TSTP Solution File: SEV529^1 by Leo-III-SAT---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEV529^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 04:11:38 EDT 2024
% Result : Theorem 59.70s 9.68s
% Output : Refutation 59.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 38 ( 13 unt; 8 typ; 0 def)
% Number of atoms : 92 ( 10 equ; 1 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 900 ( 21 ~; 6 |; 0 &; 806 @)
% ( 0 <=>; 67 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 523 ( 523 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 388 ( 265 ^ 113 !; 10 ?; 388 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_False_type,type,
c_False: $o ).
thf(c_not_type,type,
c_not: $o > $o ).
thf(c_In_type,type,
c_In: $i > $i > $o ).
thf(c_Empty_type,type,
c_Empty: $i ).
thf(c_Inj1_type,type,
c_Inj1: $i > $i ).
thf(c_Inj0_type,type,
c_Inj0: $i > $i ).
thf(c_setsum_type,type,
c_setsum: $i > $i > $i ).
thf(sk1_type,type,
sk1: ( $i > $i ) > $i > $o ).
thf(1,conjecture,
! [A: ( $i > $i ) > $i > $o,B: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o,C: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $i > ( $i > $i ) > $i > $i ) > $i > ( ( $i > $i ) > $i > $i ) > $o,D: ( ( $i > $i ) > $i ) > ( $i > $i ) > ( $i > $i ) > $i > $o] :
( ! [E: $i,F: $i,G: $i > ( $i > $i ) > $i,H: $i] :
( D
@ ^ [I: $i > $i] : ( c_Inj0 @ ( I @ c_Empty ) )
@ ^ [I: $i] : F
@ ^ [I: $i] :
( G @ c_Empty
@ ^ [J: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) )
=> ( ! [E: $i > ( $i > $i ) > $i > $i > $i,F: $i,G: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i,H: $i] :
( ( D
@ ^ [I: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( G
@ ^ [J: ( $i > $i ) > $i,K: $i > $i,L: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [I: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ I ) )
@ ^ [I: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) )
=> ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) ) )
=> ( ! [E: $i > $i > $i,F: ( ( $i > $i > $i ) > $i ) > $i,G: $i > ( $i > $i > $i ) > $i,H: ( $i > $i > $i > $i ) > $i] :
( C
@ ^ [I: $i > ( ( $i > $i ) > $i ) > $i,J: $i,K: $i,L: $i > $i,M: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ M ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [I: $i > $i,J: $i] :
( c_setsum @ J
@ ( H
@ ^ [K: $i,L: $i,M: $i] : c_Empty ) ) )
=> ( ! [E: ( $i > ( $i > $i ) > $i > $i ) > $i,F: $i,G: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,H: $i] :
( ( c_In @ ( c_Inj0 @ ( c_Inj1 @ H ) )
@ ( E
@ ^ [I: $i,J: $i > $i,K: $i] : c_Empty ) )
=> ( ( C
@ ^ [I: $i > ( ( $i > $i ) > $i ) > $i,J: $i,K: $i,L: $i > $i,M: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( E
@ ^ [I: $i,J: $i > $i,K: $i] : c_Empty )
@ c_Empty )
@ ^ [I: $i > $i,J: $i] : ( c_Inj1 @ c_Empty ) )
=> ( C
@ ^ [I: $i > ( ( $i > $i ) > $i ) > $i,J: $i,K: $i,L: $i > $i,M: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [I: $i > $i,J: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) )
=> ( ! [E: $i,F: ( $i > $i > $i ) > $i > $i,G: ( $i > $i > $i > $i ) > $i,H: $i > $i] :
( ( c_In
@ ( G
@ ^ [I: $i,J: $i,K: $i] : ( c_Inj1 @ J ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( A
@ ^ [I: $i] : I
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) )
=> ( B
@ ^ [I: $i,J: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ J ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( H @ ( H @ c_Empty ) ) ) )
@ ^ [I: $i > $i] : c_Empty ) ) )
=> ( ! [E: $i,F: $i,G: $i > $i,H: $i] :
( ( B
@ ^ [I: $i,J: $i] : I
@ ^ [I: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
=> c_False )
=> ( ! [E: $i,F: $i,G: ( $i > ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i ) > $i > $i,H: $i > $i] :
( A
@ ^ [I: $i] : I
@ ( c_Inj0 @ c_Empty ) )
=> ( ! [E: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i,F: $i > $i > $i,G: $i > $i > $i > $i,H: $i] :
( ( A
@ ^ [I: $i] : I
@ ( G @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( F @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( G @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( E
@ ^ [I: $i] : c_Empty
@ ^ [I: $i > $i,J: $i] : ( c_setsum @ J @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( c_In @ ( c_Inj0 @ c_Empty )
@ ( E
@ ^ [I: $i] : I
@ ^ [I: $i > $i,J: $i] : c_Empty ) ) )
=> c_False ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: ( $i > $i ) > $i > $o,B: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o,C: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $i > ( $i > $i ) > $i > $i ) > $i > ( ( $i > $i ) > $i > $i ) > $o,D: ( ( $i > $i ) > $i ) > ( $i > $i ) > ( $i > $i ) > $i > $o] :
( ! [E: $i,F: $i,G: $i > ( $i > $i ) > $i,H: $i] :
( D
@ ^ [I: $i > $i] : ( c_Inj0 @ ( I @ c_Empty ) )
@ ^ [I: $i] : F
@ ^ [I: $i] :
( G @ c_Empty
@ ^ [J: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) )
=> ( ! [E: $i > ( $i > $i ) > $i > $i > $i,F: $i,G: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i,H: $i] :
( ( D
@ ^ [I: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( G
@ ^ [J: ( $i > $i ) > $i,K: $i > $i,L: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [I: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ I ) )
@ ^ [I: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) )
=> ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) ) )
=> ( ! [E: $i > $i > $i,F: ( ( $i > $i > $i ) > $i ) > $i,G: $i > ( $i > $i > $i ) > $i,H: ( $i > $i > $i > $i ) > $i] :
( C
@ ^ [I: $i > ( ( $i > $i ) > $i ) > $i,J: $i,K: $i,L: $i > $i,M: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ M ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [I: $i > $i,J: $i] :
( c_setsum @ J
@ ( H
@ ^ [K: $i,L: $i,M: $i] : c_Empty ) ) )
=> ( ! [E: ( $i > ( $i > $i ) > $i > $i ) > $i,F: $i,G: $i > ( ( $i > $i ) > $i > $i ) > $i > $i,H: $i] :
( ( c_In @ ( c_Inj0 @ ( c_Inj1 @ H ) )
@ ( E
@ ^ [I: $i,J: $i > $i,K: $i] : c_Empty ) )
=> ( ( C
@ ^ [I: $i > ( ( $i > $i ) > $i ) > $i,J: $i,K: $i,L: $i > $i,M: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( E
@ ^ [I: $i,J: $i > $i,K: $i] : c_Empty )
@ c_Empty )
@ ^ [I: $i > $i,J: $i] : ( c_Inj1 @ c_Empty ) )
=> ( C
@ ^ [I: $i > ( ( $i > $i ) > $i ) > $i,J: $i,K: $i,L: $i > $i,M: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [I: $i > $i,J: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) )
=> ( ! [E: $i,F: ( $i > $i > $i ) > $i > $i,G: ( $i > $i > $i > $i ) > $i,H: $i > $i] :
( ( c_In
@ ( G
@ ^ [I: $i,J: $i,K: $i] : ( c_Inj1 @ J ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( A
@ ^ [I: $i] : I
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) )
=> ( B
@ ^ [I: $i,J: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ J ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( H @ ( H @ c_Empty ) ) ) )
@ ^ [I: $i > $i] : c_Empty ) ) )
=> ( ! [E: $i,F: $i,G: $i > $i,H: $i] :
( ( B
@ ^ [I: $i,J: $i] : I
@ ^ [I: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
=> c_False )
=> ( ! [E: $i,F: $i,G: ( $i > ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i ) > $i > $i,H: $i > $i] :
( A
@ ^ [I: $i] : I
@ ( c_Inj0 @ c_Empty ) )
=> ( ! [E: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i,F: $i > $i > $i,G: $i > $i > $i > $i,H: $i] :
( ( A
@ ^ [I: $i] : I
@ ( G @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( F @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( G @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( E
@ ^ [I: $i] : c_Empty
@ ^ [I: $i > $i,J: $i] : ( c_setsum @ J @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( c_In @ ( c_Inj0 @ c_Empty )
@ ( E
@ ^ [I: $i] : I
@ ^ [I: $i > $i,J: $i] : c_Empty ) ) )
=> c_False ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(106,plain,
~ ! [A: ( $i > $i ) > $i > $o,B: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o,C: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $i > ( $i > $i ) > $i > $i ) > $i > ( ( $i > $i ) > $i > $i ) > $o,D: ( ( $i > $i ) > $i ) > ( $i > $i ) > ( $i > $i ) > $i > $o] :
( ! [E: $i,F: $i > ( $i > $i ) > $i] :
( D
@ ^ [G: $i > $i] : ( c_Inj0 @ ( G @ c_Empty ) )
@ ^ [G: $i] : E
@ ^ [G: $i] :
( F @ c_Empty
@ ^ [H: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) )
=> ( ! [E: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( ( D
@ ^ [F: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( E
@ ^ [G: ( $i > $i ) > $i,H: $i > $i,I: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [F: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ F ) )
@ ^ [F: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) )
=> ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) ) )
=> ( ! [E: ( $i > $i > $i > $i ) > $i] :
( C
@ ^ [F: $i > ( ( $i > $i ) > $i ) > $i,G: $i,H: $i,I: $i > $i,J: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ J ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [F: $i > $i,G: $i] :
( c_setsum @ G
@ ( E
@ ^ [H: $i,I: $i,J: $i] : c_Empty ) ) )
=> ( ! [E: ( $i > ( $i > $i ) > $i > $i ) > $i,F: $i] :
( ( c_In @ ( c_Inj0 @ ( c_Inj1 @ F ) )
@ ( E
@ ^ [G: $i,H: $i > $i,I: $i] : c_Empty ) )
=> ( ( C
@ ^ [G: $i > ( ( $i > $i ) > $i ) > $i,H: $i,I: $i,J: $i > $i,K: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( E
@ ^ [G: $i,H: $i > $i,I: $i] : c_Empty )
@ c_Empty )
@ ^ [G: $i > $i,H: $i] : ( c_Inj1 @ c_Empty ) )
=> ( C
@ ^ [G: $i > ( ( $i > $i ) > $i ) > $i,H: $i,I: $i,J: $i > $i,K: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [G: $i > $i,H: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) )
=> ( ! [E: ( $i > $i > $i > $i ) > $i,F: $i > $i] :
( ( c_In
@ ( E
@ ^ [G: $i,H: $i,I: $i] : ( c_Inj1 @ H ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( A
@ ^ [G: $i] : G
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) )
=> ( B
@ ^ [G: $i,H: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ H ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( F @ ( F @ c_Empty ) ) ) )
@ ^ [G: $i > $i] : c_Empty ) ) )
=> ( ( ( B
@ ^ [E: $i,F: $i] : E
@ ^ [E: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
=> c_False )
=> ( ( A
@ ^ [E: $i] : E
@ ( c_Inj0 @ c_Empty ) )
=> ( ! [E: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i,F: $i > $i > $i,G: $i > $i > $i > $i] :
( ( A
@ ^ [H: $i] : H
@ ( G @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( F @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( G @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( E
@ ^ [H: $i] : c_Empty
@ ^ [H: $i > $i,I: $i] : ( c_setsum @ I @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( c_In @ ( c_Inj0 @ c_Empty )
@ ( E
@ ^ [H: $i] : H
@ ^ [H: $i > $i,I: $i] : c_Empty ) ) )
=> c_False ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(107,plain,
~ ! [A: ( $i > $i ) > $i > $o,B: ( $i > $i > $i ) > ( ( $i > $i ) > $i ) > $o,C: ( ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $i > ( $i > $i ) > $i > $i ) > $i > ( ( $i > $i ) > $i > $i ) > $o,D: ( ( $i > $i ) > $i ) > ( $i > $i ) > ( $i > $i ) > $i > $o] :
( ! [E: $i,F: $i > ( $i > $i ) > $i] :
( D
@ ^ [G: $i > $i] : ( c_Inj0 @ ( G @ c_Empty ) )
@ ^ [G: $i] : E
@ ^ [G: $i] :
( F @ c_Empty
@ ^ [H: $i] : c_Empty )
@ ( c_Inj1 @ c_Empty ) )
=> ( ( ? [E: ( ( ( $i > $i ) > $i ) > ( $i > $i ) > $i > $i ) > $i] :
( D
@ ^ [F: $i > $i] :
( c_Inj1
@ ( c_Inj1
@ ( E
@ ^ [G: ( $i > $i ) > $i,H: $i > $i,I: $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
@ ^ [F: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ F ) )
@ ^ [F: $i] : c_Empty
@ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) )
=> ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) ) )
=> ( ! [E: ( $i > $i > $i > $i ) > $i] :
( C
@ ^ [F: $i > ( ( $i > $i ) > $i ) > $i,G: $i,H: $i,I: $i > $i,J: $i] : ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_Inj0 @ J ) )
@ ( c_setsum @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) @ c_Empty )
@ ^ [F: $i > $i,G: $i] :
( c_setsum @ G
@ ( E
@ ^ [H: $i,I: $i,J: $i] : c_Empty ) ) )
=> ( ! [E: ( $i > ( $i > $i ) > $i > $i ) > $i] :
( ? [F: $i] :
( c_In @ ( c_Inj0 @ ( c_Inj1 @ F ) )
@ ( E
@ ^ [G: $i,H: $i > $i,I: $i] : c_Empty ) )
=> ( ( C
@ ^ [F: $i > ( ( $i > $i ) > $i ) > $i,G: $i,H: $i,I: $i > $i,J: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ c_Empty ) ) ) )
@ ( c_setsum
@ ( E
@ ^ [F: $i,G: $i > $i,H: $i] : c_Empty )
@ c_Empty )
@ ^ [F: $i > $i,G: $i] : ( c_Inj1 @ c_Empty ) )
=> ( C
@ ^ [F: $i > ( ( $i > $i ) > $i ) > $i,G: $i,H: $i,I: $i > $i,J: $i] : ( c_Inj0 @ ( c_Inj0 @ c_Empty ) )
@ c_Empty
@ ^ [F: $i > $i,G: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) ) ) ) ) )
=> ( ( ? [E: ( $i > $i > $i > $i ) > $i] :
( c_In
@ ( E
@ ^ [F: $i,G: $i,H: $i] : ( c_Inj1 @ G ) )
@ ( c_setsum @ ( c_Inj0 @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) @ ( c_setsum @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( ( A
@ ^ [E: $i] : E
@ ( c_setsum @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj1 @ ( c_Inj1 @ c_Empty ) ) ) )
=> ! [E: $i > $i] :
( B
@ ^ [F: $i,G: $i] : ( c_setsum @ ( c_setsum @ ( c_Inj1 @ G ) @ ( c_Inj1 @ c_Empty ) ) @ ( c_setsum @ c_Empty @ ( E @ ( E @ c_Empty ) ) ) )
@ ^ [F: $i > $i] : c_Empty ) ) )
=> ( ( ( B
@ ^ [E: $i,F: $i] : E
@ ^ [E: $i > $i] : ( c_setsum @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ c_Empty ) @ ( c_Inj0 @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) ) )
=> c_False )
=> ( ( A
@ ^ [E: $i] : E
@ ( c_Inj0 @ c_Empty ) )
=> ( ! [E: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( ? [F: $i > $i > $i,G: $i > $i > $i > $i] :
( A
@ ^ [H: $i] : H
@ ( G @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( F @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( G @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( E
@ ^ [H: $i] : c_Empty
@ ^ [H: $i > $i,I: $i] : ( c_setsum @ I @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
=> ( c_In @ ( c_Inj0 @ c_Empty )
@ ( E
@ ^ [F: $i] : F
@ ^ [F: $i > $i,G: $i] : c_Empty ) ) )
=> c_False ) ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[106]) ).
thf(114,plain,
( sk1
@ ^ [A: $i] : A
@ ( c_Inj0 @ c_Empty ) ),
inference(cnf,[status(esa)],[107]) ).
thf(108,plain,
! [C: $i > $i > $i > $i,B: $i > $i > $i,A: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( ~ ( sk1
@ ^ [D: $i] : D
@ ( C @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( B @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( C @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( A
@ ^ [D: $i] : c_Empty
@ ^ [D: $i > $i,E: $i] : ( c_setsum @ E @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
| ( c_In @ ( c_Inj0 @ c_Empty )
@ ( A
@ ^ [D: $i] : D
@ ^ [D: $i > $i,E: $i] : c_Empty ) ) ),
inference(cnf,[status(esa)],[107]) ).
thf(121,plain,
! [C: $i > $i > $i > $i,B: $i > $i > $i,A: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( ~ ( sk1
@ ^ [D: $i] : D
@ ( C @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( B @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( C @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( A
@ ^ [D: $i] : c_Empty
@ ^ [D: $i > $i,E: $i] : ( c_setsum @ E @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
| ( c_In @ ( c_Inj0 @ c_Empty )
@ ( A
@ ^ [D: $i] : D
@ ^ [D: $i > $i,E: $i] : c_Empty ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(740,plain,
! [C: $i > $i > $i > $i,B: $i > $i > $i,A: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( ( c_In @ ( c_Inj0 @ c_Empty )
@ ( A
@ ^ [D: $i] : D
@ ^ [D: $i > $i,E: $i] : c_Empty ) )
| ( ( sk1
@ ^ [D: $i] : D
@ ( C @ ( c_setsum @ ( c_Inj1 @ ( c_Inj0 @ c_Empty ) ) @ ( B @ c_Empty @ c_Empty ) ) @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( C @ ( c_Inj0 @ c_Empty ) @ ( c_Inj1 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) )
@ ( A
@ ^ [D: $i] : c_Empty
@ ^ [D: $i > $i,E: $i] : ( c_setsum @ E @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
!= ( sk1
@ ^ [D: $i] : D
@ ( c_Inj0 @ c_Empty ) ) ) ),
inference(paramod_ordered,[status(thm)],[114,121]) ).
thf(751,plain,
! [A: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( c_In @ ( c_Inj0 @ c_Empty )
@ ( A
@ ^ [B: $i] : B
@ ^ [B: $i > $i,C: $i] : c_Empty ) ),
inference(pre_uni,[status(thm)],[740:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: $i] : ^ [E: $i] : ^ [F: $i] : ( c_Inj0 @ c_Empty ) ))]]) ).
thf(96,axiom,
( c_not
@ ? [A: $i] : ( c_In @ A @ c_Empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
thf(322,plain,
( c_not
@ ? [A: $i] : ( c_In @ A @ c_Empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(24,axiom,
! [A: $o] :
( ( c_not @ ( c_not @ A ) )
=> A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(166,plain,
! [A: $o] :
( ( c_not @ ( c_not @ A ) )
=> A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(169,plain,
( ( c_not @ ( c_not @ $false ) )
=> $false ),
inference(instance,[status(thm)],[166]) ).
thf(170,plain,
~ ( c_not @ ( c_not @ $false ) ),
inference(simp,[status(thm)],[169]) ).
thf(1081,plain,
( ( c_not
@ ? [A: $i] : ( c_In @ A @ c_Empty ) )
!= ( c_not @ ( c_not @ $false ) ) ),
inference(paramod_ordered,[status(thm)],[322,170]) ).
thf(1096,plain,
( ( ? [A: $i] : ( c_In @ A @ c_Empty ) )
!= ( c_not @ $false ) ),
inference(simp,[status(thm)],[1081]) ).
thf(1716,plain,
( ~ ? [A: $i] : ( c_In @ A @ c_Empty )
| ~ ( c_not @ $false ) ),
inference(bool_ext,[status(thm)],[1096]) ).
thf(1738,plain,
! [A: $i] :
( ~ ( c_not @ $false )
| ~ ( c_In @ A @ c_Empty ) ),
inference(cnf,[status(esa)],[1716]) ).
thf(1745,plain,
! [B: $i,A: ( $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i] :
( ~ ( c_not @ $false )
| ( ( c_In @ ( c_Inj0 @ c_Empty )
@ ( A
@ ^ [C: $i] : C
@ ^ [C: $i > $i,D: $i] : c_Empty ) )
!= ( c_In @ B @ c_Empty ) ) ),
inference(paramod_ordered,[status(thm)],[751,1738]) ).
thf(1758,plain,
~ ( c_not @ $false ),
inference(pre_uni,[status(thm)],[1745:[bind(A,$thf( ^ [C: $i > $i] : ^ [D: ( $i > $i ) > $i > $i] : c_Empty )),bind(B,$thf( c_Inj0 @ c_Empty ))]]) ).
thf(81,axiom,
( c_not
= ( ^ [A: $o] :
( A
=> c_False ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).
thf(292,plain,
( c_not
= ( ^ [A: $o] :
( A
=> c_False ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(293,plain,
( ( ^ [A: $o] :
( A
=> c_False ) )
= c_not ),
inference(lifteq,[status(thm)],[292]) ).
thf(112,plain,
~ c_False,
inference(cnf,[status(esa)],[107]) ).
thf(917,plain,
( ( ^ [A: $o] :
( A
=> $false ) )
= c_not ),
inference(rewrite,[status(thm)],[293,112]) ).
thf(918,plain,
(~) = c_not,
inference(simp,[status(thm)],[917]) ).
thf(919,plain,
! [A: $o] :
( ( c_not @ A )
= ~ A ),
inference(func_ext,[status(esa)],[918]) ).
thf(4103,plain,
~ ~ $false,
inference(rewrite,[status(thm)],[1758,919]) ).
thf(4104,plain,
$false,
inference(simp,[status(thm)],[4103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEV529^1 : TPTP v8.2.0. Released v7.5.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 18:33:54 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.92/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.81/1.14 % [INFO] Parsing done (233ms).
% 1.81/1.14 % [INFO] Running in sequential loop mode.
% 2.29/1.36 % [INFO] nitpick registered as external prover.
% 2.29/1.36 % [INFO] Scanning for conjecture ...
% 2.63/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 108 axioms. Running axiom selection ...
% 2.99/1.57 % [INFO] Axiom selection finished. Selected 103 axioms (removed 5 axioms).
% 2.99/1.64 % [INFO] Problem is higher-order (TPTP THF).
% 3.31/1.66 % [INFO] Type checking passed.
% 3.31/1.66 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 59.70/9.67 % [INFO] Killing All external provers ...
% 59.70/9.67 % Time passed: 9147ms (effective reasoning time: 8524ms)
% 59.70/9.67 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 59.70/9.67 % Axioms used in derivation (3): ax5, ax2, ax13
% 59.70/9.67 % No. of inferences in proof: 30
% 59.70/9.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9147 ms resp. 8524 ms w/o parsing
% 59.70/9.70 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 59.70/9.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------