%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE035+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 : n015.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 07:44:09 AM UTC 2026
% Result : Theorem 14.02s 2.21s
% Output : CNFRefutation 14.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 72 ( 44 unt; 0 def)
% Number of atoms : 126 ( 65 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 95 ( 41 ~; 30 |; 16 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 79 ( 3 sgn 30 !; 5 ?)
% 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_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(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(right_annihilation,axiom,
! [A] : multiplication(A,zero) = zero,
file('theBenchmark.p',right_annihilation) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
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(test_3,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('theBenchmark.p',test_3) ).
fof(test_4,axiom,
! [X0] :
( ~ test(X0)
=> c(X0) = zero ),
file('theBenchmark.p',test_4) ).
fof(goals,conjecture,
! [X0,X1,X2,X3] :
( ( leq(multiplication(multiplication(X2,X1),c(X3)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X2)
& test(X3) )
=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( leq(multiplication(multiplication(X2,X1),c(X3)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X2)
& test(X3) )
=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_18,plain,
( ~ complement(B,A)
| test(A) ),
inference(clausify,[status(thm)],[test_1]) ).
cnf(c_21,plain,
( ~ complement(A,B)
| c(A) = B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
cnf(c_22,plain,
( c(A) = zero
| test(A) ),
inference(clausify,[status(thm)],[test_4]) ).
cnf(c_33,plain,
( ~ complement(A,B)
| c(A) = B
| c(A) = zero ),
inference(resolve,[status(thm)],[c_22,c_21]) ).
cnf(c_34,plain,
( ~ complement(C,A)
| ~ complement(A,B)
| c(A) = B ),
inference(resolve,[status(thm)],[c_21,c_18]) ).
fof(nnf_17,plain,
? [X0,X1,X2,X3] :
( ~ leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero)
& leq(multiplication(multiplication(X2,X1),c(X3)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X2)
& test(X3) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ~ leq(multiplication(multiplication(sK0,addition(sK1,sK2)),c(sK3)),zero)
& leq(multiplication(multiplication(sK0,sK2),c(sK3)),zero)
& leq(multiplication(multiplication(sK0,sK1),c(sK3)),zero)
& test(sK0)
& test(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK0,sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK0),skolemize(X3,sK3)],[nnf_17]) ).
cnf(c_37,negated_conjecture,
~ leq(multiplication(multiplication(sK0,addition(sK1,sK2)),c(sK3)),zero),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_38,negated_conjecture,
leq(multiplication(multiplication(sK0,sK2),c(sK3)),zero),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_39,negated_conjecture,
leq(multiplication(multiplication(sK0,sK1),c(sK3)),zero),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_40,plain,
( addition(B,A) != one
| multiplication(A,B) != zero
| multiplication(B,A) != zero
| complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_44,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_45,plain,
( addition(A,B) = B
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_47,plain,
multiplication(A,zero) = zero,
inference(clausify,[status(thm)],[right_annihilation]) ).
cnf(c_48,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_49,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_50,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_51,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_50]) ).
cnf(c_53,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_54,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_56,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_58,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_59,plain,
( ~ complement(A,zero)
| c(A) = zero ),
inference(factor,[status(thm)],[c_33]) ).
cnf(c_62,negated_conjecture,
leq(multiplication(sK0,multiplication(sK1,c(sK3))),zero),
inference(paramod,[status(thm)],[c_54,c_39]) ).
cnf(c_63,negated_conjecture,
leq(multiplication(sK0,multiplication(sK2,c(sK3))),zero),
inference(paramod,[status(thm)],[c_54,c_38]) ).
cnf(c_64,negated_conjecture,
~ leq(multiplication(sK0,multiplication(addition(sK1,sK2),c(sK3))),zero),
inference(paramod,[status(thm)],[c_54,c_37]) ).
cnf(c_4822,plain,
( multiplication(zero,one) != zero
| multiplication(one,zero) != zero
| complement(zero,one) ),
inference(resolve,[status(thm)],[c_56,c_40]) ).
cnf(c_4823,plain,
( multiplication(zero,one) != zero
| zero != zero
| complement(zero,one) ),
inference(paramod,[status(thm)],[c_47,c_4822]) ).
cnf(c_4824,plain,
( zero != zero
| zero != zero
| complement(zero,one) ),
inference(paramod,[status(thm)],[c_53,c_4823]) ).
cnf(c_4825,plain,
( zero != zero
| complement(zero,one) ),
inference(copy,[status(thm)],[c_4824]) ).
cnf(c_101,plain,
complement(zero,one),
inference(copy,[status(thm)],[c_4825]) ).
cnf(c_119,plain,
addition(zero,A) = A,
inference(paramod,[status(thm)],[c_58,c_56]) ).
cnf(c_4826,negated_conjecture,
addition(multiplication(sK0,multiplication(sK1,c(sK3))),zero) = zero,
inference(resolve,[status(thm)],[c_62,c_45]) ).
cnf(c_4827,negated_conjecture,
addition(zero,multiplication(sK0,multiplication(sK1,c(sK3)))) = zero,
inference(paramod,[status(thm)],[c_58,c_4826]) ).
cnf(c_121,negated_conjecture,
multiplication(sK0,multiplication(sK1,c(sK3))) = zero,
inference(paramod,[status(thm)],[c_119,c_4827]) ).
cnf(c_4828,negated_conjecture,
addition(multiplication(sK0,multiplication(sK2,c(sK3))),zero) = zero,
inference(resolve,[status(thm)],[c_63,c_45]) ).
cnf(c_4829,negated_conjecture,
addition(zero,multiplication(sK0,multiplication(sK2,c(sK3)))) = zero,
inference(paramod,[status(thm)],[c_58,c_4828]) ).
cnf(c_122,negated_conjecture,
multiplication(sK0,multiplication(sK2,c(sK3))) = zero,
inference(paramod,[status(thm)],[c_119,c_4829]) ).
cnf(c_4830,negated_conjecture,
addition(multiplication(sK0,multiplication(addition(sK1,sK2),c(sK3))),zero) != zero,
inference(resolve,[status(thm)],[c_44,c_64]) ).
cnf(c_4831,negated_conjecture,
addition(zero,multiplication(sK0,multiplication(addition(sK1,sK2),c(sK3)))) != zero,
inference(paramod,[status(thm)],[c_58,c_4830]) ).
cnf(c_123,negated_conjecture,
multiplication(sK0,multiplication(addition(sK1,sK2),c(sK3))) != zero,
inference(paramod,[status(thm)],[c_119,c_4831]) ).
cnf(c_135,plain,
( ~ complement(one,A)
| c(one) = A ),
inference(resolve,[status(thm)],[c_101,c_34]) ).
cnf(c_4832,plain,
( multiplication(one,zero) != zero
| multiplication(zero,one) != zero
| complement(one,zero) ),
inference(resolve,[status(thm)],[c_119,c_40]) ).
cnf(c_4833,plain,
( multiplication(one,zero) != zero
| zero != zero
| complement(one,zero) ),
inference(paramod,[status(thm)],[c_53,c_4832]) ).
cnf(c_4834,plain,
( zero != zero
| zero != zero
| complement(one,zero) ),
inference(paramod,[status(thm)],[c_47,c_4833]) ).
cnf(c_4835,plain,
( zero != zero
| complement(one,zero) ),
inference(copy,[status(thm)],[c_4834]) ).
cnf(c_152,plain,
complement(one,zero),
inference(copy,[status(thm)],[c_4835]) ).
cnf(c_154,plain,
c(one) = zero,
inference(resolve,[status(thm)],[c_152,c_59]) ).
cnf(c_158,plain,
( ~ complement(one,A)
| zero = A ),
inference(paramod,[status(thm)],[c_154,c_135]) ).
cnf(c_4836,plain,
zero != multiplication(sK0,multiplication(addition(sK1,sK2),c(sK3))),
inference(copy,[status(thm)],[c_123]) ).
cnf(c_233,plain,
~ complement(one,multiplication(sK0,multiplication(addition(sK1,sK2),c(sK3)))),
inference(resolve,[status(thm)],[c_158,c_4836]) ).
cnf(c_4837,plain,
addition(zero,multiplication(sK0,A)) = multiplication(sK0,addition(multiplication(sK1,c(sK3)),A)),
inference(paramod,[status(thm)],[c_121,c_51]) ).
cnf(c_4838,plain,
multiplication(sK0,A) = multiplication(sK0,addition(multiplication(sK1,c(sK3)),A)),
inference(paramod,[status(thm)],[c_119,c_4837]) ).
cnf(c_272,plain,
multiplication(sK0,addition(multiplication(sK1,c(sK3)),A)) = multiplication(sK0,A),
inference(copy,[status(thm)],[c_4838]) ).
cnf(c_4797,plain,
multiplication(sK0,multiplication(addition(sK1,A),c(sK3))) = multiplication(sK0,multiplication(A,c(sK3))),
inference(paramod,[status(thm)],[c_49,c_272]) ).
cnf(c_4839,plain,
~ complement(one,multiplication(sK0,multiplication(sK2,c(sK3)))),
inference(paramod,[status(thm)],[c_4797,c_233]) ).
cnf(c_4840,plain,
~ complement(one,zero),
inference(paramod,[status(thm)],[c_122,c_4839]) ).
cnf(c_4821,plain,
$false,
inference(resolve,[status(thm)],[c_152,c_4840]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE035+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n015.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Fri Sep 25 19:19:29 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.41 % Process 2032705 was started by sandbox2 on n015,
% 0.15/0.41 % Fri Sep 25 19:19:29 2026
% 0.15/0.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.42
% 0.15/0.42 % From the command line: assign(max_seconds, 300).
% 14.02/2.21
% 14.02/2.21 % SZS status Theorem for theBenchmark
% 14.02/2.21
% 14.02/2.21 % Proof 1 at 1.25 (+ 0.51) seconds.
% 14.02/2.21 % Length of proof is 50.
% 14.02/2.21 % Level of proof is 7.
% 14.02/2.21 % Maximum clause weight is 18.000.
% 14.02/2.21 % Given clauses 486.
% 14.02/2.21
% 14.02/2.21 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------