TSTP Solution File: SYN333+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN333+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n020.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 : 600s
% DateTime : Thu Jul 21 08:25:15 EDT 2022
% Result : Theorem 0.11s 0.32s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 26 unt; 3 typ; 0 def)
% Number of atoms : 358 ( 70 equ; 0 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 1230 ( 190 ~; 146 |; 22 &; 864 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 89 ( 0 ^ 81 !; 8 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_big_f,type,
big_f: $i > $i > $o ).
thf(tp_big_g,type,
big_g: $i > $i > $o ).
thf(tp_sK1_Z,type,
sK1_Z: $i > $i > $i ).
thf(1,conjecture,
? [X: $i,Y: $i] :
! [Z: $i] :
( ( big_f @ X @ Y )
=> ( ( big_f @ Y @ Z )
& ( big_f @ Z @ Z )
& ( ( ( big_f @ X @ Y )
& ( big_g @ X @ Y ) )
=> ( ( big_g @ X @ Z )
& ( big_g @ Z @ Z ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_14_5) ).
thf(2,negated_conjecture,
( ( ? [X: $i,Y: $i] :
! [Z: $i] :
( ( big_f @ X @ Y )
=> ( ( big_f @ Y @ Z )
& ( big_f @ Z @ Z )
& ( ( ( big_f @ X @ Y )
& ( big_g @ X @ Y ) )
=> ( ( big_g @ X @ Z )
& ( big_g @ Z @ Z ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [X: $i,Y: $i] :
! [Z: $i] :
( ( big_f @ X @ Y )
=> ( ( big_f @ Y @ Z )
& ( big_f @ Z @ Z )
& ( ( ( big_f @ X @ Y )
& ( big_g @ X @ Y ) )
=> ( ( big_g @ X @ Z )
& ( big_g @ Z @ Z ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ? [X: $i,Y: $i] :
! [Z: $i] :
( ( big_f @ X @ Y )
=> ( ( big_f @ Y @ Z )
& ( big_f @ Z @ Z )
& ( ( ( big_f @ X @ Y )
& ( big_g @ X @ Y ) )
=> ( ( big_g @ X @ Z )
& ( big_g @ Z @ Z ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [X: $i] :
( ! [Y: $i] : ( big_f @ X @ Y )
& ! [Y: $i] :
( ( ~ ( big_f @ Y @ ( sK1_Z @ Y @ X ) )
| ~ ( big_f @ ( sK1_Z @ Y @ X ) @ ( sK1_Z @ Y @ X ) )
| ( big_f @ X @ Y ) )
& ( ~ ( big_f @ Y @ ( sK1_Z @ Y @ X ) )
| ~ ( big_f @ ( sK1_Z @ Y @ X ) @ ( sK1_Z @ Y @ X ) )
| ( big_g @ X @ Y ) )
& ( ~ ( big_f @ Y @ ( sK1_Z @ Y @ X ) )
| ~ ( big_f @ ( sK1_Z @ Y @ X ) @ ( sK1_Z @ Y @ X ) )
| ~ ( big_g @ X @ ( sK1_Z @ Y @ X ) )
| ~ ( big_g @ ( sK1_Z @ Y @ X ) @ ( sK1_Z @ Y @ X ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [X: $i] :
( ! [Y: $i] : ( big_f @ X @ Y )
& ! [Y: $i] :
( ( ~ ( big_f @ Y @ ( sK1_Z @ Y @ X ) )
| ~ ( big_f @ ( sK1_Z @ Y @ X ) @ ( sK1_Z @ Y @ X ) )
| ( big_f @ X @ Y ) )
& ( ~ ( big_f @ Y @ ( sK1_Z @ Y @ X ) )
| ~ ( big_f @ ( sK1_Z @ Y @ X ) @ ( sK1_Z @ Y @ X ) )
| ( big_g @ X @ Y ) )
& ( ~ ( big_f @ Y @ ( sK1_Z @ Y @ X ) )
| ~ ( big_f @ ( sK1_Z @ Y @ X ) @ ( sK1_Z @ Y @ X ) )
| ~ ( big_g @ X @ ( sK1_Z @ Y @ X ) )
| ~ ( big_g @ ( sK1_Z @ Y @ X ) @ ( sK1_Z @ Y @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] : ( big_f @ SX0 @ SX1 )
| ~ ! [SX1: $i] :
~ ( ~ ~ ( ~ ( ~ ( big_f @ SX1 @ ( sK1_Z @ SX1 @ SX0 ) )
| ~ ( big_f @ ( sK1_Z @ SX1 @ SX0 ) @ ( sK1_Z @ SX1 @ SX0 ) )
| ( big_f @ SX0 @ SX1 ) )
| ~ ( ~ ( big_f @ SX1 @ ( sK1_Z @ SX1 @ SX0 ) )
| ~ ( big_f @ ( sK1_Z @ SX1 @ SX0 ) @ ( sK1_Z @ SX1 @ SX0 ) )
| ( big_g @ SX0 @ SX1 ) ) )
| ~ ( ~ ( big_f @ SX1 @ ( sK1_Z @ SX1 @ SX0 ) )
| ~ ( big_f @ ( sK1_Z @ SX1 @ SX0 ) @ ( sK1_Z @ SX1 @ SX0 ) )
| ~ ( big_g @ SX0 @ ( sK1_Z @ SX1 @ SX0 ) )
| ~ ( big_g @ ( sK1_Z @ SX1 @ SX0 ) @ ( sK1_Z @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
! [SV1: $i] :
( ( ~ ( ~ ! [SY3: $i] : ( big_f @ SV1 @ SY3 )
| ~ ! [SY4: $i] :
~ ( ~ ~ ( ~ ( ~ ( big_f @ SY4 @ ( sK1_Z @ SY4 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SY4 @ SV1 ) @ ( sK1_Z @ SY4 @ SV1 ) )
| ( big_f @ SV1 @ SY4 ) )
| ~ ( ~ ( big_f @ SY4 @ ( sK1_Z @ SY4 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SY4 @ SV1 ) @ ( sK1_Z @ SY4 @ SV1 ) )
| ( big_g @ SV1 @ SY4 ) ) )
| ~ ( ~ ( big_f @ SY4 @ ( sK1_Z @ SY4 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SY4 @ SV1 ) @ ( sK1_Z @ SY4 @ SV1 ) )
| ~ ( big_g @ SV1 @ ( sK1_Z @ SY4 @ SV1 ) )
| ~ ( big_g @ ( sK1_Z @ SY4 @ SV1 ) @ ( sK1_Z @ SY4 @ SV1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7]) ).
thf(9,plain,
! [SV1: $i] :
( ( ~ ! [SY3: $i] : ( big_f @ SV1 @ SY3 )
| ~ ! [SY4: $i] :
~ ( ~ ~ ( ~ ( ~ ( big_f @ SY4 @ ( sK1_Z @ SY4 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SY4 @ SV1 ) @ ( sK1_Z @ SY4 @ SV1 ) )
| ( big_f @ SV1 @ SY4 ) )
| ~ ( ~ ( big_f @ SY4 @ ( sK1_Z @ SY4 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SY4 @ SV1 ) @ ( sK1_Z @ SY4 @ SV1 ) )
| ( big_g @ SV1 @ SY4 ) ) )
| ~ ( ~ ( big_f @ SY4 @ ( sK1_Z @ SY4 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SY4 @ SV1 ) @ ( sK1_Z @ SY4 @ SV1 ) )
| ~ ( big_g @ SV1 @ ( sK1_Z @ SY4 @ SV1 ) )
| ~ ( big_g @ ( sK1_Z @ SY4 @ SV1 ) @ ( sK1_Z @ SY4 @ SV1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: $i] :
( ( ~ ! [SY3: $i] : ( big_f @ SV1 @ SY3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[9]) ).
thf(11,plain,
! [SV1: $i] :
( ( ~ ! [SY4: $i] :
~ ( ~ ~ ( ~ ( ~ ( big_f @ SY4 @ ( sK1_Z @ SY4 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SY4 @ SV1 ) @ ( sK1_Z @ SY4 @ SV1 ) )
| ( big_f @ SV1 @ SY4 ) )
| ~ ( ~ ( big_f @ SY4 @ ( sK1_Z @ SY4 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SY4 @ SV1 ) @ ( sK1_Z @ SY4 @ SV1 ) )
| ( big_g @ SV1 @ SY4 ) ) )
| ~ ( ~ ( big_f @ SY4 @ ( sK1_Z @ SY4 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SY4 @ SV1 ) @ ( sK1_Z @ SY4 @ SV1 ) )
| ~ ( big_g @ SV1 @ ( sK1_Z @ SY4 @ SV1 ) )
| ~ ( big_g @ ( sK1_Z @ SY4 @ SV1 ) @ ( sK1_Z @ SY4 @ SV1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY3: $i] : ( big_f @ SV1 @ SY3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[10]) ).
thf(13,plain,
! [SV1: $i] :
( ( ! [SY4: $i] :
~ ( ~ ~ ( ~ ( ~ ( big_f @ SY4 @ ( sK1_Z @ SY4 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SY4 @ SV1 ) @ ( sK1_Z @ SY4 @ SV1 ) )
| ( big_f @ SV1 @ SY4 ) )
| ~ ( ~ ( big_f @ SY4 @ ( sK1_Z @ SY4 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SY4 @ SV1 ) @ ( sK1_Z @ SY4 @ SV1 ) )
| ( big_g @ SV1 @ SY4 ) ) )
| ~ ( ~ ( big_f @ SY4 @ ( sK1_Z @ SY4 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SY4 @ SV1 ) @ ( sK1_Z @ SY4 @ SV1 ) )
| ~ ( big_g @ SV1 @ ( sK1_Z @ SY4 @ SV1 ) )
| ~ ( big_g @ ( sK1_Z @ SY4 @ SV1 ) @ ( sK1_Z @ SY4 @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[11]) ).
thf(14,plain,
! [SV2: $i,SV1: $i] :
( ( big_f @ SV1 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
| ( big_f @ SV1 @ SV3 ) )
| ~ ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
| ( big_g @ SV1 @ SV3 ) ) )
| ~ ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_g @ SV1 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_g @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ~ ( ~ ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
| ( big_f @ SV1 @ SV3 ) )
| ~ ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
| ( big_g @ SV1 @ SV3 ) ) )
| ~ ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_g @ SV1 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_g @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(17,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ~ ( ~ ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
| ( big_f @ SV1 @ SV3 ) )
| ~ ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
| ( big_g @ SV1 @ SV3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(18,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_g @ SV1 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_g @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(19,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
| ( big_f @ SV1 @ SV3 ) )
| ~ ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
| ( big_g @ SV1 @ SV3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(20,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_g @ SV1 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_g @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(21,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
| ( big_f @ SV1 @ SV3 ) )
| ~ ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
| ( big_g @ SV1 @ SV3 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(22,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) ) )
= $true )
| ( ( ~ ( big_g @ SV1 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_g @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
| ( big_f @ SV1 @ SV3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(24,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
| ( big_g @ SV1 @ SV3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) ) )
= $true )
| ( ( ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) ) )
= $true )
| ( ( ~ ( big_g @ SV1 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_g @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
| ( big_f @ SV1 @ SV3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(27,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
| ( big_g @ SV1 @ SV3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
! [SV1: $i,SV3: $i] :
( ( ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
= $false )
| ( ( ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) ) )
= $true )
| ( ( ~ ( big_g @ SV1 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_g @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) ) )
= $true )
| ( ( big_f @ SV1 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) ) )
= $true )
| ( ( big_g @ SV1 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV1: $i,SV3: $i] :
( ( ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
= $false )
| ( ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
= $false )
| ( ( ~ ( big_g @ SV1 @ ( sK1_Z @ SV3 @ SV1 ) )
| ~ ( big_g @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) ) )
= $true )
| ( ( ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) ) )
= $true )
| ( ( big_f @ SV1 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) ) )
= $true )
| ( ( ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) ) )
= $true )
| ( ( big_g @ SV1 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( big_g @ SV1 @ ( sK1_Z @ SV3 @ SV1 ) ) )
= $true )
| ( ( ~ ( big_g @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) ) )
= $true )
| ( ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
= $false )
| ( ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV1: $i,SV3: $i] :
( ( ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
= $false )
| ( ( ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) ) )
= $true )
| ( ( big_f @ SV1 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV1: $i,SV3: $i] :
( ( ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
= $false )
| ( ( ~ ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) ) )
= $true )
| ( ( big_g @ SV1 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV3: $i,SV1: $i] :
( ( ( big_g @ SV1 @ ( sK1_Z @ SV3 @ SV1 ) )
= $false )
| ( ( ~ ( big_g @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) ) )
= $true )
| ( ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
= $false )
| ( ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV1: $i,SV3: $i] :
( ( ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
= $false )
| ( ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
= $false )
| ( ( big_f @ SV1 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV1: $i,SV3: $i] :
( ( ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
= $false )
| ( ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
= $false )
| ( ( big_g @ SV1 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV1: $i,SV3: $i] :
( ( ( big_g @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
= $false )
| ( ( big_g @ SV1 @ ( sK1_Z @ SV3 @ SV1 ) )
= $false )
| ( ( big_f @ SV3 @ ( sK1_Z @ SV3 @ SV1 ) )
= $false )
| ( ( big_f @ ( sK1_Z @ SV3 @ SV1 ) @ ( sK1_Z @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(41,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,40,39,38]) ).
thf(42,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.08 % Problem : SYN333+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.08 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.08/0.27 % Computer : n020.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 600
% 0.08/0.27 % DateTime : Mon Jul 11 18:31:42 EDT 2022
% 0.08/0.27 % CPUTime :
% 0.08/0.28
% 0.08/0.28 No.of.Axioms: 0
% 0.08/0.28
% 0.08/0.28 Length.of.Defs: 0
% 0.08/0.28
% 0.08/0.28 Contains.Choice.Funs: false
% 0.08/0.28 (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.11/0.32
% 0.11/0.32 ********************************
% 0.11/0.32 * All subproblems solved! *
% 0.11/0.32 ********************************
% 0.11/0.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:41,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.32
% 0.11/0.32 %**** Beginning of derivation protocol ****
% 0.11/0.32 % SZS output start CNFRefutation
% See solution above
% 0.11/0.32
% 0.11/0.32 %**** End of derivation protocol ****
% 0.11/0.32 %**** no. of clauses in derivation: 42 ****
% 0.11/0.32 %**** clause counter: 41 ****
% 0.11/0.32
% 0.11/0.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:41,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------