%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE025+2 : 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 : n012.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 117.87s 21.60s
% Output : CNFRefutation 117.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 15
% Syntax : Number of formulae : 122 ( 69 unt; 0 def)
% Number of atoms : 219 ( 147 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 173 ( 76 ~; 75 |; 13 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 134 ( 3 sgn 38 !; 5 ?)
% 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_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(test_4,axiom,
! [X0] :
( ~ test(X0)
=> c(X0) = zero ),
file('theBenchmark.p',test_4) ).
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]) ).
cnf(c_22,plain,
( complement(A,B)
| c(A) != B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
cnf(c_23,plain,
( ~ complement(A,B)
| c(A) = B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
cnf(c_24,plain,
( addition(B,A) != one
| multiplication(A,B) != zero
| multiplication(B,A) != zero
| complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_25,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_26,plain,
( multiplication(A,B) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_27,plain,
( multiplication(B,A) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
fof(nnf_13,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( ? [X3] : complement(X3,X0)
| ~ test(X0) ) ),
inference(fof_nnf,[status(thm)],[test_1]) ).
fof(sk_test_1_sk,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( complement(sK0(X0),X0)
| ~ test(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0))],[nnf_13]) ).
fof(sk_test_1,plain,
( ! [VAR_0,VAR_1] :
( ~ complement(VAR_1,VAR_0)
| test(VAR_0) )
& ! [VAR_0] :
( complement(sK0(VAR_0),VAR_0)
| ~ test(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_test_1_sk]) ).
cnf(c_28,plain,
( ~ complement(B,A)
| test(A) ),
inference(split_conjunct,[status(thm)],[sk_test_1]) ).
cnf(c_29,plain,
( complement(sK0(A),A)
| ~ test(A) ),
inference(split_conjunct,[status(thm)],[sk_test_1]) ).
cnf(c_30,plain,
( c(sK0(A)) = A
| ~ test(sK0(A))
| ~ test(A) ),
inference(resolve,[status(thm)],[c_29,c_23]) ).
cnf(c_31,plain,
( addition(A,sK0(A)) = one
| ~ test(A) ),
inference(resolve,[status(thm)],[c_29,c_25]) ).
cnf(c_34,plain,
( c(B) != A
| ~ test(B)
| test(A) ),
inference(resolve,[status(thm)],[c_28,c_22]) ).
cnf(c_35,plain,
( addition(A,B) != one
| multiplication(B,A) != zero
| multiplication(A,B) != zero
| test(A) ),
inference(resolve,[status(thm)],[c_28,c_24]) ).
cnf(c_36,plain,
( c(B) != A
| ~ test(B)
| multiplication(A,B) = zero ),
inference(resolve,[status(thm)],[c_27,c_22]) ).
cnf(c_37,plain,
( c(A) != B
| ~ test(A)
| multiplication(A,B) = zero ),
inference(resolve,[status(thm)],[c_26,c_22]) ).
cnf(c_38,plain,
( c(B) != A
| ~ test(B)
| addition(A,B) = one ),
inference(resolve,[status(thm)],[c_25,c_22]) ).
cnf(c_39,plain,
( c(B) = A
| ~ test(B)
| addition(A,B) != one
| multiplication(B,A) != zero
| multiplication(A,B) != zero ),
inference(resolve,[status(thm)],[c_24,c_23]) ).
cnf(c_40,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_41,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_42,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_43,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_44,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_45,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_46,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_47,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_48,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_47]) ).
cnf(c_49,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_50,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_49]) ).
cnf(c_51,plain,
multiplication(A,zero) = zero,
inference(clausify,[status(thm)],[right_annihilation]) ).
cnf(c_53,plain,
( c(A) = zero
| test(A) ),
inference(clausify,[status(thm)],[test_4]) ).
fof(nnf_19,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(sK2,sK3),sK1) != multiplication(sK2,sK3)
& multiplication(multiplication(sK2,sK3),c(sK1)) = zero
& test(sK1)
& test(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK1,sK3]),skolemize(X0,sK3),skolemize(X1,sK2),skolemize(X2,sK1)],[nnf_19]) ).
cnf(c_59,negated_conjecture,
test(sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_60,negated_conjecture,
multiplication(multiplication(sK2,sK3),c(sK1)) = zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_61,negated_conjecture,
multiplication(sK2,multiplication(sK3,c(sK1))) = zero,
inference(paramod,[status(thm)],[c_44,c_60]) ).
cnf(c_62,negated_conjecture,
multiplication(multiplication(sK2,sK3),sK1) != multiplication(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_63,negated_conjecture,
multiplication(sK2,multiplication(sK3,sK1)) != multiplication(sK2,sK3),
inference(paramod,[status(thm)],[c_44,c_62]) ).
cnf(c_21725,plain,
( multiplication(zero,one) != zero
| multiplication(one,zero) != zero
| test(one) ),
inference(resolve,[status(thm)],[c_42,c_35]) ).
cnf(c_21726,plain,
( multiplication(zero,one) != zero
| zero != zero
| test(one) ),
inference(paramod,[status(thm)],[c_51,c_21725]) ).
cnf(c_21727,plain,
( zero != zero
| zero != zero
| test(one) ),
inference(paramod,[status(thm)],[c_45,c_21726]) ).
cnf(c_21728,plain,
( zero != zero
| test(one) ),
inference(copy,[status(thm)],[c_21727]) ).
cnf(c_70,plain,
test(one),
inference(copy,[status(thm)],[c_21728]) ).
cnf(c_21729,plain,
A = addition(zero,A),
inference(paramod,[status(thm)],[c_42,c_40]) ).
cnf(c_71,plain,
addition(zero,A) = A,
inference(copy,[status(thm)],[c_21729]) ).
cnf(c_21730,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_43,c_41]) ).
cnf(c_72,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_21730]) ).
cnf(c_91,plain,
( c(sK0(A)) = A
| ~ test(A)
| c(sK0(A)) = zero ),
inference(resolve,[status(thm)],[c_53,c_30]) ).
cnf(c_93,plain,
( ~ test(zero)
| c(sK0(zero)) = zero ),
inference(factor,[status(thm)],[c_91]) ).
cnf(c_116,plain,
( c(sK1) != A
| addition(A,sK1) = one ),
inference(resolve,[status(thm)],[c_59,c_38]) ).
cnf(c_117,plain,
( c(sK1) != A
| multiplication(sK1,A) = zero ),
inference(resolve,[status(thm)],[c_59,c_37]) ).
cnf(c_118,plain,
( c(sK1) != A
| multiplication(A,sK1) = zero ),
inference(resolve,[status(thm)],[c_59,c_36]) ).
cnf(c_122,plain,
addition(sK1,sK0(sK1)) = one,
inference(resolve,[status(thm)],[c_59,c_31]) ).
cnf(c_21731,plain,
addition(zero,multiplication(sK2,A)) = multiplication(sK2,addition(multiplication(sK3,c(sK1)),A)),
inference(paramod,[status(thm)],[c_61,c_48]) ).
cnf(c_21732,plain,
multiplication(sK2,A) = multiplication(sK2,addition(multiplication(sK3,c(sK1)),A)),
inference(paramod,[status(thm)],[c_71,c_21731]) ).
cnf(c_125,plain,
multiplication(sK2,addition(multiplication(sK3,c(sK1)),A)) = multiplication(sK2,A),
inference(copy,[status(thm)],[c_21732]) ).
cnf(c_147,plain,
( c(one) != A
| test(A) ),
inference(resolve,[status(thm)],[c_70,c_34]) ).
cnf(c_21733,plain,
( multiplication(one,zero) != zero
| multiplication(zero,one) != zero
| test(zero) ),
inference(resolve,[status(thm)],[c_71,c_35]) ).
cnf(c_21734,plain,
( multiplication(one,zero) != zero
| zero != zero
| test(zero) ),
inference(paramod,[status(thm)],[c_45,c_21733]) ).
cnf(c_21735,plain,
( zero != zero
| zero != zero
| test(zero) ),
inference(paramod,[status(thm)],[c_51,c_21734]) ).
cnf(c_21736,plain,
( zero != zero
| test(zero) ),
inference(copy,[status(thm)],[c_21735]) ).
cnf(c_149,plain,
test(zero),
inference(copy,[status(thm)],[c_21736]) ).
cnf(c_150,plain,
c(sK0(zero)) = zero,
inference(resolve,[status(thm)],[c_149,c_93]) ).
cnf(c_21737,plain,
addition(zero,sK0(zero)) = one,
inference(resolve,[status(thm)],[c_149,c_31]) ).
cnf(c_159,plain,
sK0(zero) = one,
inference(paramod,[status(thm)],[c_71,c_21737]) ).
cnf(c_160,plain,
c(one) = zero,
inference(paramod,[status(thm)],[c_159,c_150]) ).
cnf(c_161,plain,
( zero != A
| test(A) ),
inference(paramod,[status(thm)],[c_160,c_147]) ).
cnf(c_21738,plain,
( zero = c(A)
| test(A) ),
inference(copy,[status(thm)],[c_53]) ).
cnf(c_165,plain,
( test(A)
| test(c(A)) ),
inference(resolve,[status(thm)],[c_161,c_21738]) ).
cnf(c_192,plain,
( c(A) != B
| test(B)
| test(c(A)) ),
inference(resolve,[status(thm)],[c_165,c_34]) ).
cnf(c_21739,plain,
( c(A) != c(A)
| test(c(A)) ),
inference(factor,[status(thm)],[c_192]) ).
cnf(c_198,plain,
test(c(A)),
inference(copy,[status(thm)],[c_21739]) ).
cnf(c_214,plain,
( c(c(B)) = A
| addition(A,c(B)) != one
| multiplication(c(B),A) != zero
| multiplication(A,c(B)) != zero ),
inference(resolve,[status(thm)],[c_198,c_39]) ).
cnf(c_215,plain,
( c(c(B)) != A
| addition(A,c(B)) = one ),
inference(resolve,[status(thm)],[c_198,c_38]) ).
cnf(c_21740,plain,
A = addition(zero,A),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_21741,plain,
addition(addition(zero,c(sK1)),sK1) = one,
inference(resolve,[status(thm)],[c_116,c_21740]) ).
cnf(c_21742,plain,
addition(c(sK1),sK1) = one,
inference(paramod,[status(thm)],[c_71,c_21741]) ).
cnf(c_325,plain,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_40,c_21742]) ).
cnf(c_21743,plain,
A = addition(zero,A),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_21744,plain,
multiplication(sK1,addition(zero,c(sK1))) = zero,
inference(resolve,[status(thm)],[c_117,c_21743]) ).
cnf(c_326,plain,
multiplication(sK1,c(sK1)) = zero,
inference(paramod,[status(thm)],[c_71,c_21744]) ).
cnf(c_21745,plain,
A = addition(zero,A),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_21746,plain,
multiplication(addition(zero,c(sK1)),sK1) = zero,
inference(resolve,[status(thm)],[c_118,c_21745]) ).
cnf(c_327,plain,
multiplication(c(sK1),sK1) = zero,
inference(paramod,[status(thm)],[c_71,c_21746]) ).
cnf(c_21747,plain,
addition(sK1,one) = addition(sK1,sK0(sK1)),
inference(paramod,[status(thm)],[c_122,c_72]) ).
cnf(c_21748,plain,
addition(one,sK1) = addition(sK1,sK0(sK1)),
inference(paramod,[status(thm)],[c_40,c_21747]) ).
cnf(c_391,plain,
addition(one,sK1) = one,
inference(paramod,[status(thm)],[c_122,c_21748]) ).
cnf(c_21749,plain,
addition(multiplication(one,A),multiplication(sK1,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_391,c_50]) ).
cnf(c_21750,plain,
addition(A,multiplication(sK1,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_46,c_21749]) ).
cnf(c_397,plain,
addition(A,multiplication(sK1,A)) = A,
inference(paramod,[status(thm)],[c_46,c_21750]) ).
cnf(c_650,plain,
multiplication(sK2,multiplication(sK3,addition(c(sK1),A))) = multiplication(sK2,multiplication(sK3,A)),
inference(paramod,[status(thm)],[c_48,c_125]) ).
cnf(c_21751,plain,
A = addition(A,multiplication(sK1,A)),
inference(copy,[status(thm)],[c_397]) ).
cnf(c_21752,plain,
addition(addition(c(c(A)),multiplication(sK1,c(c(A)))),c(A)) = one,
inference(resolve,[status(thm)],[c_215,c_21751]) ).
cnf(c_21753,plain,
addition(c(c(A)),c(A)) = one,
inference(paramod,[status(thm)],[c_397,c_21752]) ).
cnf(c_1448,plain,
addition(c(A),c(c(A))) = one,
inference(paramod,[status(thm)],[c_40,c_21753]) ).
cnf(c_21754,plain,
( c(c(sK1)) = sK1
| multiplication(c(sK1),sK1) != zero
| multiplication(sK1,c(sK1)) != zero ),
inference(resolve,[status(thm)],[c_214,c_325]) ).
cnf(c_21755,plain,
( c(c(sK1)) = sK1
| multiplication(c(sK1),sK1) != zero
| zero != zero ),
inference(paramod,[status(thm)],[c_326,c_21754]) ).
cnf(c_21756,plain,
( c(c(sK1)) = sK1
| zero != zero
| zero != zero ),
inference(paramod,[status(thm)],[c_327,c_21755]) ).
cnf(c_21757,plain,
( c(c(sK1)) = sK1
| zero != zero ),
inference(copy,[status(thm)],[c_21756]) ).
cnf(c_1560,plain,
c(c(sK1)) = sK1,
inference(copy,[status(thm)],[c_21757]) ).
cnf(c_21758,plain,
multiplication(sK2,multiplication(sK3,one)) = multiplication(sK2,multiplication(sK3,c(c(sK1)))),
inference(paramod,[status(thm)],[c_1448,c_650]) ).
cnf(c_21759,plain,
multiplication(sK2,sK3) = multiplication(sK2,multiplication(sK3,c(c(sK1)))),
inference(paramod,[status(thm)],[c_45,c_21758]) ).
cnf(c_21760,plain,
multiplication(sK2,sK3) = multiplication(sK2,multiplication(sK3,sK1)),
inference(paramod,[status(thm)],[c_1560,c_21759]) ).
cnf(c_21761,plain,
multiplication(sK2,multiplication(sK3,sK1)) = multiplication(sK2,sK3),
inference(copy,[status(thm)],[c_21760]) ).
cnf(c_21724,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_63,c_21761]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE025+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/5.73 % Computer : n012.cluster.edu
% 0.03/5.73 % Model : x86_64 x86_64
% 0.03/5.73 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/5.73 % Memory : 8046.5625MB
% 0.03/5.73 % OS : Linux 6.8.0-71-generic
% 0.03/5.73 % CPULimit : 300
% 0.03/5.73 % WCLimit : 300
% 0.03/5.73 % DateTime : Fri Sep 25 19:14:39 UTC 2026
% 0.03/5.73 % CPUTime :
% 0.03/5.73 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/5.73 % Process 2746374 was started by sandbox on n012,
% 0.03/5.73 % Fri Sep 25 19:14:39 2026
% 0.03/5.73 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/5.73
% 0.03/5.73 % From the command line: assign(max_seconds, 300).
% 117.87/21.60
% 117.87/21.60 % given #500 (W,wt=30): 12960 multiplication(addition(A,c3),multiplication(c3,B)) = multiplication(addition(A,one),multiplication(c3,B)). [para(12921(a,1),44(a,1,1)),rewrite([44(5)]),flip(a)].
% 117.87/21.60
% 117.87/21.60 % SZS status Theorem for theBenchmark
% 117.87/21.60
% 117.87/21.60 % Proof 1 at 6.53 (+ 1.26) seconds.
% 117.87/21.60 % Length of proof is 79.
% 117.87/21.60 % Level of proof is 13.
% 117.87/21.60 % Maximum clause weight is 39.000.
% 117.87/21.60 % Given clauses 772.
% 117.87/21.60
% 117.87/21.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
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