%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE129+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 : n015.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 07:44:21 AM UTC 2026
% Result : Theorem 80.28s 21.62s
% Output : CNFRefutation 80.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 14
% Syntax : Number of formulae : 91 ( 69 unt; 0 def)
% Number of atoms : 117 ( 116 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 56 ( 30 ~; 20 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 116 ( 1 sgn 25 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
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(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('theBenchmark.p',left_annihilation) ).
fof(domain1,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('theBenchmark.p',domain1) ).
fof(domain3,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('theBenchmark.p',domain3) ).
fof(domain4,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('theBenchmark.p',domain4) ).
fof(forward_diamond,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('theBenchmark.p',forward_diamond) ).
fof(divergence1,axiom,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
file('theBenchmark.p',divergence1) ).
fof(goals,conjecture,
! [X0] :
( ! [X1] :
( addition(domain(X1),forward_diamond(X0,domain(X1))) = forward_diamond(X0,domain(X1))
=> domain(X1) = zero )
=> divergence(X0) = zero ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( addition(domain(X1),forward_diamond(X0,domain(X1))) = forward_diamond(X0,domain(X1))
=> domain(X1) = zero )
=> divergence(X0) = zero ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_29,plain,
? [X0] :
( ! [X1] :
( domain(X1) = zero
| forward_diamond(X0,domain(X1)) != addition(domain(X1),forward_diamond(X0,domain(X1))) )
& divergence(X0) != zero ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ! [X1] :
( domain(X1) = zero
| forward_diamond(sK0,domain(X1)) != addition(domain(X1),forward_diamond(sK0,domain(X1))) )
& divergence(sK0) != zero ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_29]) ).
cnf(c_32,negated_conjecture,
( domain(A) = zero
| forward_diamond(sK0,domain(A)) != addition(domain(A),forward_diamond(sK0,domain(A))) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_33,negated_conjecture,
( domain(A) = zero
| addition(domain(A),forward_diamond(sK0,domain(A))) != forward_diamond(sK0,domain(A)) ),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_34,negated_conjecture,
divergence(sK0) != zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_37,plain,
divergence(A) = forward_diamond(A,divergence(A)),
inference(clausify,[status(thm)],[divergence1]) ).
cnf(c_38,plain,
forward_diamond(A,divergence(A)) = divergence(A),
inference(copy,[status(thm)],[c_37]) ).
cnf(c_42,plain,
forward_diamond(A,B) = domain(multiplication(A,domain(B))),
inference(clausify,[status(thm)],[forward_diamond]) ).
cnf(c_50,plain,
domain(A) = antidomain(antidomain(A)),
inference(clausify,[status(thm)],[domain4]) ).
cnf(c_51,plain,
addition(antidomain(antidomain(A)),antidomain(A)) = one,
inference(clausify,[status(thm)],[domain3]) ).
cnf(c_54,plain,
multiplication(antidomain(A),A) = zero,
inference(clausify,[status(thm)],[domain1]) ).
cnf(c_55,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_57,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_58,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_57]) ).
cnf(c_59,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_60,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_59]) ).
cnf(c_61,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_62,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_64,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_65,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_67,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_21309,plain,
domain(multiplication(A,domain(divergence(A)))) = divergence(A),
inference(paramod,[status(thm)],[c_42,c_38]) ).
cnf(c_21310,plain,
domain(multiplication(A,antidomain(antidomain(divergence(A))))) = divergence(A),
inference(paramod,[status(thm)],[c_50,c_21309]) ).
cnf(c_70,plain,
antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A)))))) = divergence(A),
inference(paramod,[status(thm)],[c_50,c_21310]) ).
cnf(c_21311,negated_conjecture,
( domain(A) = zero
| addition(antidomain(antidomain(A)),forward_diamond(sK0,domain(A))) != forward_diamond(sK0,domain(A)) ),
inference(paramod,[status(thm)],[c_50,c_33]) ).
cnf(c_21312,negated_conjecture,
( domain(A) = zero
| addition(antidomain(antidomain(A)),forward_diamond(sK0,antidomain(antidomain(A)))) != forward_diamond(sK0,domain(A)) ),
inference(paramod,[status(thm)],[c_50,c_21311]) ).
cnf(c_21313,negated_conjecture,
( domain(A) = zero
| addition(antidomain(antidomain(A)),domain(multiplication(sK0,domain(antidomain(antidomain(A)))))) != forward_diamond(sK0,domain(A)) ),
inference(paramod,[status(thm)],[c_42,c_21312]) ).
cnf(c_21314,negated_conjecture,
( domain(A) = zero
| addition(antidomain(antidomain(A)),domain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A))))))) != forward_diamond(sK0,domain(A)) ),
inference(paramod,[status(thm)],[c_50,c_21313]) ).
cnf(c_21315,negated_conjecture,
( domain(A) = zero
| addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A)))))))) != forward_diamond(sK0,domain(A)) ),
inference(paramod,[status(thm)],[c_50,c_21314]) ).
cnf(c_21316,negated_conjecture,
( domain(A) = zero
| addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A)))))))) != forward_diamond(sK0,antidomain(antidomain(A))) ),
inference(paramod,[status(thm)],[c_50,c_21315]) ).
cnf(c_21317,negated_conjecture,
( domain(A) = zero
| addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A)))))))) != domain(multiplication(sK0,domain(antidomain(antidomain(A))))) ),
inference(paramod,[status(thm)],[c_42,c_21316]) ).
cnf(c_21318,negated_conjecture,
( domain(A) = zero
| addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A)))))))) != domain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A)))))) ),
inference(paramod,[status(thm)],[c_50,c_21317]) ).
cnf(c_21319,negated_conjecture,
( domain(A) = zero
| addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A)))))))) != antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A))))))) ),
inference(paramod,[status(thm)],[c_50,c_21318]) ).
cnf(c_72,negated_conjecture,
( antidomain(antidomain(A)) = zero
| addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A)))))))) != antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A))))))) ),
inference(paramod,[status(thm)],[c_50,c_21319]) ).
cnf(c_77,plain,
addition(antidomain(A),antidomain(antidomain(A))) = one,
inference(paramod,[status(thm)],[c_67,c_51]) ).
cnf(c_21320,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(antidomain(B),A),B),
inference(paramod,[status(thm)],[c_54,c_58]) ).
cnf(c_89,plain,
multiplication(addition(antidomain(A),B),A) = addition(zero,multiplication(B,A)),
inference(copy,[status(thm)],[c_21320]) ).
cnf(c_91,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(zero,A),B),
inference(paramod,[status(thm)],[c_55,c_58]) ).
cnf(c_21321,plain,
addition(multiplication(A,B),zero) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_55,c_58]) ).
cnf(c_21322,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_67,c_21321]) ).
cnf(c_21323,plain,
multiplication(addition(zero,A),B) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_91,c_21322]) ).
cnf(c_92,plain,
multiplication(addition(zero,A),B) = multiplication(A,B),
inference(paramod,[status(thm)],[c_65,c_21323]) ).
cnf(c_21324,plain,
multiplication(addition(antidomain(A),B),A) = multiplication(addition(zero,B),A),
inference(paramod,[status(thm)],[c_91,c_89]) ).
cnf(c_94,plain,
multiplication(addition(antidomain(A),B),A) = multiplication(B,A),
inference(paramod,[status(thm)],[c_92,c_21324]) ).
cnf(c_97,plain,
addition(zero,multiplication(A,B)) = multiplication(A,B),
inference(paramod,[status(thm)],[c_92,c_91]) ).
cnf(c_21325,plain,
addition(multiplication(antidomain(A),B),zero) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_54,c_60]) ).
cnf(c_21326,plain,
addition(zero,multiplication(antidomain(A),B)) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_67,c_21325]) ).
cnf(c_21327,plain,
multiplication(antidomain(A),B) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_97,c_21326]) ).
cnf(c_101,plain,
multiplication(antidomain(A),addition(B,A)) = multiplication(antidomain(A),B),
inference(copy,[status(thm)],[c_21327]) ).
cnf(c_21328,plain,
( antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A)))))) = zero
| addition(divergence(A),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A)))))))))))) != antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A))))))))))) ),
inference(paramod,[status(thm)],[c_70,c_72]) ).
cnf(c_21329,plain,
( antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A)))))) = zero
| addition(divergence(A),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(A))))))) != antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A))))))))))) ),
inference(paramod,[status(thm)],[c_70,c_21328]) ).
cnf(c_21330,plain,
( antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A)))))) = zero
| addition(divergence(A),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(A))))))) != antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(A)))))) ),
inference(paramod,[status(thm)],[c_70,c_21329]) ).
cnf(c_153,plain,
( divergence(A) = zero
| addition(divergence(A),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(A))))))) != antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(A)))))) ),
inference(paramod,[status(thm)],[c_70,c_21330]) ).
cnf(c_21331,plain,
addition(divergence(A),antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A)))))))) = one,
inference(paramod,[status(thm)],[c_70,c_77]) ).
cnf(c_156,plain,
addition(divergence(A),antidomain(divergence(A))) = one,
inference(paramod,[status(thm)],[c_70,c_21331]) ).
cnf(c_21332,plain,
multiplication(one,A) = multiplication(antidomain(antidomain(A)),A),
inference(paramod,[status(thm)],[c_77,c_94]) ).
cnf(c_21333,plain,
A = multiplication(antidomain(antidomain(A)),A),
inference(paramod,[status(thm)],[c_61,c_21332]) ).
cnf(c_214,plain,
multiplication(antidomain(antidomain(A)),A) = A,
inference(copy,[status(thm)],[c_21333]) ).
cnf(c_21334,plain,
multiplication(antidomain(antidomain(antidomain(A))),one) = multiplication(antidomain(antidomain(antidomain(A))),antidomain(A)),
inference(paramod,[status(thm)],[c_77,c_101]) ).
cnf(c_21335,plain,
antidomain(antidomain(antidomain(A))) = multiplication(antidomain(antidomain(antidomain(A))),antidomain(A)),
inference(paramod,[status(thm)],[c_62,c_21334]) ).
cnf(c_420,plain,
antidomain(antidomain(antidomain(A))) = antidomain(A),
inference(paramod,[status(thm)],[c_214,c_21335]) ).
cnf(c_21336,plain,
multiplication(antidomain(antidomain(divergence(A))),one) = multiplication(antidomain(antidomain(divergence(A))),divergence(A)),
inference(paramod,[status(thm)],[c_156,c_101]) ).
cnf(c_21337,plain,
antidomain(antidomain(divergence(A))) = multiplication(antidomain(antidomain(divergence(A))),divergence(A)),
inference(paramod,[status(thm)],[c_62,c_21336]) ).
cnf(c_422,plain,
antidomain(antidomain(divergence(A))) = divergence(A),
inference(paramod,[status(thm)],[c_214,c_21337]) ).
cnf(c_21338,plain,
( divergence(A) = zero
| addition(divergence(A),antidomain(antidomain(multiplication(sK0,divergence(A))))) != antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(A)))))) ),
inference(paramod,[status(thm)],[c_422,c_153]) ).
cnf(c_459,plain,
( divergence(A) = zero
| addition(divergence(A),antidomain(antidomain(multiplication(sK0,divergence(A))))) != antidomain(antidomain(multiplication(sK0,divergence(A)))) ),
inference(paramod,[status(thm)],[c_422,c_21338]) ).
cnf(c_463,plain,
antidomain(antidomain(multiplication(A,divergence(A)))) = divergence(A),
inference(paramod,[status(thm)],[c_422,c_70]) ).
cnf(c_21339,plain,
antidomain(divergence(A)) = antidomain(multiplication(A,divergence(A))),
inference(paramod,[status(thm)],[c_463,c_420]) ).
cnf(c_765,plain,
antidomain(multiplication(A,divergence(A))) = antidomain(divergence(A)),
inference(copy,[status(thm)],[c_21339]) ).
cnf(c_21340,negated_conjecture,
addition(divergence(sK0),antidomain(antidomain(multiplication(sK0,divergence(sK0))))) != antidomain(antidomain(multiplication(sK0,divergence(sK0)))),
inference(resolve,[status(thm)],[c_459,c_34]) ).
cnf(c_21341,negated_conjecture,
addition(divergence(sK0),antidomain(antidomain(divergence(sK0)))) != antidomain(antidomain(multiplication(sK0,divergence(sK0)))),
inference(paramod,[status(thm)],[c_765,c_21340]) ).
cnf(c_21342,negated_conjecture,
addition(divergence(sK0),divergence(sK0)) != antidomain(antidomain(multiplication(sK0,divergence(sK0)))),
inference(paramod,[status(thm)],[c_422,c_21341]) ).
cnf(c_21343,negated_conjecture,
divergence(sK0) != antidomain(antidomain(multiplication(sK0,divergence(sK0)))),
inference(paramod,[status(thm)],[c_64,c_21342]) ).
cnf(c_21344,negated_conjecture,
divergence(sK0) != antidomain(antidomain(divergence(sK0))),
inference(paramod,[status(thm)],[c_765,c_21343]) ).
cnf(c_21345,negated_conjecture,
divergence(sK0) != divergence(sK0),
inference(paramod,[status(thm)],[c_422,c_21344]) ).
cnf(c_21308,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_21345]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE129+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.37 % Computer : n015.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Fri Sep 25 19:28:39 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.38 % Process 2056397 was started by sandbox on n015,
% 0.09/10.38 % Fri Sep 25 19:28:39 2026
% 0.09/10.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/10.39
% 0.09/10.39 % From the command line: assign(max_seconds, 300).
% 80.28/21.62
% 80.28/21.62 % given #500 (A,wt=14): 345 multiplication(coantidomain(coantidomain(A)),addition(coantidomain(A),B)) = multiplication(coantidomain(coantidomain(A)),B). [para(334(a,1),98(a,1,2,1))].
% 80.28/21.62
% 80.28/21.62 % SZS status Theorem for theBenchmark
% 80.28/21.62
% 80.28/21.62 % Proof 1 at 8.27 (+ 2.32) seconds.
% 80.28/21.62 % Length of proof is 51.
% 80.28/21.62 % Level of proof is 10.
% 80.28/21.62 % Maximum clause weight is 28.000.
% 80.28/21.62 % Given clauses 800.
% 80.28/21.62
% 80.28/21.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------