAR_0,VAR_1] :
( ~ complement(VAR_1,VAR_0)
| test(VAR_0) )
& ! [VAR_0] :
( complement(sK2(VAR_0),VAR_0)
| ~ test(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_test_1_sk]) ).
cnf(c_26,plain,
( complement(sK2(A),A)
| ~ test(A) ),
inference(split_conjunct,[status(thm)],[sk_test_1]) ).
cnf(c_27,negated_conjecture,
complement(sK2(sK1),sK1),
inference(resolve,[status(thm)],[c_26,c_23]) ).
cnf(c_28,negated_conjecture,
complement(sK2(sK0),sK0),
inference(resolve,[status(thm)],[c_26,c_22]) ).
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_36,negated_conjecture,
( ~ complement(sK1,A)
| c(sK1) = A ),
inference(resolve,[status(thm)],[c_20,c_23]) ).
cnf(c_37,negated_conjecture,
( ~ complement(sK0,A)
| c(sK0) = A ),
inference(resolve,[status(thm)],[c_20,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_43,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
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_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_52,plain,
( multiplication(B,A) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_53,plain,
( multiplication(A,B) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
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,
multiplication(multiplication(addition(sK1,sK0),c(sK1)),c(sK0)) != zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_57,negated_conjecture,
multiplication(addition(sK1,sK0),multiplication(c(sK1),c(sK0))) != zero,
inference(paramod,[status(thm)],[c_43,c_56]) ).
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_824,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_824]) ).
cnf(c_825,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_825]) ).
cnf(c_91,plain,
multiplication(sK0,sK2(sK0)) = zero,
inference(resolve,[status(thm)],[c_52,c_28]) ).
cnf(c_92,plain,
multiplication(sK1,sK2(sK1)) = zero,
inference(resolve,[status(thm)],[c_52,c_27]) ).
cnf(c_94,plain,
multiplication(sK2(sK0),sK0) = zero,
inference(resolve,[status(thm)],[c_53,c_28]) ).
cnf(c_95,plain,
multiplication(sK2(sK1),sK1) = zero,
inference(resolve,[status(thm)],[c_53,c_27]) ).
cnf(c_97,plain,
addition(sK0,sK2(sK0)) = one,
inference(resolve,[status(thm)],[c_54,c_28]) ).
cnf(c_98,plain,
addition(sK1,sK2(sK1)) = one,
inference(resolve,[status(thm)],[c_54,c_27]) ).
cnf(c_826,plain,
addition(c(sK1),sK1) = one,
inference(resolve,[status(thm)],[c_65,c_54]) ).
cnf(c_118,plain,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_39,c_826]) ).
cnf(c_125,plain,
multiplication(sK0,c(sK0)) = zero,
inference(resolve,[status(thm)],[c_66,c_53]) ).
cnf(c_827,plain,
( addition(sK2(sK0),sK0) != one
| multiplication(sK2(sK0),sK0) != zero
| complement(sK0,sK2(sK0)) ),
inference(resolve,[status(thm)],[c_91,c_55]) ).
cnf(c_828,plain,
( addition(sK2(sK0),sK0) != one
| zero != zero
| complement(sK0,sK2(sK0)) ),
inference(paramod,[status(thm)],[c_94,c_827]) ).
cnf(c_829,plain,
( addition(sK0,sK2(sK0)) != one
| zero != zero
| complement(sK0,sK2(sK0)) ),
inference(paramod,[status(thm)],[c_39,c_828]) ).
cnf(c_830,plain,
( one != one
| zero != zero
| complement(sK0,sK2(sK0)) ),
inference(paramod,[status(thm)],[c_97,c_829]) ).
cnf(c_831,plain,
( one != one
| complement(sK0,sK2(sK0)) ),
inference(copy,[status(thm)],[c_830]) ).
cnf(c_147,plain,
complement(sK0,sK2(sK0)),
inference(copy,[status(thm)],[c_831]) ).
cnf(c_832,plain,
addition(zero,multiplication(A,sK2(sK0))) = multiplication(addition(sK0,A),sK2(sK0)),
inference(paramod,[status(thm)],[c_91,c_49]) ).
cnf(c_833,plain,
multiplication(A,sK2(sK0)) = multiplication(addition(sK0,A),sK2(sK0)),
inference(paramod,[status(thm)],[c_78,c_832]) ).
cnf(c_151,plain,
multiplication(addition(sK0,A),sK2(sK0)) = multiplication(A,sK2(sK0)),
inference(copy,[status(thm)],[c_833]) ).
cnf(c_834,negated_conjecture,
c(sK0) = sK2(sK0),
inference(resolve,[status(thm)],[c_147,c_37]) ).
cnf(c_156,negated_conjecture,
sK2(sK0) = c(sK0),
inference(copy,[status(thm)],[c_834]) ).
cnf(c_835,plain,
multiplication(addition(sK0,A),c(sK0)) = multiplication(A,sK2(sK0)),
inference(paramod,[status(thm)],[c_156,c_151]) ).
cnf(c_159,plain,
multiplication(addition(sK0,A),c(sK0)) = multiplication(A,c(sK0)),
inference(paramod,[status(thm)],[c_156,c_835]) ).
cnf(c_836,plain,
( addition(sK2(sK1),sK1) != one
| multiplication(sK2(sK1),sK1) != zero
| complement(sK1,sK2(sK1)) ),
inference(resolve,[status(thm)],[c_92,c_55]) ).
cnf(c_837,plain,
( addition(sK2(sK1),sK1) != one
| zero != zero
| complement(sK1,sK2(sK1)) ),
inference(paramod,[status(thm)],[c_95,c_836]) ).
cnf(c_838,plain,
( addition(sK1,sK2(sK1)) != one
| zero != zero
| complement(sK1,sK2(sK1)) ),
inference(paramod,[status(thm)],[c_39,c_837]) ).
cnf(c_839,plain,
( one != one
| zero != zero
| complement(sK1,sK2(sK1)) ),
inference(paramod,[status(thm)],[c_98,c_838]) ).
cnf(c_840,plain,
( one != one
| complement(sK1,sK2(sK1)) ),
inference(copy,[status(thm)],[c_839]) ).
cnf(c_171,plain,
complement(sK1,sK2(sK1)),
inference(copy,[status(thm)],[c_840]) ).
cnf(c_841,plain,
addition(zero,multiplication(A,sK2(sK1))) = multiplication(addition(sK1,A),sK2(sK1)),
inference(paramod,[status(thm)],[c_92,c_49]) ).
cnf(c_842,plain,
multiplication(A,sK2(sK1)) = multiplication(addition(sK1,A),sK2(sK1)),
inference(paramod,[status(thm)],[c_78,c_841]) ).
cnf(c_175,plain,
multiplication(addition(sK1,A),sK2(sK1)) = multiplication(A,sK2(sK1)),
inference(copy,[status(thm)],[c_842]) ).
cnf(c_843,negated_conjecture,
c(sK1) = sK2(sK1),
inference(resolve,[status(thm)],[c_171,c_36]) ).
cnf(c_180,negated_conjecture,
sK2(sK1) = c(sK1),
inference(copy,[status(thm)],[c_843]) ).
cnf(c_844,plain,
multiplication(addition(sK1,A),c(sK1)) = multiplication(A,sK2(sK1)),
inference(paramod,[status(thm)],[c_180,c_175]) ).
cnf(c_183,plain,
multiplication(addition(sK1,A),c(sK1)) = multiplication(A,c(sK1)),
inference(paramod,[status(thm)],[c_180,c_844]) ).
cnf(c_845,plain,
addition(c(sK1),one) = addition(sK1,c(sK1)),
inference(paramod,[status(thm)],[c_118,c_81]) ).
cnf(c_846,plain,
addition(one,c(sK1)) = addition(sK1,c(sK1)),
inference(paramod,[status(thm)],[c_39,c_845]) ).
cnf(c_232,plain,
addition(one,c(sK1)) = one,
inference(paramod,[status(thm)],[c_118,c_846]) ).
cnf(c_847,plain,
addition(multiplication(A,one),multiplication(A,c(sK1))) = multiplication(A,one),
inference(paramod,[status(thm)],[c_232,c_47]) ).
cnf(c_848,plain,
addition(A,multiplication(A,c(sK1))) = multiplication(A,one),
inference(paramod,[status(thm)],[c_44,c_847]) ).
cnf(c_242,plain,
addition(A,multiplication(A,c(sK1))) = A,
inference(paramod,[status(thm)],[c_44,c_848]) ).
cnf(c_849,plain,
multiplication(multiplication(A,c(sK1)),B) = multiplication(addition(sK1,A),multiplication(c(sK1),B)),
inference(paramod,[status(thm)],[c_183,c_43]) ).
cnf(c_850,plain,
multiplication(A,multiplication(c(sK1),B)) = multiplication(addition(sK1,A),multiplication(c(sK1),B)),
inference(paramod,[status(thm)],[c_43,c_849]) ).
cnf(c_475,plain,
multiplication(addition(sK1,A),multiplication(c(sK1),B)) = multiplication(A,multiplication(c(sK1),B)),
inference(copy,[status(thm)],[c_850]) ).
cnf(c_484,negated_conjecture,
multiplication(sK0,multiplication(c(sK1),c(sK0))) != zero,
inference(paramod,[status(thm)],[c_475,c_57]) ).
cnf(c_851,plain,
multiplication(sK0,c(sK0)) = multiplication(multiplication(sK0,c(sK1)),c(sK0)),
inference(paramod,[status(thm)],[c_242,c_159]) ).
cnf(c_852,plain,
zero = multiplication(multiplication(sK0,c(sK1)),c(sK0)),
inference(paramod,[status(thm)],[c_125,c_851]) ).
cnf(c_853,plain,
zero = multiplication(sK0,multiplication(c(sK1),c(sK0))),
inference(paramod,[status(thm)],[c_43,c_852]) ).
cnf(c_854,plain,
multiplication(sK0,multiplication(c(sK1),c(sK0))) = zero,
inference(copy,[status(thm)],[c_853]) ).
cnf(c_823,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_484,c_854]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE015+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n010.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 19:13:44 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.35 % Process 1423372 was started by sandbox on n010,
% 0.10/0.35 % Fri Sep 25 19:13:44 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 1.75/0.67
% 1.75/0.67 % SZS status Theorem for theBenchmark
% 1.75/0.67
% 1.75/0.67 % Proof 1 at 0.14 (+ 0.06) seconds.
% 1.75/0.67 % Length of proof is 64.
% 1.75/0.67 % Level of proof is 9.
% 1.75/0.67 % Maximum clause weight is 39.000.
% 1.75/0.67 % Given clauses 184.
% 1.75/0.67
% 1.75/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------