%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE085+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 : 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 07:44:17 AM UTC 2026
% Result : Theorem 0.22s 0.55s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 24 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 1 sgn 10 !; 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_idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',additive_idempotence) ).
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(goals,conjecture,
! [X0] : addition(domain(X0),one) = one,
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : addition(domain(X0),one) = one,
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_21,plain,
? [X0] : addition(domain(X0),one) != one,
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
addition(domain(sK0),one) != one,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_21]) ).
cnf(c_24,negated_conjecture,
addition(domain(sK0),one) != one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_30,plain,
domain(A) = antidomain(antidomain(A)),
inference(clausify,[status(thm)],[domain4]) ).
cnf(c_31,plain,
addition(antidomain(antidomain(A)),antidomain(A)) = one,
inference(clausify,[status(thm)],[domain3]) ).
cnf(c_44,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_46,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_47,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_177,negated_conjecture,
addition(antidomain(antidomain(sK0)),one) != one,
inference(paramod,[status(thm)],[c_30,c_24]) ).
cnf(c_48,negated_conjecture,
addition(one,antidomain(antidomain(sK0))) != one,
inference(paramod,[status(thm)],[c_47,c_177]) ).
cnf(c_49,plain,
addition(antidomain(A),antidomain(antidomain(A))) = one,
inference(paramod,[status(thm)],[c_47,c_31]) ).
cnf(c_178,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_44,c_46]) ).
cnf(c_101,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_178]) ).
cnf(c_179,plain,
addition(antidomain(A),one) = addition(antidomain(A),antidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_49,c_101]) ).
cnf(c_180,plain,
addition(one,antidomain(A)) = addition(antidomain(A),antidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_47,c_179]) ).
cnf(c_175,plain,
addition(one,antidomain(A)) = one,
inference(paramod,[status(thm)],[c_49,c_180]) ).
cnf(c_176,plain,
$false,
inference(resolve,[status(thm)],[c_175,c_48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE085+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.43 % Computer : n007.cluster.edu
% 0.10/0.43 % Model : x86_64 x86_64
% 0.10/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.43 % Memory : 8046.5625MB
% 0.10/0.43 % OS : Linux 6.8.0-71-generic
% 0.10/0.43 % CPULimit : 300
% 0.10/0.43 % WCLimit : 300
% 0.10/0.43 % DateTime : Fri Sep 25 19:18:23 UTC 2026
% 0.10/0.43 % CPUTime :
% 0.10/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.43 % Process 1658767 was started by sandbox on n007,
% 0.10/0.43 % Fri Sep 25 19:18:23 2026
% 0.10/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.44
% 0.10/0.44 % From the command line: assign(max_seconds, 300).
% 0.22/0.55
% 0.22/0.55 % SZS status Theorem for theBenchmark
% 0.22/0.55
% 0.22/0.55 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.22/0.55 % Length of proof is 17.
% 0.22/0.55 % Level of proof is 4.
% 0.22/0.55 % Maximum clause weight is 11.000.
% 0.22/0.55 % Given clauses 34.
% 0.22/0.55
% 0.22/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------