%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE079+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 : n016.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 07:44:16 AM UTC 2026
% Result : Theorem 7.54s 1.46s
% Output : CNFRefutation 7.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of formulae : 94 ( 90 unt; 0 def)
% Number of atoms : 102 ( 101 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 4 ~; 0 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 158 ( 22 sgn 28 !; 1 ?)
% 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_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] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('theBenchmark.p',domain1) ).
fof(domain2,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('theBenchmark.p',domain2) ).
fof(domain3,axiom,
! [X0] : addition(domain(X0),one) = one,
file('theBenchmark.p',domain3) ).
fof(domain5,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('theBenchmark.p',domain5) ).
fof(goals,conjecture,
! [X0] :
( ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
=> multiplication(antidomain(X0),domain(X0)) = zero ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
=> multiplication(antidomain(X0),domain(X0)) = zero ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_17,plain,
? [X0] :
( multiplication(antidomain(X0),domain(X0)) != zero
& ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one ) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( multiplication(antidomain(sK0),domain(sK0)) != zero
& ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_17]) ).
cnf(c_20,negated_conjecture,
multiplication(antidomain(sK0),domain(sK0)) != zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_21,negated_conjecture,
multiplication(domain(A),antidomain(A)) = zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_22,negated_conjecture,
addition(domain(A),antidomain(A)) = one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_23,plain,
domain(addition(A,B)) = addition(domain(A),domain(B)),
inference(clausify,[status(thm)],[domain5]) ).
fof(domain4,axiom,
domain(zero) = zero,
file('theBenchmark.p',domain4) ).
cnf(c_24,plain,
domain(zero) = zero,
inference(clausify,[status(thm)],[domain4]) ).
cnf(c_25,plain,
addition(domain(A),one) = one,
inference(clausify,[status(thm)],[domain3]) ).
cnf(c_26,plain,
domain(multiplication(A,domain(B))) = domain(multiplication(A,B)),
inference(clausify,[status(thm)],[domain2]) ).
cnf(c_27,plain,
multiplication(domain(A),A) = addition(A,multiplication(domain(A),A)),
inference(clausify,[status(thm)],[domain1]) ).
cnf(c_28,plain,
addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A),
inference(copy,[status(thm)],[c_27]) ).
cnf(c_29,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_31,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_32,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_31]) ).
cnf(c_33,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_34,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_33]) ).
cnf(c_35,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_36,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_38,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_39,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
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,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_42,plain,
addition(one,domain(A)) = one,
inference(paramod,[status(thm)],[c_41,c_25]) ).
cnf(c_1000,plain,
addition(zero,multiplication(A,antidomain(B))) = multiplication(addition(domain(B),A),antidomain(B)),
inference(paramod,[status(thm)],[c_21,c_32]) ).
cnf(c_53,plain,
multiplication(addition(domain(A),B),antidomain(A)) = addition(zero,multiplication(B,antidomain(A))),
inference(copy,[status(thm)],[c_1000]) ).
cnf(c_55,plain,
domain(multiplication(addition(A,B),C)) = addition(domain(multiplication(A,C)),domain(multiplication(B,C))),
inference(paramod,[status(thm)],[c_32,c_23]) ).
cnf(c_57,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(zero,A),B),
inference(paramod,[status(thm)],[c_29,c_32]) ).
cnf(c_1001,plain,
addition(multiplication(A,B),zero) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_29,c_32]) ).
cnf(c_1002,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_41,c_1001]) ).
cnf(c_1003,plain,
multiplication(addition(zero,A),B) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_57,c_1002]) ).
cnf(c_58,plain,
multiplication(addition(zero,A),B) = multiplication(A,B),
inference(paramod,[status(thm)],[c_39,c_1003]) ).
cnf(c_1004,plain,
multiplication(addition(domain(A),B),antidomain(A)) = multiplication(addition(zero,B),antidomain(A)),
inference(paramod,[status(thm)],[c_57,c_53]) ).
cnf(c_60,plain,
multiplication(addition(domain(A),B),antidomain(A)) = multiplication(B,antidomain(A)),
inference(paramod,[status(thm)],[c_58,c_1004]) ).
cnf(c_1005,plain,
domain(domain(A)) = domain(multiplication(one,A)),
inference(paramod,[status(thm)],[c_35,c_26]) ).
cnf(c_66,plain,
domain(domain(A)) = domain(A),
inference(paramod,[status(thm)],[c_35,c_1005]) ).
cnf(c_1006,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_36,c_34]) ).
cnf(c_72,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_1006]) ).
cnf(c_1007,plain,
addition(addition(A,B),B) = addition(A,B),
inference(paramod,[status(thm)],[c_38,c_40]) ).
cnf(c_84,plain,
addition(A,addition(B,A)) = addition(B,A),
inference(paramod,[status(thm)],[c_41,c_1007]) ).
cnf(c_1008,plain,
addition(multiplication(one,A),multiplication(domain(B),A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_42,c_32]) ).
cnf(c_1009,plain,
addition(A,multiplication(domain(B),A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_35,c_1008]) ).
cnf(c_91,plain,
addition(A,multiplication(domain(B),A)) = A,
inference(paramod,[status(thm)],[c_35,c_1009]) ).
cnf(c_1010,plain,
addition(multiplication(A,one),multiplication(A,domain(B))) = multiplication(A,one),
inference(paramod,[status(thm)],[c_42,c_34]) ).
cnf(c_1011,plain,
addition(A,multiplication(A,domain(B))) = multiplication(A,one),
inference(paramod,[status(thm)],[c_36,c_1010]) ).
cnf(c_92,plain,
addition(A,multiplication(A,domain(B))) = A,
inference(paramod,[status(thm)],[c_36,c_1011]) ).
cnf(c_1012,plain,
A = multiplication(domain(A),A),
inference(paramod,[status(thm)],[c_91,c_28]) ).
cnf(c_94,plain,
multiplication(domain(A),A) = A,
inference(copy,[status(thm)],[c_1012]) ).
cnf(c_109,plain,
multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))) = multiplication(A,domain(B)),
inference(paramod,[status(thm)],[c_26,c_94]) ).
cnf(c_131,plain,
multiplication(domain(A),domain(A)) = domain(A),
inference(paramod,[status(thm)],[c_66,c_94]) ).
cnf(c_1013,plain,
addition(multiplication(domain(A),B),domain(A)) = multiplication(domain(A),addition(B,domain(A))),
inference(paramod,[status(thm)],[c_131,c_34]) ).
cnf(c_1014,plain,
addition(domain(A),multiplication(domain(A),B)) = multiplication(domain(A),addition(B,domain(A))),
inference(paramod,[status(thm)],[c_41,c_1013]) ).
cnf(c_136,plain,
multiplication(domain(A),addition(one,B)) = multiplication(domain(A),addition(B,domain(A))),
inference(paramod,[status(thm)],[c_72,c_1014]) ).
cnf(c_1015,plain,
domain(A) = addition(domain(A),domain(multiplication(A,domain(B)))),
inference(paramod,[status(thm)],[c_92,c_23]) ).
cnf(c_1016,plain,
domain(A) = addition(domain(A),domain(multiplication(A,B))),
inference(paramod,[status(thm)],[c_26,c_1015]) ).
cnf(c_150,plain,
addition(domain(A),domain(multiplication(A,B))) = domain(A),
inference(copy,[status(thm)],[c_1016]) ).
cnf(c_1017,plain,
addition(antidomain(A),one) = addition(domain(A),antidomain(A)),
inference(paramod,[status(thm)],[c_22,c_84]) ).
cnf(c_1018,plain,
addition(one,antidomain(A)) = addition(domain(A),antidomain(A)),
inference(paramod,[status(thm)],[c_41,c_1017]) ).
cnf(c_243,plain,
addition(one,antidomain(A)) = one,
inference(paramod,[status(thm)],[c_22,c_1018]) ).
cnf(c_1019,plain,
domain(multiplication(one,A)) = addition(domain(multiplication(one,A)),domain(multiplication(antidomain(B),A))),
inference(paramod,[status(thm)],[c_243,c_55]) ).
cnf(c_1020,plain,
domain(A) = addition(domain(multiplication(one,A)),domain(multiplication(antidomain(B),A))),
inference(paramod,[status(thm)],[c_35,c_1019]) ).
cnf(c_1021,plain,
domain(A) = addition(domain(A),domain(multiplication(antidomain(B),A))),
inference(paramod,[status(thm)],[c_35,c_1020]) ).
cnf(c_248,plain,
addition(domain(A),domain(multiplication(antidomain(B),A))) = domain(A),
inference(copy,[status(thm)],[c_1021]) ).
cnf(c_1022,plain,
multiplication(domain(A),antidomain(A)) = multiplication(domain(multiplication(antidomain(B),A)),antidomain(A)),
inference(paramod,[status(thm)],[c_248,c_60]) ).
cnf(c_1023,plain,
zero = multiplication(domain(multiplication(antidomain(B),A)),antidomain(A)),
inference(paramod,[status(thm)],[c_21,c_1022]) ).
cnf(c_720,plain,
multiplication(domain(multiplication(antidomain(A),B)),antidomain(B)) = zero,
inference(copy,[status(thm)],[c_1023]) ).
cnf(c_1024,plain,
multiplication(domain(zero),multiplication(domain(multiplication(antidomain(A),B)),domain(antidomain(B)))) = multiplication(domain(multiplication(antidomain(A),B)),domain(antidomain(B))),
inference(paramod,[status(thm)],[c_720,c_109]) ).
cnf(c_1025,plain,
multiplication(zero,multiplication(domain(multiplication(antidomain(A),B)),domain(antidomain(B)))) = multiplication(domain(multiplication(antidomain(A),B)),domain(antidomain(B))),
inference(paramod,[status(thm)],[c_24,c_1024]) ).
cnf(c_1026,plain,
zero = multiplication(domain(multiplication(antidomain(A),B)),domain(antidomain(B))),
inference(paramod,[status(thm)],[c_29,c_1025]) ).
cnf(c_738,plain,
multiplication(domain(multiplication(antidomain(A),B)),domain(antidomain(B))) = zero,
inference(copy,[status(thm)],[c_1026]) ).
cnf(c_1027,plain,
multiplication(domain(multiplication(A,B)),addition(one,domain(A))) = multiplication(domain(multiplication(A,B)),domain(A)),
inference(paramod,[status(thm)],[c_150,c_136]) ).
cnf(c_1028,plain,
multiplication(domain(multiplication(A,B)),one) = multiplication(domain(multiplication(A,B)),domain(A)),
inference(paramod,[status(thm)],[c_42,c_1027]) ).
cnf(c_1029,plain,
domain(multiplication(A,B)) = multiplication(domain(multiplication(A,B)),domain(A)),
inference(paramod,[status(thm)],[c_36,c_1028]) ).
cnf(c_926,plain,
multiplication(domain(multiplication(A,B)),domain(A)) = domain(multiplication(A,B)),
inference(copy,[status(thm)],[c_1029]) ).
cnf(c_980,plain,
domain(multiplication(antidomain(A),A)) = zero,
inference(paramod,[status(thm)],[c_926,c_738]) ).
cnf(c_1030,plain,
multiplication(zero,multiplication(antidomain(A),domain(A))) = multiplication(antidomain(A),domain(A)),
inference(paramod,[status(thm)],[c_980,c_109]) ).
cnf(c_1031,plain,
zero = multiplication(antidomain(A),domain(A)),
inference(paramod,[status(thm)],[c_29,c_1030]) ).
cnf(c_998,plain,
multiplication(antidomain(A),domain(A)) = zero,
inference(copy,[status(thm)],[c_1031]) ).
cnf(c_999,plain,
$false,
inference(resolve,[status(thm)],[c_998,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE079+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n016.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 19:24:59 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 3088203 was started by sandbox on n016,
% 0.17/0.45 % Fri Sep 25 19:24:59 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 7.54/1.46
% 7.54/1.46 % SZS status Theorem for theBenchmark
% 7.54/1.46
% 7.54/1.46 % Proof 1 at 0.59 (+ 0.21) seconds.
% 7.54/1.46 % Length of proof is 58.
% 7.54/1.46 % Level of proof is 10.
% 7.54/1.46 % Maximum clause weight is 24.000.
% 7.54/1.46 % Given clauses 165.
% 7.54/1.46
% 7.54/1.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------