%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE023+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 : n018.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 43.25s 5.86s
% Output : CNFRefutation 43.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 87 ( 76 unt; 0 def)
% Number of atoms : 110 ( 88 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 11 ~; 6 |; 10 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 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 : 103 ( 1 sgn 29 !; 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_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(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_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) )
=> ( addition(multiplication(X1,X0),multiplication(X0,X2)) = multiplication(X0,X2)
=> addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( addition(multiplication(X1,X0),multiplication(X0,X2)) = multiplication(X0,X2)
=> addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_17,plain,
? [X0,X1,X2] :
( multiplication(c(X1),X0) != addition(multiplication(X0,c(X2)),multiplication(c(X1),X0))
& multiplication(X0,X2) = addition(multiplication(X1,X0),multiplication(X0,X2))
& test(X2)
& test(X1) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( multiplication(c(sK0),sK2) != addition(multiplication(sK2,c(sK1)),multiplication(c(sK0),sK2))
& multiplication(sK2,sK1) = addition(multiplication(sK0,sK2),multiplication(sK2,sK1))
& test(sK1)
& test(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK2),skolemize(X1,sK0),skolemize(X2,sK1)],[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_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_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_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_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_56,negated_conjecture,
multiplication(sK2,sK1) = addition(multiplication(sK0,sK2),multiplication(sK2,sK1)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_16607,negated_conjecture,
multiplication(sK2,sK1) = addition(multiplication(sK2,sK1),multiplication(sK0,sK2)),
inference(paramod,[status(thm)],[c_39,c_56]) ).
cnf(c_57,negated_conjecture,
addition(multiplication(sK2,sK1),multiplication(sK0,sK2)) = multiplication(sK2,sK1),
inference(copy,[status(thm)],[c_16607]) ).
cnf(c_58,negated_conjecture,
multiplication(c(sK0),sK2) != addition(multiplication(sK2,c(sK1)),multiplication(c(sK0),sK2)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_59,negated_conjecture,
addition(multiplication(sK2,c(sK1)),multiplication(c(sK0),sK2)) != multiplication(c(sK0),sK2),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_67,plain,
complement(sK1,c(sK1)),
inference(xxres,[status(thm)],[c_33]) ).
cnf(c_68,plain,
complement(sK0,c(sK0)),
inference(xxres,[status(thm)],[c_34]) ).
cnf(c_16608,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_39,c_40]) ).
cnf(c_75,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_40,c_16608]) ).
cnf(c_16609,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_16609]) ).
cnf(c_16610,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_42,c_40]) ).
cnf(c_81,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_16610]) ).
cnf(c_16611,plain,
addition(addition(A,B),B) = addition(A,B),
inference(paramod,[status(thm)],[c_42,c_40]) ).
cnf(c_83,plain,
addition(A,addition(B,A)) = addition(B,A),
inference(paramod,[status(thm)],[c_39,c_16611]) ).
cnf(c_16612,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_44,c_47]) ).
cnf(c_85,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_16612]) ).
cnf(c_16613,plain,
addition(multiplication(sK2,sK1),A) = addition(multiplication(sK2,sK1),addition(multiplication(sK0,sK2),A)),
inference(paramod,[status(thm)],[c_57,c_40]) ).
cnf(c_106,plain,
addition(multiplication(sK2,sK1),addition(multiplication(sK0,sK2),A)) = addition(multiplication(sK2,sK1),A),
inference(copy,[status(thm)],[c_16613]) ).
cnf(c_16614,plain,
addition(c(sK1),sK1) = one,
inference(resolve,[status(thm)],[c_67,c_54]) ).
cnf(c_120,plain,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_39,c_16614]) ).
cnf(c_121,plain,
multiplication(sK1,c(sK1)) = zero,
inference(resolve,[status(thm)],[c_67,c_53]) ).
cnf(c_16615,plain,
addition(c(sK0),sK0) = one,
inference(resolve,[status(thm)],[c_68,c_54]) ).
cnf(c_126,plain,
addition(sK0,c(sK0)) = one,
inference(paramod,[status(thm)],[c_39,c_16615]) ).
cnf(c_16616,plain,
addition(A,multiplication(addition(B,C),D)) = addition(multiplication(B,D),addition(A,multiplication(C,D))),
inference(paramod,[status(thm)],[c_49,c_75]) ).
cnf(c_194,plain,
addition(multiplication(A,B),addition(C,multiplication(D,B))) = addition(C,multiplication(addition(A,D),B)),
inference(copy,[status(thm)],[c_16616]) ).
cnf(c_16617,plain,
addition(sK1,one) = addition(sK1,c(sK1)),
inference(paramod,[status(thm)],[c_120,c_81]) ).
cnf(c_16618,plain,
addition(one,sK1) = addition(sK1,c(sK1)),
inference(paramod,[status(thm)],[c_39,c_16617]) ).
cnf(c_214,plain,
addition(one,sK1) = one,
inference(paramod,[status(thm)],[c_120,c_16618]) ).
cnf(c_16619,plain,
addition(c(sK1),one) = addition(sK1,c(sK1)),
inference(paramod,[status(thm)],[c_120,c_83]) ).
cnf(c_16620,plain,
addition(one,c(sK1)) = addition(sK1,c(sK1)),
inference(paramod,[status(thm)],[c_39,c_16619]) ).
cnf(c_235,plain,
addition(one,c(sK1)) = one,
inference(paramod,[status(thm)],[c_120,c_16620]) ).
cnf(c_16621,plain,
addition(multiplication(A,one),multiplication(A,c(sK1))) = multiplication(A,one),
inference(paramod,[status(thm)],[c_235,c_47]) ).
cnf(c_16622,plain,
addition(A,multiplication(A,c(sK1))) = multiplication(A,one),
inference(paramod,[status(thm)],[c_44,c_16621]) ).
cnf(c_245,plain,
addition(A,multiplication(A,c(sK1))) = A,
inference(paramod,[status(thm)],[c_44,c_16622]) ).
cnf(c_573,plain,
addition(multiplication(sK2,sK1),multiplication(addition(sK0,A),sK2)) = addition(multiplication(sK2,sK1),multiplication(A,sK2)),
inference(paramod,[status(thm)],[c_49,c_106]) ).
cnf(c_16623,plain,
addition(multiplication(A,c(sK1)),B) = addition(B,multiplication(addition(A,B),c(sK1))),
inference(paramod,[status(thm)],[c_245,c_194]) ).
cnf(c_1234,plain,
addition(A,multiplication(addition(B,A),c(sK1))) = addition(multiplication(B,c(sK1)),A),
inference(copy,[status(thm)],[c_16623]) ).
cnf(c_16624,plain,
addition(multiplication(sK2,sK1),multiplication(one,sK2)) = addition(multiplication(sK2,sK1),multiplication(c(sK0),sK2)),
inference(paramod,[status(thm)],[c_126,c_573]) ).
cnf(c_16625,plain,
addition(multiplication(sK2,sK1),sK2) = addition(multiplication(sK2,sK1),multiplication(c(sK0),sK2)),
inference(paramod,[status(thm)],[c_45,c_16624]) ).
cnf(c_16626,plain,
addition(sK2,multiplication(sK2,sK1)) = addition(multiplication(sK2,sK1),multiplication(c(sK0),sK2)),
inference(paramod,[status(thm)],[c_39,c_16625]) ).
cnf(c_16627,plain,
multiplication(sK2,addition(one,sK1)) = addition(multiplication(sK2,sK1),multiplication(c(sK0),sK2)),
inference(paramod,[status(thm)],[c_85,c_16626]) ).
cnf(c_16628,plain,
multiplication(sK2,one) = addition(multiplication(sK2,sK1),multiplication(c(sK0),sK2)),
inference(paramod,[status(thm)],[c_214,c_16627]) ).
cnf(c_16629,plain,
sK2 = addition(multiplication(sK2,sK1),multiplication(c(sK0),sK2)),
inference(paramod,[status(thm)],[c_44,c_16628]) ).
cnf(c_16538,plain,
addition(multiplication(sK2,sK1),multiplication(c(sK0),sK2)) = sK2,
inference(copy,[status(thm)],[c_16629]) ).
cnf(c_16630,plain,
addition(multiplication(c(sK0),sK2),multiplication(sK2,c(sK1))) = addition(multiplication(multiplication(sK2,sK1),c(sK1)),multiplication(c(sK0),sK2)),
inference(paramod,[status(thm)],[c_16538,c_1234]) ).
cnf(c_16631,plain,
addition(multiplication(sK2,c(sK1)),multiplication(c(sK0),sK2)) = addition(multiplication(multiplication(sK2,sK1),c(sK1)),multiplication(c(sK0),sK2)),
inference(paramod,[status(thm)],[c_39,c_16630]) ).
cnf(c_16632,plain,
addition(multiplication(sK2,c(sK1)),multiplication(c(sK0),sK2)) = addition(multiplication(sK2,multiplication(sK1,c(sK1))),multiplication(c(sK0),sK2)),
inference(paramod,[status(thm)],[c_43,c_16631]) ).
cnf(c_16633,plain,
addition(multiplication(sK2,c(sK1)),multiplication(c(sK0),sK2)) = addition(multiplication(sK2,zero),multiplication(c(sK0),sK2)),
inference(paramod,[status(thm)],[c_121,c_16632]) ).
cnf(c_16634,plain,
addition(multiplication(sK2,c(sK1)),multiplication(c(sK0),sK2)) = addition(zero,multiplication(c(sK0),sK2)),
inference(paramod,[status(thm)],[c_50,c_16633]) ).
cnf(c_16635,plain,
addition(multiplication(sK2,c(sK1)),multiplication(c(sK0),sK2)) = multiplication(c(sK0),sK2),
inference(paramod,[status(thm)],[c_80,c_16634]) ).
cnf(c_16606,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_59,c_16635]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE023+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 19:16:06 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 2618117 was started by sandbox2 on n018,
% 0.13/0.36 % Fri Sep 25 19:16:06 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 43.25/5.86
% 43.25/5.86 % given #500 (W,wt=34): 6816 c(A) = zero | complement(one,multiplication(f1(f1(A)),f1(A))). [resolve(3178,b,119,a(flip))].
% 43.25/5.86
% 43.25/5.86 % SZS status Theorem for theBenchmark
% 43.25/5.86
% 43.25/5.86 % Proof 1 at 4.42 (+ 0.96) seconds.
% 43.25/5.86 % Length of proof is 55.
% 43.25/5.86 % Level of proof is 8.
% 43.25/5.86 % Maximum clause weight is 39.000.
% 43.25/5.86 % Given clauses 673.
% 43.25/5.86
% 43.25/5.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------