%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE011+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 : n011.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 2.28s 0.78s
% Output : CNFRefutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 77 ( 62 unt; 0 def)
% Number of atoms : 106 ( 67 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 58 ( 29 ~; 12 |; 11 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 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 : 80 ( 0 sgn 30 !; 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_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(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(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(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(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_17,plain,
? [X0,X1] :
( addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(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(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(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]) ).
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_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_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_54,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_56,negated_conjecture,
addition(addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0)),multiplication(c(sK1),c(sK0))) != one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_970,negated_conjecture,
addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK1),c(sK0))) != one,
inference(paramod,[status(thm)],[c_39,c_56]) ).
cnf(c_57,negated_conjecture,
addition(multiplication(c(sK1),c(sK0)),addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1))) != one,
inference(paramod,[status(thm)],[c_39,c_970]) ).
cnf(c_64,plain,
complement(sK1,c(sK1)),
inference(xxres,[status(thm)],[c_33]) ).
cnf(c_65,plain,
complement(sK0,c(sK0)),
inference(xxres,[status(thm)],[c_34]) ).
cnf(c_971,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_39,c_40]) ).
cnf(c_72,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_40,c_971]) ).
cnf(c_73,negated_conjecture,
addition(multiplication(addition(sK1,c(sK1)),sK0),addition(multiplication(c(sK1),c(sK0)),multiplication(addition(sK0,c(sK0)),sK1))) != one,
inference(paramod,[status(thm)],[c_72,c_57]) ).
cnf(c_972,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_42,c_40]) ).
cnf(c_78,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_972]) ).
cnf(c_84,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_89,negated_conjecture,
addition(multiplication(sK1,sK0),addition(multiplication(c(sK1),sK0),addition(multiplication(c(sK1),c(sK0)),multiplication(addition(sK0,c(sK0)),sK1)))) != one,
inference(paramod,[status(thm)],[c_84,c_73]) ).
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_973,plain,
addition(c(sK1),sK1) = one,
inference(resolve,[status(thm)],[c_64,c_54]) ).
cnf(c_114,plain,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_39,c_973]) ).
cnf(c_974,plain,
addition(c(sK0),sK0) = one,
inference(resolve,[status(thm)],[c_65,c_54]) ).
cnf(c_120,plain,
addition(sK0,c(sK0)) = one,
inference(paramod,[status(thm)],[c_39,c_974]) ).
cnf(c_975,negated_conjecture,
addition(multiplication(sK1,sK0),addition(multiplication(c(sK1),sK0),addition(multiplication(c(sK1),c(sK0)),multiplication(one,sK1)))) != one,
inference(paramod,[status(thm)],[c_120,c_89]) ).
cnf(c_976,negated_conjecture,
addition(multiplication(sK1,sK0),addition(multiplication(c(sK1),sK0),addition(multiplication(c(sK1),c(sK0)),sK1))) != one,
inference(paramod,[status(thm)],[c_45,c_975]) ).
cnf(c_977,negated_conjecture,
addition(multiplication(sK1,sK0),addition(multiplication(c(sK1),sK0),addition(sK1,multiplication(c(sK1),c(sK0))))) != one,
inference(paramod,[status(thm)],[c_39,c_976]) ).
cnf(c_978,negated_conjecture,
addition(multiplication(sK1,sK0),addition(sK1,addition(multiplication(c(sK1),sK0),multiplication(c(sK1),c(sK0))))) != one,
inference(paramod,[status(thm)],[c_72,c_977]) ).
cnf(c_979,negated_conjecture,
addition(multiplication(sK1,sK0),addition(sK1,multiplication(c(sK1),addition(sK0,c(sK0))))) != one,
inference(paramod,[status(thm)],[c_47,c_978]) ).
cnf(c_980,negated_conjecture,
addition(multiplication(sK1,sK0),addition(sK1,multiplication(c(sK1),one))) != one,
inference(paramod,[status(thm)],[c_120,c_979]) ).
cnf(c_981,negated_conjecture,
addition(multiplication(sK1,sK0),addition(sK1,c(sK1))) != one,
inference(paramod,[status(thm)],[c_44,c_980]) ).
cnf(c_982,negated_conjecture,
addition(multiplication(sK1,sK0),one) != one,
inference(paramod,[status(thm)],[c_114,c_981]) ).
cnf(c_127,negated_conjecture,
addition(one,multiplication(sK1,sK0)) != one,
inference(paramod,[status(thm)],[c_39,c_982]) ).
cnf(c_983,plain,
addition(sK0,one) = addition(sK0,sK2(sK0)),
inference(paramod,[status(thm)],[c_97,c_78]) ).
cnf(c_984,plain,
addition(one,sK0) = addition(sK0,sK2(sK0)),
inference(paramod,[status(thm)],[c_39,c_983]) ).
cnf(c_232,plain,
addition(one,sK0) = one,
inference(paramod,[status(thm)],[c_97,c_984]) ).
cnf(c_985,plain,
addition(sK1,one) = addition(sK1,sK2(sK1)),
inference(paramod,[status(thm)],[c_98,c_78]) ).
cnf(c_986,plain,
addition(one,sK1) = addition(sK1,sK2(sK1)),
inference(paramod,[status(thm)],[c_39,c_985]) ).
cnf(c_233,plain,
addition(one,sK1) = one,
inference(paramod,[status(thm)],[c_98,c_986]) ).
cnf(c_987,plain,
addition(one,A) = addition(one,addition(sK0,A)),
inference(paramod,[status(thm)],[c_232,c_40]) ).
cnf(c_235,plain,
addition(one,addition(sK0,A)) = addition(one,A),
inference(copy,[status(thm)],[c_987]) ).
cnf(c_988,plain,
addition(multiplication(one,A),multiplication(sK1,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_233,c_49]) ).
cnf(c_989,plain,
addition(A,multiplication(sK1,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_45,c_988]) ).
cnf(c_244,plain,
addition(A,multiplication(sK1,A)) = A,
inference(paramod,[status(thm)],[c_45,c_989]) ).
cnf(c_990,plain,
addition(one,sK0) = addition(one,multiplication(sK1,sK0)),
inference(paramod,[status(thm)],[c_244,c_235]) ).
cnf(c_991,plain,
one = addition(one,multiplication(sK1,sK0)),
inference(paramod,[status(thm)],[c_232,c_990]) ).
cnf(c_992,plain,
addition(one,multiplication(sK1,sK0)) = one,
inference(copy,[status(thm)],[c_991]) ).
cnf(c_969,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_127,c_992]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE011+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n011.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 19:12:29 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 2648268 was started by sandbox2 on n011,
% 0.16/0.43 % Fri Sep 25 19:12:29 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 2.28/0.78
% 2.28/0.78 % SZS status Theorem for theBenchmark
% 2.28/0.78
% 2.28/0.78 % Proof 1 at 0.24 (+ 0.09) seconds.
% 2.28/0.78 % Length of proof is 48.
% 2.28/0.78 % Level of proof is 6.
% 2.28/0.78 % Maximum clause weight is 23.000.
% 2.28/0.78 % Given clauses 174.
% 2.28/0.78
% 2.28/0.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------