%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN077+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 : Wed Oct 7 11:02:54 AM UTC 2026
% Result : Theorem 0.12s 0.29s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 2
% Syntax : Number of formulae : 78 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 641 ( 180 equ; 0 cnn)
% Maximal formula atoms : 5 ( 8 avg)
% Number of connectives : 1516 ( 546 ~; 230 |; 10 &; 717 @)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 251 ( 0 ^; 233 !; 18 ?; 251 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_big_f,type,
big_f: $i > $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY8,type,
sK2_SY8: $i > $i ).
thf(tp_sK3_SY21,type,
sK3_SY21: $i > $i ).
thf(tp_sK4_SY24,type,
sK4_SY24: $i > $i > $i ).
thf(tp_sK5_SY28,type,
sK5_SY28: $i > $i > $i ).
thf(1,axiom,
! [Y: $i] :
? [Z: $i] :
! [X: $i] :
( ( big_f @ X @ Z )
<=> ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel54_1) ).
thf(2,conjecture,
~ ? [W: $i] :
! [X: $i] :
( ( big_f @ X @ W )
<=> ! [U: $i] :
( ( big_f @ X @ U )
=> ? [Y: $i] :
( ( big_f @ Y @ U )
& ~ ? [Z: $i] :
( ( big_f @ Z @ U )
& ( big_f @ Z @ Y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel54) ).
thf(3,negated_conjecture,
( ( ~ ? [W: $i] :
! [X: $i] :
( ( big_f @ X @ W )
<=> ! [U: $i] :
( ( big_f @ X @ U )
=> ? [Y: $i] :
( ( big_f @ Y @ U )
& ~ ? [Z: $i] :
( ( big_f @ Z @ U )
& ( big_f @ Z @ Y ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,plain,
( ( ~ ? [W: $i] :
! [X: $i] :
( ( big_f @ X @ W )
<=> ! [U: $i] :
( ( big_f @ X @ U )
=> ? [Y: $i] :
( ( big_f @ Y @ U )
& ~ ? [Z: $i] :
( ( big_f @ Z @ U )
& ( big_f @ Z @ Y ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Y: $i] :
? [Z: $i] :
! [X: $i] :
( ( big_f @ X @ Z )
<=> ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(6,plain,
( ( ? [W: $i] :
! [X: $i] :
( ( big_f @ X @ W )
<=> ! [U: $i] :
( ( big_f @ X @ U )
=> ? [Y: $i] :
( ( big_f @ Y @ U )
& ~ ? [Z: $i] :
( ( big_f @ Z @ U )
& ( big_f @ Z @ Y ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(7,plain,
( ( ! [Y: $i] :
? [Z: $i] :
! [X: $i] :
( ( big_f @ X @ Z )
<=> ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(8,plain,
( ( ? [W: $i] :
! [X: $i] :
( ( big_f @ X @ W )
<=> ! [U: $i] :
( ( big_f @ X @ U )
=> ? [Y: $i] :
( ( big_f @ Y @ U )
& ~ ? [Z: $i] :
( ( big_f @ Z @ U )
& ( big_f @ Z @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( ~ ( ~ ( big_f @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( big_f @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( big_f @ SX3 @ SX2 )
| ~ ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( big_f @ SX4 @ SX2 )
| ~ ( big_f @ SX4 @ SX3 ) ) ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( big_f @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( big_f @ SX3 @ SX2 )
| ~ ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( big_f @ SX4 @ SX2 )
| ~ ( big_f @ SX4 @ SX3 ) ) ) )
| ( big_f @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ( ~ ( ~ ( big_f @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( big_f @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( ~ ( ~ ( big_f @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( big_f @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( big_f @ SX3 @ SX2 )
| ~ ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( big_f @ SX4 @ SX2 )
| ~ ( big_f @ SX4 @ SX3 ) ) ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( big_f @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( big_f @ SX3 @ SX2 )
| ~ ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( big_f @ SX4 @ SX2 )
| ~ ( big_f @ SX4 @ SX3 ) ) ) )
| ( big_f @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i] :
( ( ~ ! [SY8: $i] :
~ ! [SY9: $i] :
~ ( ~ ( ~ ( big_f @ SY9 @ SY8 )
| ( SY9 = SV1 ) )
| ~ ( ( SY9 != SV1 )
| ( big_f @ SY9 @ SY8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ! [SY10: $i] :
~ ( ~ ( ~ ( big_f @ SY10 @ sK1_SX0 )
| ! [SX2: $i] :
( ~ ( big_f @ SY10 @ SX2 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( big_f @ SX3 @ SX2 )
| ~ ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( big_f @ SX4 @ SX2 )
| ~ ( big_f @ SX4 @ SX3 ) ) ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( big_f @ SY10 @ SX2 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( big_f @ SX3 @ SX2 )
| ~ ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( big_f @ SX4 @ SX2 )
| ~ ( big_f @ SX4 @ SX3 ) ) ) )
| ( big_f @ SY10 @ sK1_SX0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(14,plain,
! [SV1: $i] :
( ( ! [SY8: $i] :
~ ! [SY9: $i] :
~ ( ~ ( ~ ( big_f @ SY9 @ SY8 )
| ( SY9 = SV1 ) )
| ~ ( ( SY9 != SV1 )
| ( big_f @ SY9 @ SY8 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ! [SY10: $i] :
~ ( ~ ( ~ ( big_f @ SY10 @ sK1_SX0 )
| ! [SX2: $i] :
( ~ ( big_f @ SY10 @ SX2 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( big_f @ SX3 @ SX2 )
| ~ ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( big_f @ SX4 @ SX2 )
| ~ ( big_f @ SX4 @ SX3 ) ) ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( big_f @ SY10 @ SX2 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( big_f @ SX3 @ SX2 )
| ~ ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( big_f @ SX4 @ SX2 )
| ~ ( big_f @ SX4 @ SX3 ) ) ) )
| ( big_f @ SY10 @ sK1_SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(16,plain,
! [SV1: $i] :
( ( ~ ! [SY17: $i] :
~ ( ~ ( ~ ( big_f @ SY17 @ ( sK2_SY8 @ SV1 ) )
| ( SY17 = SV1 ) )
| ~ ( ( SY17 != SV1 )
| ( big_f @ SY17 @ ( sK2_SY8 @ SV1 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(17,plain,
! [SV2: $i] :
( ( ~ ( ~ ( ~ ( big_f @ SV2 @ sK1_SX0 )
| ! [SY18: $i] :
( ~ ( big_f @ SV2 @ SY18 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( big_f @ SX3 @ SY18 )
| ~ ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( big_f @ SX4 @ SY18 )
| ~ ( big_f @ SX4 @ SX3 ) ) ) ) )
| ~ ( ~ ! [SY21: $i] :
( ~ ( big_f @ SV2 @ SY21 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( big_f @ SX3 @ SY21 )
| ~ ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( big_f @ SX4 @ SY21 )
| ~ ( big_f @ SX4 @ SX3 ) ) ) )
| ( big_f @ SV2 @ sK1_SX0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(18,plain,
! [SV1: $i] :
( ( ! [SY17: $i] :
~ ( ~ ( ~ ( big_f @ SY17 @ ( sK2_SY8 @ SV1 ) )
| ( SY17 = SV1 ) )
| ~ ( ( SY17 != SV1 )
| ( big_f @ SY17 @ ( sK2_SY8 @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(19,plain,
! [SV2: $i] :
( ( ~ ( ~ ( big_f @ SV2 @ sK1_SX0 )
| ! [SY18: $i] :
( ~ ( big_f @ SV2 @ SY18 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( big_f @ SX3 @ SY18 )
| ~ ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( big_f @ SX4 @ SY18 )
| ~ ( big_f @ SX4 @ SX3 ) ) ) ) )
| ~ ( ~ ! [SY21: $i] :
( ~ ( big_f @ SV2 @ SY21 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( big_f @ SX3 @ SY21 )
| ~ ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( big_f @ SX4 @ SY21 )
| ~ ( big_f @ SX4 @ SX3 ) ) ) )
| ( big_f @ SV2 @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(20,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( big_f @ SV3 @ ( sK2_SY8 @ SV1 ) )
| ( SV3 = SV1 ) )
| ~ ( ( SV3 != SV1 )
| ( big_f @ SV3 @ ( sK2_SY8 @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(21,plain,
! [SV2: $i] :
( ( ~ ( ~ ( big_f @ SV2 @ sK1_SX0 )
| ! [SY18: $i] :
( ~ ( big_f @ SV2 @ SY18 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( big_f @ SX3 @ SY18 )
| ~ ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( big_f @ SX4 @ SY18 )
| ~ ( big_f @ SX4 @ SX3 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(22,plain,
! [SV2: $i] :
( ( ~ ( ~ ! [SY21: $i] :
( ~ ( big_f @ SV2 @ SY21 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( big_f @ SX3 @ SY21 )
| ~ ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( big_f @ SX4 @ SY21 )
| ~ ( big_f @ SX4 @ SX3 ) ) ) )
| ( big_f @ SV2 @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(23,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ( ~ ( big_f @ SV3 @ ( sK2_SY8 @ SV1 ) )
| ( SV3 = SV1 ) )
| ~ ( ( SV3 != SV1 )
| ( big_f @ SV3 @ ( sK2_SY8 @ SV1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV2: $i] :
( ( ~ ( big_f @ SV2 @ sK1_SX0 )
| ! [SY18: $i] :
( ~ ( big_f @ SV2 @ SY18 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( big_f @ SX3 @ SY18 )
| ~ ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( big_f @ SX4 @ SY18 )
| ~ ( big_f @ SX4 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV2: $i] :
( ( ~ ! [SY21: $i] :
( ~ ( big_f @ SV2 @ SY21 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( big_f @ SX3 @ SY21 )
| ~ ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( big_f @ SX4 @ SY21 )
| ~ ( big_f @ SX4 @ SX3 ) ) ) )
| ( big_f @ SV2 @ sK1_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(26,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ( ~ ( big_f @ SV3 @ ( sK2_SY8 @ SV1 ) )
| ( SV3 = SV1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(27,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ( ( SV3 != SV1 )
| ( big_f @ SV3 @ ( sK2_SY8 @ SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(28,plain,
! [SV2: $i] :
( ( ( ~ ( big_f @ SV2 @ sK1_SX0 ) )
= $true )
| ( ( ! [SY18: $i] :
( ~ ( big_f @ SV2 @ SY18 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( big_f @ SX3 @ SY18 )
| ~ ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( big_f @ SX4 @ SY18 )
| ~ ( big_f @ SX4 @ SX3 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV2: $i] :
( ( ( ~ ! [SY21: $i] :
( ~ ( big_f @ SV2 @ SY21 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( big_f @ SX3 @ SY21 )
| ~ ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( big_f @ SX4 @ SY21 )
| ~ ( big_f @ SX4 @ SX3 ) ) ) ) )
= $true )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ( big_f @ SV3 @ ( sK2_SY8 @ SV1 ) )
| ( SV3 = SV1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(31,plain,
! [SV1: $i,SV3: $i] :
( ( ( SV3 != SV1 )
| ( big_f @ SV3 @ ( sK2_SY8 @ SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(32,plain,
! [SV2: $i] :
( ( ( big_f @ SV2 @ sK1_SX0 )
= $false )
| ( ( ! [SY18: $i] :
( ~ ( big_f @ SV2 @ SY18 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( big_f @ SX3 @ SY18 )
| ~ ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( big_f @ SX4 @ SY18 )
| ~ ( big_f @ SX4 @ SX3 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV2: $i] :
( ( ( ! [SY21: $i] :
( ~ ( big_f @ SV2 @ SY21 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( big_f @ SX3 @ SY21 )
| ~ ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( big_f @ SX4 @ SY21 )
| ~ ( big_f @ SX4 @ SX3 ) ) ) ) )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( big_f @ SV3 @ ( sK2_SY8 @ SV1 ) ) )
= $true )
| ( ( SV3 = SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV1: $i,SV3: $i] :
( ( ( SV3 != SV1 )
= $true )
| ( ( big_f @ SV3 @ ( sK2_SY8 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( big_f @ SV2 @ SV4 )
| ~ ! [SY24: $i] :
~ ~ ( ~ ( big_f @ SY24 @ SV4 )
| ~ ~ ~ ! [SY25: $i] :
~ ~ ( ~ ( big_f @ SY25 @ SV4 )
| ~ ( big_f @ SY25 @ SY24 ) ) ) )
= $true )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV2: $i] :
( ( ( ~ ( big_f @ SV2 @ ( sK3_SY21 @ SV2 ) )
| ~ ! [SY26: $i] :
~ ~ ( ~ ( big_f @ SY26 @ ( sK3_SY21 @ SV2 ) )
| ~ ~ ~ ! [SY27: $i] :
~ ~ ( ~ ( big_f @ SY27 @ ( sK3_SY21 @ SV2 ) )
| ~ ( big_f @ SY27 @ SY26 ) ) ) )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[33]) ).
thf(38,plain,
! [SV1: $i,SV3: $i] :
( ( ( big_f @ SV3 @ ( sK2_SY8 @ SV1 ) )
= $false )
| ( ( SV3 = SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV1: $i,SV3: $i] :
( ( ( SV3 = SV1 )
= $false )
| ( ( big_f @ SV3 @ ( sK2_SY8 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( big_f @ SV2 @ SV4 ) )
= $true )
| ( ( ~ ! [SY24: $i] :
~ ~ ( ~ ( big_f @ SY24 @ SV4 )
| ~ ~ ~ ! [SY25: $i] :
~ ~ ( ~ ( big_f @ SY25 @ SV4 )
| ~ ( big_f @ SY25 @ SY24 ) ) ) )
= $true )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV2: $i] :
( ( ( ~ ( big_f @ SV2 @ ( sK3_SY21 @ SV2 ) ) )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(42,plain,
! [SV2: $i] :
( ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ( big_f @ SY26 @ ( sK3_SY21 @ SV2 ) )
| ~ ~ ~ ! [SY27: $i] :
~ ~ ( ~ ( big_f @ SY27 @ ( sK3_SY21 @ SV2 ) )
| ~ ( big_f @ SY27 @ SY26 ) ) ) )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(43,plain,
! [SV4: $i,SV2: $i] :
( ( ( big_f @ SV2 @ SV4 )
= $false )
| ( ( ~ ! [SY24: $i] :
~ ~ ( ~ ( big_f @ SY24 @ SV4 )
| ~ ~ ~ ! [SY25: $i] :
~ ~ ( ~ ( big_f @ SY25 @ SV4 )
| ~ ( big_f @ SY25 @ SY24 ) ) ) )
= $true )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV2: $i] :
( ( ( big_f @ SV2 @ ( sK3_SY21 @ SV2 ) )
= $true )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV2: $i] :
( ( ( ! [SY26: $i] :
~ ~ ( ~ ( big_f @ SY26 @ ( sK3_SY21 @ SV2 ) )
| ~ ~ ~ ! [SY27: $i] :
~ ~ ( ~ ( big_f @ SY27 @ ( sK3_SY21 @ SV2 ) )
| ~ ( big_f @ SY27 @ SY26 ) ) ) )
= $true )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(46,plain,
! [SV2: $i,SV4: $i] :
( ( ( ! [SY24: $i] :
~ ~ ( ~ ( big_f @ SY24 @ SV4 )
| ~ ~ ~ ! [SY25: $i] :
~ ~ ( ~ ( big_f @ SY25 @ SV4 )
| ~ ( big_f @ SY25 @ SY24 ) ) ) )
= $false )
| ( ( big_f @ SV2 @ SV4 )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( big_f @ SV5 @ ( sK3_SY21 @ SV2 ) )
| ~ ~ ~ ! [SY28: $i] :
~ ~ ( ~ ( big_f @ SY28 @ ( sK3_SY21 @ SV2 ) )
| ~ ( big_f @ SY28 @ SV5 ) ) ) )
= $true )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( big_f @ ( sK4_SY24 @ SV2 @ SV4 ) @ SV4 )
| ~ ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( big_f @ SY29 @ SV4 )
| ~ ( big_f @ SY29 @ ( sK4_SY24 @ SV2 @ SV4 ) ) ) ) )
= $false )
| ( ( big_f @ SV2 @ SV4 )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[46]) ).
thf(49,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( ~ ( big_f @ SV5 @ ( sK3_SY21 @ SV2 ) )
| ~ ~ ~ ! [SY28: $i] :
~ ~ ( ~ ( big_f @ SY28 @ ( sK3_SY21 @ SV2 ) )
| ~ ( big_f @ SY28 @ SV5 ) ) ) )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(50,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( ~ ( big_f @ ( sK4_SY24 @ SV2 @ SV4 ) @ SV4 )
| ~ ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( big_f @ SY29 @ SV4 )
| ~ ( big_f @ SY29 @ ( sK4_SY24 @ SV2 @ SV4 ) ) ) ) )
= $true )
| ( ( big_f @ SV2 @ SV4 )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(51,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( big_f @ SV5 @ ( sK3_SY21 @ SV2 ) )
| ~ ~ ~ ! [SY28: $i] :
~ ~ ( ~ ( big_f @ SY28 @ ( sK3_SY21 @ SV2 ) )
| ~ ( big_f @ SY28 @ SV5 ) ) )
= $true )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(52,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( big_f @ ( sK4_SY24 @ SV2 @ SV4 ) @ SV4 )
| ~ ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( big_f @ SY29 @ SV4 )
| ~ ( big_f @ SY29 @ ( sK4_SY24 @ SV2 @ SV4 ) ) ) )
= $false )
| ( ( big_f @ SV2 @ SV4 )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(53,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( big_f @ SV5 @ ( sK3_SY21 @ SV2 ) ) )
= $true )
| ( ( ~ ~ ~ ! [SY28: $i] :
~ ~ ( ~ ( big_f @ SY28 @ ( sK3_SY21 @ SV2 ) )
| ~ ( big_f @ SY28 @ SV5 ) ) )
= $true )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(54,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( big_f @ ( sK4_SY24 @ SV2 @ SV4 ) @ SV4 ) )
= $false )
| ( ( big_f @ SV2 @ SV4 )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(55,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( big_f @ SY29 @ SV4 )
| ~ ( big_f @ SY29 @ ( sK4_SY24 @ SV2 @ SV4 ) ) ) )
= $false )
| ( ( big_f @ SV2 @ SV4 )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(56,plain,
! [SV2: $i,SV5: $i] :
( ( ( big_f @ SV5 @ ( sK3_SY21 @ SV2 ) )
= $false )
| ( ( ~ ~ ~ ! [SY28: $i] :
~ ~ ( ~ ( big_f @ SY28 @ ( sK3_SY21 @ SV2 ) )
| ~ ( big_f @ SY28 @ SV5 ) ) )
= $true )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(57,plain,
! [SV4: $i,SV2: $i] :
( ( ( big_f @ ( sK4_SY24 @ SV2 @ SV4 ) @ SV4 )
= $true )
| ( ( big_f @ SV2 @ SV4 )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(58,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( big_f @ SY29 @ SV4 )
| ~ ( big_f @ SY29 @ ( sK4_SY24 @ SV2 @ SV4 ) ) ) )
= $true )
| ( ( big_f @ SV2 @ SV4 )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(59,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ~ ! [SY28: $i] :
~ ~ ( ~ ( big_f @ SY28 @ ( sK3_SY21 @ SV2 ) )
| ~ ( big_f @ SY28 @ SV5 ) ) )
= $false )
| ( ( big_f @ SV5 @ ( sK3_SY21 @ SV2 ) )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(60,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ! [SY29: $i] :
~ ~ ( ~ ( big_f @ SY29 @ SV4 )
| ~ ( big_f @ SY29 @ ( sK4_SY24 @ SV2 @ SV4 ) ) ) )
= $false )
| ( ( big_f @ SV2 @ SV4 )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(61,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ! [SY28: $i] :
~ ~ ( ~ ( big_f @ SY28 @ ( sK3_SY21 @ SV2 ) )
| ~ ( big_f @ SY28 @ SV5 ) ) )
= $true )
| ( ( big_f @ SV5 @ ( sK3_SY21 @ SV2 ) )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(62,plain,
! [SV2: $i,SV4: $i] :
( ( ( ! [SY29: $i] :
~ ~ ( ~ ( big_f @ SY29 @ SV4 )
| ~ ( big_f @ SY29 @ ( sK4_SY24 @ SV2 @ SV4 ) ) ) )
= $true )
| ( ( big_f @ SV2 @ SV4 )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(63,plain,
! [SV5: $i,SV2: $i] :
( ( ( ! [SY28: $i] :
~ ~ ( ~ ( big_f @ SY28 @ ( sK3_SY21 @ SV2 ) )
| ~ ( big_f @ SY28 @ SV5 ) ) )
= $false )
| ( ( big_f @ SV5 @ ( sK3_SY21 @ SV2 ) )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV2: $i,SV4: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( big_f @ SV6 @ SV4 )
| ~ ( big_f @ SV6 @ ( sK4_SY24 @ SV2 @ SV4 ) ) ) )
= $true )
| ( ( big_f @ SV2 @ SV4 )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(65,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( big_f @ ( sK5_SY28 @ SV5 @ SV2 ) @ ( sK3_SY21 @ SV2 ) )
| ~ ( big_f @ ( sK5_SY28 @ SV5 @ SV2 ) @ SV5 ) ) )
= $false )
| ( ( big_f @ SV5 @ ( sK3_SY21 @ SV2 ) )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[63]) ).
thf(66,plain,
! [SV2: $i,SV4: $i,SV6: $i] :
( ( ( ~ ( ~ ( big_f @ SV6 @ SV4 )
| ~ ( big_f @ SV6 @ ( sK4_SY24 @ SV2 @ SV4 ) ) ) )
= $false )
| ( ( big_f @ SV2 @ SV4 )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(67,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( ~ ( big_f @ ( sK5_SY28 @ SV5 @ SV2 ) @ ( sK3_SY21 @ SV2 ) )
| ~ ( big_f @ ( sK5_SY28 @ SV5 @ SV2 ) @ SV5 ) ) )
= $true )
| ( ( big_f @ SV5 @ ( sK3_SY21 @ SV2 ) )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(68,plain,
! [SV2: $i,SV4: $i,SV6: $i] :
( ( ( ~ ( big_f @ SV6 @ SV4 )
| ~ ( big_f @ SV6 @ ( sK4_SY24 @ SV2 @ SV4 ) ) )
= $true )
| ( ( big_f @ SV2 @ SV4 )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(69,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( big_f @ ( sK5_SY28 @ SV5 @ SV2 ) @ ( sK3_SY21 @ SV2 ) )
| ~ ( big_f @ ( sK5_SY28 @ SV5 @ SV2 ) @ SV5 ) )
= $false )
| ( ( big_f @ SV5 @ ( sK3_SY21 @ SV2 ) )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(70,plain,
! [SV2: $i,SV4: $i,SV6: $i] :
( ( ( ~ ( big_f @ SV6 @ SV4 ) )
= $true )
| ( ( ~ ( big_f @ SV6 @ ( sK4_SY24 @ SV2 @ SV4 ) ) )
= $true )
| ( ( big_f @ SV2 @ SV4 )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(71,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( big_f @ ( sK5_SY28 @ SV5 @ SV2 ) @ ( sK3_SY21 @ SV2 ) ) )
= $false )
| ( ( big_f @ SV5 @ ( sK3_SY21 @ SV2 ) )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(72,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( big_f @ ( sK5_SY28 @ SV5 @ SV2 ) @ SV5 ) )
= $false )
| ( ( big_f @ SV5 @ ( sK3_SY21 @ SV2 ) )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(73,plain,
! [SV2: $i,SV4: $i,SV6: $i] :
( ( ( big_f @ SV6 @ SV4 )
= $false )
| ( ( ~ ( big_f @ SV6 @ ( sK4_SY24 @ SV2 @ SV4 ) ) )
= $true )
| ( ( big_f @ SV2 @ SV4 )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(74,plain,
! [SV2: $i,SV5: $i] :
( ( ( big_f @ ( sK5_SY28 @ SV5 @ SV2 ) @ ( sK3_SY21 @ SV2 ) )
= $true )
| ( ( big_f @ SV5 @ ( sK3_SY21 @ SV2 ) )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(75,plain,
! [SV2: $i,SV5: $i] :
( ( ( big_f @ ( sK5_SY28 @ SV5 @ SV2 ) @ SV5 )
= $true )
| ( ( big_f @ SV5 @ ( sK3_SY21 @ SV2 ) )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(76,plain,
! [SV4: $i,SV2: $i,SV6: $i] :
( ( ( big_f @ SV6 @ ( sK4_SY24 @ SV2 @ SV4 ) )
= $false )
| ( ( big_f @ SV6 @ SV4 )
= $false )
| ( ( big_f @ SV2 @ SV4 )
= $false )
| ( ( big_f @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(77,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[38,76,75,74,57,44,39]) ).
thf(78,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN077+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.17 % Computer : n019.cluster.edu
% 0.12/0.17 % Model : x86_64 x86_64
% 0.12/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.17 % Memory : 8046.5625MB
% 0.12/0.17 % OS : Linux 6.8.0-71-generic
% 0.12/0.17 % CPULimit : 300
% 0.12/0.17 % WCLimit : 300
% 0.12/0.17 % DateTime : Tue Oct 6 17:16:31 UTC 2026
% 0.12/0.17 % CPUTime :
% 0.12/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.29
% 0.12/0.29 No.of.Axioms: 1
% 0.12/0.29
% 0.12/0.29 Length.of.Defs: 0
% 0.12/0.29
% 0.12/0.29 Contains.Choice.Funs: false
% 0.12/0.29 ..
% 0.12/0.29
% 0.12/0.29 ********************************
% 0.12/0.29 * All subproblems solved! *
% 0.12/0.29 ********************************
% 0.12/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:77,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.29
% 0.12/0.29 %**** Beginning of derivation protocol ****
% 0.12/0.29 % SZS output start CNFRefutation
% See solution above
% 0.12/0.29
% 0.12/0.29 %**** End of derivation protocol ****
% 0.12/0.29 %**** no. of clauses in derivation: 78 ****
% 0.12/0.29 %**** clause counter: 77 ****
% 0.12/0.29
% 0.12/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:77,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------