%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE099+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 : n007.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 07:44:19 AM UTC 2026
% Result : Theorem 67.36s 10.01s
% Output : CNFRefutation 67.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of formulae : 79 ( 75 unt; 0 def)
% Number of atoms : 83 ( 82 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 119 ( 9 sgn 30 !; 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(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(goals,conjecture,
! [X0,X1,X2] :
( addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2)
=> multiplication(antidomain(X2),multiplication(X0,domain(X1))) = zero ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2)
=> multiplication(antidomain(X2),multiplication(X0,domain(X1))) = zero ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_27,plain,
? [X0,X1,X2] :
( multiplication(antidomain(X2),multiplication(X0,domain(X1))) != zero
& domain(X2) = addition(forward_diamond(X0,domain(X1)),domain(X2)) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( multiplication(antidomain(sK0),multiplication(sK1,domain(sK2))) != zero
& domain(sK0) = addition(forward_diamond(sK1,domain(sK2)),domain(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK0)],[nnf_27]) ).
cnf(c_30,negated_conjecture,
multiplication(antidomain(sK0),multiplication(sK1,domain(sK2))) != zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_31,negated_conjecture,
domain(sK0) = addition(forward_diamond(sK1,domain(sK2)),domain(sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_32,negated_conjecture,
addition(forward_diamond(sK1,domain(sK2)),domain(sK0)) = domain(sK0),
inference(copy,[status(thm)],[c_31]) ).
cnf(c_36,plain,
forward_diamond(A,B) = domain(multiplication(A,domain(B))),
inference(clausify,[status(thm)],[forward_diamond]) ).
cnf(c_44,plain,
domain(A) = antidomain(antidomain(A)),
inference(clausify,[status(thm)],[domain4]) ).
cnf(c_45,plain,
addition(antidomain(antidomain(A)),antidomain(A)) = one,
inference(clausify,[status(thm)],[domain3]) ).
cnf(c_48,plain,
multiplication(antidomain(A),A) = zero,
inference(clausify,[status(thm)],[domain1]) ).
cnf(c_49,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_51,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_52,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_51]) ).
cnf(c_53,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_54,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_53]) ).
cnf(c_55,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_56,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_57,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_58,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_59,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_60,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_61,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_15343,negated_conjecture,
addition(forward_diamond(sK1,antidomain(antidomain(sK2))),domain(sK0)) = domain(sK0),
inference(paramod,[status(thm)],[c_44,c_32]) ).
cnf(c_15344,negated_conjecture,
addition(domain(multiplication(sK1,domain(antidomain(antidomain(sK2))))),domain(sK0)) = domain(sK0),
inference(paramod,[status(thm)],[c_36,c_15343]) ).
cnf(c_15345,negated_conjecture,
addition(domain(multiplication(sK1,antidomain(antidomain(antidomain(antidomain(sK2)))))),domain(sK0)) = domain(sK0),
inference(paramod,[status(thm)],[c_44,c_15344]) ).
cnf(c_15346,negated_conjecture,
addition(antidomain(antidomain(multiplication(sK1,antidomain(antidomain(antidomain(antidomain(sK2))))))),domain(sK0)) = domain(sK0),
inference(paramod,[status(thm)],[c_44,c_15345]) ).
cnf(c_15347,negated_conjecture,
addition(antidomain(antidomain(multiplication(sK1,antidomain(antidomain(antidomain(antidomain(sK2))))))),antidomain(antidomain(sK0))) = domain(sK0),
inference(paramod,[status(thm)],[c_44,c_15346]) ).
cnf(c_15348,negated_conjecture,
addition(antidomain(antidomain(sK0)),antidomain(antidomain(multiplication(sK1,antidomain(antidomain(antidomain(antidomain(sK2)))))))) = domain(sK0),
inference(paramod,[status(thm)],[c_61,c_15347]) ).
cnf(c_64,negated_conjecture,
addition(antidomain(antidomain(sK0)),antidomain(antidomain(multiplication(sK1,antidomain(antidomain(antidomain(antidomain(sK2)))))))) = antidomain(antidomain(sK0)),
inference(paramod,[status(thm)],[c_44,c_15348]) ).
cnf(c_69,negated_conjecture,
multiplication(antidomain(sK0),multiplication(sK1,antidomain(antidomain(sK2)))) != zero,
inference(paramod,[status(thm)],[c_44,c_30]) ).
cnf(c_70,plain,
addition(antidomain(A),antidomain(antidomain(A))) = one,
inference(paramod,[status(thm)],[c_61,c_45]) ).
cnf(c_15349,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(antidomain(B),A),B),
inference(paramod,[status(thm)],[c_48,c_52]) ).
cnf(c_82,plain,
multiplication(addition(antidomain(A),B),A) = addition(zero,multiplication(B,A)),
inference(copy,[status(thm)],[c_15349]) ).
cnf(c_84,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(zero,A),B),
inference(paramod,[status(thm)],[c_49,c_52]) ).
cnf(c_15350,plain,
addition(multiplication(A,B),zero) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_49,c_52]) ).
cnf(c_15351,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_61,c_15350]) ).
cnf(c_15352,plain,
multiplication(addition(zero,A),B) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_84,c_15351]) ).
cnf(c_85,plain,
multiplication(addition(zero,A),B) = multiplication(A,B),
inference(paramod,[status(thm)],[c_59,c_15352]) ).
cnf(c_15353,plain,
multiplication(addition(antidomain(A),B),A) = multiplication(addition(zero,B),A),
inference(paramod,[status(thm)],[c_84,c_82]) ).
cnf(c_87,plain,
multiplication(addition(antidomain(A),B),A) = multiplication(B,A),
inference(paramod,[status(thm)],[c_85,c_15353]) ).
cnf(c_90,plain,
addition(zero,multiplication(A,B)) = multiplication(A,B),
inference(paramod,[status(thm)],[c_85,c_84]) ).
cnf(c_15354,plain,
addition(multiplication(antidomain(A),B),zero) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_48,c_54]) ).
cnf(c_15355,plain,
addition(zero,multiplication(antidomain(A),B)) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_61,c_15354]) ).
cnf(c_15356,plain,
multiplication(antidomain(A),B) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_90,c_15355]) ).
cnf(c_94,plain,
multiplication(antidomain(A),addition(B,A)) = multiplication(antidomain(A),B),
inference(copy,[status(thm)],[c_15356]) ).
cnf(c_15357,plain,
addition(addition(A,B),B) = addition(A,B),
inference(paramod,[status(thm)],[c_58,c_60]) ).
cnf(c_123,plain,
addition(A,addition(B,A)) = addition(B,A),
inference(paramod,[status(thm)],[c_61,c_15357]) ).
cnf(c_15358,plain,
multiplication(one,A) = multiplication(antidomain(antidomain(A)),A),
inference(paramod,[status(thm)],[c_70,c_87]) ).
cnf(c_15359,plain,
A = multiplication(antidomain(antidomain(A)),A),
inference(paramod,[status(thm)],[c_55,c_15358]) ).
cnf(c_181,plain,
multiplication(antidomain(antidomain(A)),A) = A,
inference(copy,[status(thm)],[c_15359]) ).
cnf(c_15360,plain,
multiplication(antidomain(antidomain(antidomain(A))),one) = multiplication(antidomain(antidomain(antidomain(A))),antidomain(A)),
inference(paramod,[status(thm)],[c_70,c_94]) ).
cnf(c_15361,plain,
antidomain(antidomain(antidomain(A))) = multiplication(antidomain(antidomain(antidomain(A))),antidomain(A)),
inference(paramod,[status(thm)],[c_56,c_15360]) ).
cnf(c_368,plain,
antidomain(antidomain(antidomain(A))) = antidomain(A),
inference(paramod,[status(thm)],[c_181,c_15361]) ).
cnf(c_15362,plain,
multiplication(antidomain(addition(A,B)),addition(A,B)) = multiplication(antidomain(addition(A,B)),B),
inference(paramod,[status(thm)],[c_123,c_94]) ).
cnf(c_15363,plain,
zero = multiplication(antidomain(addition(A,B)),B),
inference(paramod,[status(thm)],[c_48,c_15362]) ).
cnf(c_372,plain,
multiplication(antidomain(addition(A,B)),B) = zero,
inference(copy,[status(thm)],[c_15363]) ).
cnf(c_379,negated_conjecture,
addition(antidomain(antidomain(sK0)),antidomain(antidomain(multiplication(sK1,antidomain(antidomain(sK2)))))) = antidomain(antidomain(sK0)),
inference(paramod,[status(thm)],[c_368,c_64]) ).
cnf(c_15364,plain,
multiplication(zero,A) = multiplication(antidomain(addition(B,C)),multiplication(C,A)),
inference(paramod,[status(thm)],[c_372,c_57]) ).
cnf(c_15365,plain,
zero = multiplication(antidomain(addition(B,C)),multiplication(C,A)),
inference(paramod,[status(thm)],[c_49,c_15364]) ).
cnf(c_426,plain,
multiplication(antidomain(addition(A,B)),multiplication(B,C)) = zero,
inference(copy,[status(thm)],[c_15365]) ).
cnf(c_1085,plain,
multiplication(antidomain(addition(A,antidomain(antidomain(B)))),B) = zero,
inference(paramod,[status(thm)],[c_181,c_426]) ).
cnf(c_15366,plain,
multiplication(antidomain(antidomain(antidomain(sK0))),multiplication(sK1,antidomain(antidomain(sK2)))) = zero,
inference(paramod,[status(thm)],[c_379,c_1085]) ).
cnf(c_15341,plain,
multiplication(antidomain(sK0),multiplication(sK1,antidomain(antidomain(sK2)))) = zero,
inference(paramod,[status(thm)],[c_368,c_15366]) ).
cnf(c_15342,plain,
$false,
inference(resolve,[status(thm)],[c_15341,c_69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE099+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n007.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Fri Sep 25 19:20:24 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 1666860 was started by sandbox2 on n007,
% 0.16/0.44 % Fri Sep 25 19:20:24 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.46
% 0.16/0.46 % From the command line: assign(max_seconds, 300).
% 67.36/10.01
% 67.36/10.01 % given #500 (T,wt=12): 1540 antidomain(multiplication(addition(A,one),addition(B,addition(C,one)))) = zero. [para(60(a,1),1311(a,1,1,2))].
% 67.36/10.01
% 67.36/10.01 % SZS status Theorem for theBenchmark
% 67.36/10.01
% 67.36/10.01 % Proof 1 at 7.37 (+ 2.07) seconds.
% 67.36/10.01 % Length of proof is 52.
% 67.36/10.01 % Level of proof is 11.
% 67.36/10.01 % Maximum clause weight is 17.000.
% 67.36/10.01 % Given clauses 553.
% 67.36/10.01
% 67.36/10.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------