%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE119+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 : n003.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 07:44:20 AM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 43 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 17 ( 17 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 1 sgn 15 !; 2 ?)
% 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(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('theBenchmark.p',multiplicative_left_identity) ).
fof(right_annihilation,axiom,
! [A] : multiplication(A,zero) = zero,
file('theBenchmark.p',right_annihilation) ).
fof(domain4,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('theBenchmark.p',domain4) ).
fof(codomain1,axiom,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
file('theBenchmark.p',codomain1) ).
fof(codomain3,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
file('theBenchmark.p',codomain3) ).
fof(codomain4,axiom,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
file('theBenchmark.p',codomain4) ).
fof(backward_diamond,axiom,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
file('theBenchmark.p',backward_diamond) ).
fof(goals,conjecture,
! [X0,X1] : addition(backward_diamond(zero,domain(X0)),domain(X1)) = domain(X1),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] : addition(backward_diamond(zero,domain(X0)),domain(X1)) = domain(X1),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_27,plain,
? [X0,X1] : domain(X1) != addition(backward_diamond(zero,domain(X0)),domain(X1)),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
domain(sK0) != addition(backward_diamond(zero,domain(sK1)),domain(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK1),skolemize(X1,sK0)],[nnf_27]) ).
cnf(c_30,negated_conjecture,
domain(sK0) != addition(backward_diamond(zero,domain(sK1)),domain(sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_31,negated_conjecture,
addition(backward_diamond(zero,domain(sK1)),domain(sK0)) != domain(sK0),
inference(copy,[status(thm)],[c_30]) ).
cnf(c_34,plain,
backward_diamond(A,B) = codomain(multiplication(codomain(B),A)),
inference(clausify,[status(thm)],[backward_diamond]) ).
cnf(c_38,plain,
codomain(A) = coantidomain(coantidomain(A)),
inference(clausify,[status(thm)],[codomain4]) ).
cnf(c_39,plain,
addition(coantidomain(coantidomain(A)),coantidomain(A)) = one,
inference(clausify,[status(thm)],[codomain3]) ).
cnf(c_42,plain,
multiplication(A,coantidomain(A)) = zero,
inference(clausify,[status(thm)],[codomain1]) ).
cnf(c_43,plain,
domain(A) = antidomain(antidomain(A)),
inference(clausify,[status(thm)],[domain4]) ).
cnf(c_49,plain,
multiplication(A,zero) = zero,
inference(clausify,[status(thm)],[right_annihilation]) ).
cnf(c_54,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_58,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_60,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_144,negated_conjecture,
addition(backward_diamond(zero,antidomain(antidomain(sK1))),domain(sK0)) != domain(sK0),
inference(paramod,[status(thm)],[c_43,c_31]) ).
cnf(c_145,negated_conjecture,
addition(codomain(multiplication(codomain(antidomain(antidomain(sK1))),zero)),domain(sK0)) != domain(sK0),
inference(paramod,[status(thm)],[c_34,c_144]) ).
cnf(c_146,negated_conjecture,
addition(codomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK1)))),zero)),domain(sK0)) != domain(sK0),
inference(paramod,[status(thm)],[c_38,c_145]) ).
cnf(c_147,negated_conjecture,
addition(codomain(zero),domain(sK0)) != domain(sK0),
inference(paramod,[status(thm)],[c_49,c_146]) ).
cnf(c_148,negated_conjecture,
addition(coantidomain(coantidomain(zero)),domain(sK0)) != domain(sK0),
inference(paramod,[status(thm)],[c_38,c_147]) ).
cnf(c_149,negated_conjecture,
addition(coantidomain(coantidomain(zero)),antidomain(antidomain(sK0))) != domain(sK0),
inference(paramod,[status(thm)],[c_43,c_148]) ).
cnf(c_150,negated_conjecture,
addition(antidomain(antidomain(sK0)),coantidomain(coantidomain(zero))) != domain(sK0),
inference(paramod,[status(thm)],[c_60,c_149]) ).
cnf(c_62,negated_conjecture,
addition(antidomain(antidomain(sK0)),coantidomain(coantidomain(zero))) != antidomain(antidomain(sK0)),
inference(paramod,[status(thm)],[c_43,c_150]) ).
cnf(c_69,plain,
addition(coantidomain(A),coantidomain(coantidomain(A))) = one,
inference(paramod,[status(thm)],[c_60,c_39]) ).
cnf(c_95,plain,
coantidomain(one) = zero,
inference(paramod,[status(thm)],[c_54,c_42]) ).
cnf(c_124,plain,
addition(zero,A) = A,
inference(paramod,[status(thm)],[c_60,c_58]) ).
cnf(c_151,plain,
addition(zero,coantidomain(coantidomain(one))) = one,
inference(paramod,[status(thm)],[c_95,c_69]) ).
cnf(c_152,plain,
addition(zero,coantidomain(zero)) = one,
inference(paramod,[status(thm)],[c_95,c_151]) ).
cnf(c_136,plain,
coantidomain(zero) = one,
inference(paramod,[status(thm)],[c_124,c_152]) ).
cnf(c_153,negated_conjecture,
addition(antidomain(antidomain(sK0)),coantidomain(one)) != antidomain(antidomain(sK0)),
inference(paramod,[status(thm)],[c_136,c_62]) ).
cnf(c_154,negated_conjecture,
addition(antidomain(antidomain(sK0)),zero) != antidomain(antidomain(sK0)),
inference(paramod,[status(thm)],[c_95,c_153]) ).
cnf(c_155,negated_conjecture,
addition(zero,antidomain(antidomain(sK0))) != antidomain(antidomain(sK0)),
inference(paramod,[status(thm)],[c_60,c_154]) ).
cnf(c_156,negated_conjecture,
antidomain(antidomain(sK0)) != antidomain(antidomain(sK0)),
inference(paramod,[status(thm)],[c_124,c_155]) ).
cnf(c_143,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE119+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 19:26:07 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 878595 was started by sandbox on n003,
% 0.09/0.36 % Fri Sep 25 19:26:07 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 27.
% 0.13/0.38 % Level of proof is 4.
% 0.13/0.38 % Maximum clause weight is 46.000.
% 0.13/0.38 % Given clauses 30.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------