%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE048+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 : n026.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 07:44:12 AM UTC 2026
% Result : Theorem 0.14s 5.58s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 62 ( 44 unt; 0 def)
% Number of atoms : 88 ( 47 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 43 ( 17 ~; 13 |; 7 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 29 !; 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_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(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
fof(star_unfold_left,axiom,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
file('theBenchmark.p',star_unfold_left) ).
fof(star_induction_right,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),A)
=> leq(multiplication(C,star(B)),A) ),
file('theBenchmark.p',star_induction_right) ).
fof(test_1,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('theBenchmark.p',test_1) ).
fof(test_2,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('theBenchmark.p',test_2) ).
fof(goals,conjecture,
! [X0] :
( test(X0)
=> star(X0) = one ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( test(X0)
=> star(X0) = one ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_17,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( ? [X2] : complement(X2,X0)
| ~ test(X0) ) ),
inference(fof_nnf,[status(thm)],[test_1]) ).
fof(sk_test_1_sk,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( complement(sK0(X0),X0)
| ~ test(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0))],[nnf_17]) ).
fof(sk_test_1,plain,
( ! [VAR_0,VAR_1] :
( ~ complement(VAR_1,VAR_0)
| test(VAR_0) )
& ! [VAR_0] :
( complement(sK0(VAR_0),VAR_0)
| ~ test(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_test_1_sk]) ).
cnf(c_23,plain,
( complement(sK0(A),A)
| ~ test(A) ),
inference(split_conjunct,[status(thm)],[sk_test_1]) ).
fof(nnf_21,plain,
? [X0] :
( star(X0) != one
& test(X0) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( star(sK1) != one
& test(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[nnf_21]) ).
cnf(c_27,negated_conjecture,
test(sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_28,negated_conjecture,
complement(sK0(sK1),sK1),
inference(resolve,[status(thm)],[c_27,c_23]) ).
cnf(c_37,negated_conjecture,
star(sK1) != one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_39,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_42,plain,
( leq(multiplication(C,star(B)),A)
| ~ leq(addition(multiplication(A,B),C),A) ),
inference(clausify,[status(thm)],[star_induction_right]) ).
cnf(c_44,plain,
leq(addition(one,multiplication(star(A),A)),star(A)),
inference(clausify,[status(thm)],[star_unfold_left]) ).
cnf(c_46,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_47,plain,
( addition(A,B) = B
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_52,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_53,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_52]) ).
cnf(c_54,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_55,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_57,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_59,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_60,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_72,plain,
addition(sK1,sK0(sK1)) = one,
inference(resolve,[status(thm)],[c_39,c_28]) ).
cnf(c_1897,plain,
addition(addition(one,multiplication(star(A),A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_47,c_44]) ).
cnf(c_78,plain,
addition(star(A),addition(one,multiplication(star(A),A))) = star(A),
inference(paramod,[status(thm)],[c_60,c_1897]) ).
cnf(c_1898,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_55,c_53]) ).
cnf(c_104,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_1898]) ).
cnf(c_111,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_57,c_46]) ).
cnf(c_1899,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_57,c_59]) ).
cnf(c_127,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_1899]) ).
cnf(c_133,plain,
( leq(multiplication(A,star(C)),B)
| ~ leq(addition(A,multiplication(B,C)),B) ),
inference(paramod,[status(thm)],[c_60,c_42]) ).
cnf(c_1900,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_60,c_59]) ).
cnf(c_137,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_59,c_1900]) ).
cnf(c_1901,plain,
addition(one,addition(star(A),multiplication(star(A),A))) = star(A),
inference(paramod,[status(thm)],[c_137,c_78]) ).
cnf(c_143,plain,
addition(one,multiplication(star(A),addition(one,A))) = star(A),
inference(paramod,[status(thm)],[c_104,c_1901]) ).
cnf(c_1902,plain,
addition(sK1,one) = addition(sK1,sK0(sK1)),
inference(paramod,[status(thm)],[c_72,c_127]) ).
cnf(c_1903,plain,
addition(one,sK1) = addition(sK1,sK0(sK1)),
inference(paramod,[status(thm)],[c_60,c_1902]) ).
cnf(c_374,plain,
addition(one,sK1) = one,
inference(paramod,[status(thm)],[c_72,c_1903]) ).
cnf(c_1904,plain,
addition(multiplication(A,one),multiplication(A,sK1)) = multiplication(A,one),
inference(paramod,[status(thm)],[c_374,c_53]) ).
cnf(c_1905,plain,
addition(A,multiplication(A,sK1)) = multiplication(A,one),
inference(paramod,[status(thm)],[c_55,c_1904]) ).
cnf(c_405,plain,
addition(A,multiplication(A,sK1)) = A,
inference(paramod,[status(thm)],[c_55,c_1905]) ).
cnf(c_1906,plain,
( leq(multiplication(A,star(sK1)),A)
| ~ leq(A,A) ),
inference(paramod,[status(thm)],[c_405,c_133]) ).
cnf(c_1583,plain,
leq(multiplication(A,star(sK1)),A),
inference(resolve,[status(thm)],[c_111,c_1906]) ).
cnf(c_1608,plain,
leq(star(sK1),one),
inference(paramod,[status(thm)],[c_54,c_1583]) ).
cnf(c_1907,plain,
addition(star(sK1),one) = one,
inference(resolve,[status(thm)],[c_1608,c_47]) ).
cnf(c_1611,plain,
addition(one,star(sK1)) = one,
inference(paramod,[status(thm)],[c_60,c_1907]) ).
cnf(c_1908,plain,
addition(one,star(A)) = addition(one,multiplication(star(A),addition(one,A))),
inference(paramod,[status(thm)],[c_143,c_127]) ).
cnf(c_1861,plain,
addition(one,star(A)) = star(A),
inference(paramod,[status(thm)],[c_143,c_1908]) ).
cnf(c_1909,plain,
star(sK1) = one,
inference(paramod,[status(thm)],[c_1861,c_1611]) ).
cnf(c_1896,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_37,c_1909]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE048+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n026.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Fri Sep 25 19:21:01 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.37 % Process 3212898 was started by sandbox on n026,
% 0.10/5.37 % Fri Sep 25 19:21:01 2026
% 0.10/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.38
% 0.10/5.38 % From the command line: assign(max_seconds, 300).
% 0.14/5.58
% 0.14/5.58 % SZS status Theorem for theBenchmark
% 0.14/5.58
% 0.14/5.58 % Proof 1 at 0.14 (+ 0.05) seconds.
% 0.14/5.58 % Length of proof is 43.
% 0.14/5.58 % Level of proof is 9.
% 0.14/5.58 % Maximum clause weight is 13.000.
% 0.14/5.58 % Given clauses 261.
% 0.14/5.58
% 0.14/5.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------