%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV120^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 : Wed Oct 7 10:49:35 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 1
% Syntax : Number of formulae : 78 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 434 ( 155 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 1297 ( 246 ~; 173 |; 63 &; 752 @)
% ( 0 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 153 ( 153 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 273 ( 0 ^; 273 !; 0 ?; 273 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK10_SY85,type,
sK10_SY85: ( a > a > $o ) > a ).
thf(tp_sK11_SY86,type,
sK11_SY86: ( a > a > $o ) > a ).
thf(tp_sK1_S,type,
sK1_S: ( a > a > $o ) > $o ).
thf(tp_sK2_SY16,type,
sK2_SY16: a ).
thf(tp_sK3_SY31,type,
sK3_SY31: a ).
thf(tp_sK4_SY45,type,
sK4_SY45: a ).
thf(tp_sK5_SX0,type,
sK5_SX0: a > a > $o ).
thf(tp_sK6_SY70,type,
sK6_SY70: ( a > a > $o ) > a ).
thf(tp_sK7_SY73,type,
sK7_SY73: ( a > a > $o ) > a ).
thf(tp_sK8_SY79,type,
sK8_SY79: ( a > a > $o ) > a ).
thf(tp_sK9_SY81,type,
sK9_SY81: ( a > a > $o ) > a ).
thf(1,conjecture,
! [S: ( a > a > $o ) > $o,Xx: a,Xy: a,Xz: a] :
( ( ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( Xp @ Xx0 @ Xy0 )
& ( Xp @ Xy0 @ Xz0 ) )
=> ( Xp @ Xx0 @ Xz0 ) )
& ( S @ Xp ) )
=> ( Xp @ Xx @ Xy ) )
& ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( Xp @ Xx0 @ Xy0 )
& ( Xp @ Xy0 @ Xz0 ) )
=> ( Xp @ Xx0 @ Xz0 ) )
& ( S @ Xp ) )
=> ( Xp @ Xy @ Xz ) ) )
=> ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( Xp @ Xx0 @ Xy0 )
& ( Xp @ Xy0 @ Xz0 ) )
=> ( Xp @ Xx0 @ Xz0 ) )
& ( S @ Xp ) )
=> ( Xp @ Xx @ Xz ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM70_pme) ).
thf(2,negated_conjecture,
( ( ! [S: ( a > a > $o ) > $o,Xx: a,Xy: a,Xz: a] :
( ( ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( Xp @ Xx0 @ Xy0 )
& ( Xp @ Xy0 @ Xz0 ) )
=> ( Xp @ Xx0 @ Xz0 ) )
& ( S @ Xp ) )
=> ( Xp @ Xx @ Xy ) )
& ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( Xp @ Xx0 @ Xy0 )
& ( Xp @ Xy0 @ Xz0 ) )
=> ( Xp @ Xx0 @ Xz0 ) )
& ( S @ Xp ) )
=> ( Xp @ Xy @ Xz ) ) )
=> ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( Xp @ Xx0 @ Xy0 )
& ( Xp @ Xy0 @ Xz0 ) )
=> ( Xp @ Xx0 @ Xz0 ) )
& ( S @ Xp ) )
=> ( Xp @ Xx @ Xz ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [S: ( a > a > $o ) > $o,Xx: a,Xy: a,Xz: a] :
( ( ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( Xp @ Xx0 @ Xy0 )
& ( Xp @ Xy0 @ Xz0 ) )
=> ( Xp @ Xx0 @ Xz0 ) )
& ( S @ Xp ) )
=> ( Xp @ Xx @ Xy ) )
& ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( Xp @ Xx0 @ Xy0 )
& ( Xp @ Xy0 @ Xz0 ) )
=> ( Xp @ Xx0 @ Xz0 ) )
& ( S @ Xp ) )
=> ( Xp @ Xy @ Xz ) ) )
=> ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( Xp @ Xx0 @ Xy0 )
& ( Xp @ Xy0 @ Xz0 ) )
=> ( Xp @ Xx0 @ Xz0 ) )
& ( S @ Xp ) )
=> ( Xp @ Xx @ Xz ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY16: a,SY17: a,SY18: a] :
( ( ! [SY19: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( SY19 @ Xx0 @ Xy0 )
& ( SY19 @ Xy0 @ Xz0 ) )
=> ( SY19 @ Xx0 @ Xz0 ) )
& ( sK1_S @ SY19 ) )
=> ( SY19 @ SY16 @ SY17 ) )
& ! [SY23: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( SY23 @ Xx0 @ Xy0 )
& ( SY23 @ Xy0 @ Xz0 ) )
=> ( SY23 @ Xx0 @ Xz0 ) )
& ( sK1_S @ SY23 ) )
=> ( SY23 @ SY17 @ SY18 ) ) )
=> ! [SY27: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( SY27 @ Xx0 @ Xy0 )
& ( SY27 @ Xy0 @ Xz0 ) )
=> ( SY27 @ Xx0 @ Xz0 ) )
& ( sK1_S @ SY27 ) )
=> ( SY27 @ SY16 @ SY18 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY31: a,SY32: a] :
( ( ! [SY33: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( SY33 @ Xx0 @ Xy0 )
& ( SY33 @ Xy0 @ Xz0 ) )
=> ( SY33 @ Xx0 @ Xz0 ) )
& ( sK1_S @ SY33 ) )
=> ( SY33 @ sK2_SY16 @ SY31 ) )
& ! [SY23: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( SY23 @ Xx0 @ Xy0 )
& ( SY23 @ Xy0 @ Xz0 ) )
=> ( SY23 @ Xx0 @ Xz0 ) )
& ( sK1_S @ SY23 ) )
=> ( SY23 @ SY31 @ SY32 ) ) )
=> ! [SY41: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( SY41 @ Xx0 @ Xy0 )
& ( SY41 @ Xy0 @ Xz0 ) )
=> ( SY41 @ Xx0 @ Xz0 ) )
& ( sK1_S @ SY41 ) )
=> ( SY41 @ sK2_SY16 @ SY32 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY45: a] :
( ( ! [SY46: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( SY46 @ Xx0 @ Xy0 )
& ( SY46 @ Xy0 @ Xz0 ) )
=> ( SY46 @ Xx0 @ Xz0 ) )
& ( sK1_S @ SY46 ) )
=> ( SY46 @ sK2_SY16 @ sK3_SY31 ) )
& ! [SY50: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( SY50 @ Xx0 @ Xy0 )
& ( SY50 @ Xy0 @ Xz0 ) )
=> ( SY50 @ Xx0 @ Xz0 ) )
& ( sK1_S @ SY50 ) )
=> ( SY50 @ sK3_SY31 @ SY45 ) ) )
=> ! [SY41: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( SY41 @ Xx0 @ Xy0 )
& ( SY41 @ Xy0 @ Xz0 ) )
=> ( SY41 @ Xx0 @ Xz0 ) )
& ( sK1_S @ SY41 ) )
=> ( SY41 @ sK2_SY16 @ SY45 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ( ! [SY46: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( SY46 @ Xx0 @ Xy0 )
& ( SY46 @ Xy0 @ Xz0 ) )
=> ( SY46 @ Xx0 @ Xz0 ) )
& ( sK1_S @ SY46 ) )
=> ( SY46 @ sK2_SY16 @ sK3_SY31 ) )
& ! [SY62: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( SY62 @ Xx0 @ Xy0 )
& ( SY62 @ Xy0 @ Xz0 ) )
=> ( SY62 @ Xx0 @ Xz0 ) )
& ( sK1_S @ SY62 ) )
=> ( SY62 @ sK3_SY31 @ sK4_SY45 ) ) )
=> ! [SY66: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( SY66 @ Xx0 @ Xy0 )
& ( SY66 @ Xy0 @ Xz0 ) )
=> ( SY66 @ Xx0 @ Xz0 ) )
& ( sK1_S @ SY66 ) )
=> ( SY66 @ sK2_SY16 @ sK4_SY45 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [SY46: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( SY46 @ Xx0 @ Xy0 )
& ( SY46 @ Xy0 @ Xz0 ) )
=> ( SY46 @ Xx0 @ Xz0 ) )
& ( sK1_S @ SY46 ) )
=> ( SY46 @ sK2_SY16 @ sK3_SY31 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [SY62: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( SY62 @ Xx0 @ Xy0 )
& ( SY62 @ Xy0 @ Xz0 ) )
=> ( SY62 @ Xx0 @ Xz0 ) )
& ( sK1_S @ SY62 ) )
=> ( SY62 @ sK3_SY31 @ sK4_SY45 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [SY66: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( SY66 @ Xx0 @ Xy0 )
& ( SY66 @ Xy0 @ Xz0 ) )
=> ( SY66 @ Xx0 @ Xz0 ) )
& ( sK1_S @ SY66 ) )
=> ( SY66 @ sK2_SY16 @ sK4_SY45 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ! [SY66: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( SY66 @ Xx0 @ Xy0 )
& ( SY66 @ Xy0 @ Xz0 ) )
=> ( SY66 @ Xx0 @ Xz0 ) )
& ( sK1_S @ SY66 ) )
=> ( SY66 @ sK2_SY16 @ sK4_SY45 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [SY62: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( SY62 @ Xx0 @ Xy0 )
& ( SY62 @ Xy0 @ Xz0 ) )
=> ( SY62 @ Xx0 @ Xz0 ) )
& ( sK1_S @ SY62 ) )
=> ( SY62 @ sK3_SY31 @ sK4_SY45 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ! [SY46: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( SY46 @ Xx0 @ Xy0 )
& ( SY46 @ Xy0 @ Xz0 ) )
=> ( SY46 @ Xx0 @ Xz0 ) )
& ( sK1_S @ SY46 ) )
=> ( SY46 @ sK2_SY16 @ sK3_SY31 ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ~ ! [SY66: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( SY66 @ Xx0 @ Xy0 )
& ( SY66 @ Xy0 @ Xz0 ) )
=> ( SY66 @ Xx0 @ Xz0 ) )
& ( sK1_S @ SY66 ) )
=> ( SY66 @ sK2_SY16 @ sK4_SY45 ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
( ( ~ ! [SX0: a > a > $o] :
( ~ ~ ( ~ ! [SX1: a,SX2: a,SX3: a] :
( ~ ~ ( ~ ( SX0 @ SX1 @ SX2 )
| ~ ( SX0 @ SX2 @ SX3 ) )
| ( SX0 @ SX1 @ SX3 ) )
| ~ ( sK1_S @ SX0 ) )
| ( SX0 @ sK2_SY16 @ sK4_SY45 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [SX0: a > a > $o] :
( ~ ~ ( ~ ! [SX1: a,SX2: a,SX3: a] :
( ~ ~ ( ~ ( SX0 @ SX1 @ SX2 )
| ~ ( SX0 @ SX2 @ SX3 ) )
| ( SX0 @ SX1 @ SX3 ) )
| ~ ( sK1_S @ SX0 ) )
| ( SX0 @ sK2_SY16 @ sK3_SY31 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(17,plain,
( ( ! [SX0: a > a > $o] :
( ~ ~ ( ~ ! [SX1: a,SX2: a,SX3: a] :
( ~ ~ ( ~ ( SX0 @ SX1 @ SX2 )
| ~ ( SX0 @ SX2 @ SX3 ) )
| ( SX0 @ SX1 @ SX3 ) )
| ~ ( sK1_S @ SX0 ) )
| ( SX0 @ sK3_SY31 @ sK4_SY45 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(18,plain,
( ( ! [SX0: a > a > $o] :
( ~ ~ ( ~ ! [SX1: a,SX2: a,SX3: a] :
( ~ ~ ( ~ ( SX0 @ SX1 @ SX2 )
| ~ ( SX0 @ SX2 @ SX3 ) )
| ( SX0 @ SX1 @ SX3 ) )
| ~ ( sK1_S @ SX0 ) )
| ( SX0 @ sK2_SY16 @ sK4_SY45 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV1: a > a > $o] :
( ( ~ ~ ( ~ ! [SY70: a,SY71: a,SY72: a] :
( ~ ~ ( ~ ( SV1 @ SY70 @ SY71 )
| ~ ( SV1 @ SY71 @ SY72 ) )
| ( SV1 @ SY70 @ SY72 ) )
| ~ ( sK1_S @ SV1 ) )
| ( SV1 @ sK2_SY16 @ sK3_SY31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
! [SV2: a > a > $o] :
( ( ~ ~ ( ~ ! [SY73: a,SY74: a,SY75: a] :
( ~ ~ ( ~ ( SV2 @ SY73 @ SY74 )
| ~ ( SV2 @ SY74 @ SY75 ) )
| ( SV2 @ SY73 @ SY75 ) )
| ~ ( sK1_S @ SV2 ) )
| ( SV2 @ sK3_SY31 @ sK4_SY45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ~ ( ~ ! [SY76: a,SY77: a,SY78: a] :
( ~ ~ ( ~ ( sK5_SX0 @ SY76 @ SY77 )
| ~ ( sK5_SX0 @ SY77 @ SY78 ) )
| ( sK5_SX0 @ SY76 @ SY78 ) )
| ~ ( sK1_S @ sK5_SX0 ) )
| ( sK5_SX0 @ sK2_SY16 @ sK4_SY45 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(22,plain,
! [SV1: a > a > $o] :
( ( ( ~ ~ ( ~ ! [SY70: a,SY71: a,SY72: a] :
( ~ ~ ( ~ ( SV1 @ SY70 @ SY71 )
| ~ ( SV1 @ SY71 @ SY72 ) )
| ( SV1 @ SY70 @ SY72 ) )
| ~ ( sK1_S @ SV1 ) ) )
= $true )
| ( ( SV1 @ sK2_SY16 @ sK3_SY31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV2: a > a > $o] :
( ( ( ~ ~ ( ~ ! [SY73: a,SY74: a,SY75: a] :
( ~ ~ ( ~ ( SV2 @ SY73 @ SY74 )
| ~ ( SV2 @ SY74 @ SY75 ) )
| ( SV2 @ SY73 @ SY75 ) )
| ~ ( sK1_S @ SV2 ) ) )
= $true )
| ( ( SV2 @ sK3_SY31 @ sK4_SY45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ~ ( ~ ! [SY76: a,SY77: a,SY78: a] :
( ~ ~ ( ~ ( sK5_SX0 @ SY76 @ SY77 )
| ~ ( sK5_SX0 @ SY77 @ SY78 ) )
| ( sK5_SX0 @ SY76 @ SY78 ) )
| ~ ( sK1_S @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( sK5_SX0 @ sK2_SY16 @ sK4_SY45 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV1: a > a > $o] :
( ( ( ~ ( ~ ! [SY70: a,SY71: a,SY72: a] :
( ~ ~ ( ~ ( SV1 @ SY70 @ SY71 )
| ~ ( SV1 @ SY71 @ SY72 ) )
| ( SV1 @ SY70 @ SY72 ) )
| ~ ( sK1_S @ SV1 ) ) )
= $false )
| ( ( SV1 @ sK2_SY16 @ sK3_SY31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV2: a > a > $o] :
( ( ( ~ ( ~ ! [SY73: a,SY74: a,SY75: a] :
( ~ ~ ( ~ ( SV2 @ SY73 @ SY74 )
| ~ ( SV2 @ SY74 @ SY75 ) )
| ( SV2 @ SY73 @ SY75 ) )
| ~ ( sK1_S @ SV2 ) ) )
= $false )
| ( ( SV2 @ sK3_SY31 @ sK4_SY45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( ~ ( ~ ! [SY76: a,SY77: a,SY78: a] :
( ~ ~ ( ~ ( sK5_SX0 @ SY76 @ SY77 )
| ~ ( sK5_SX0 @ SY77 @ SY78 ) )
| ( sK5_SX0 @ SY76 @ SY78 ) )
| ~ ( sK1_S @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
! [SV1: a > a > $o] :
( ( ( ~ ! [SY70: a,SY71: a,SY72: a] :
( ~ ~ ( ~ ( SV1 @ SY70 @ SY71 )
| ~ ( SV1 @ SY71 @ SY72 ) )
| ( SV1 @ SY70 @ SY72 ) )
| ~ ( sK1_S @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SY16 @ sK3_SY31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(30,plain,
! [SV2: a > a > $o] :
( ( ( ~ ! [SY73: a,SY74: a,SY75: a] :
( ~ ~ ( ~ ( SV2 @ SY73 @ SY74 )
| ~ ( SV2 @ SY74 @ SY75 ) )
| ( SV2 @ SY73 @ SY75 ) )
| ~ ( sK1_S @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY31 @ sK4_SY45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(31,plain,
( ( ~ ! [SY76: a,SY77: a,SY78: a] :
( ~ ~ ( ~ ( sK5_SX0 @ SY76 @ SY77 )
| ~ ( sK5_SX0 @ SY77 @ SY78 ) )
| ( sK5_SX0 @ SY76 @ SY78 ) )
| ~ ( sK1_S @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV1: a > a > $o] :
( ( ( ~ ! [SY70: a,SY71: a,SY72: a] :
( ~ ~ ( ~ ( SV1 @ SY70 @ SY71 )
| ~ ( SV1 @ SY71 @ SY72 ) )
| ( SV1 @ SY70 @ SY72 ) ) )
= $true )
| ( ( ~ ( sK1_S @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SY16 @ sK3_SY31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV2: a > a > $o] :
( ( ( ~ ! [SY73: a,SY74: a,SY75: a] :
( ~ ~ ( ~ ( SV2 @ SY73 @ SY74 )
| ~ ( SV2 @ SY74 @ SY75 ) )
| ( SV2 @ SY73 @ SY75 ) ) )
= $true )
| ( ( ~ ( sK1_S @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY31 @ sK4_SY45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(34,plain,
( ( ~ ! [SY76: a,SY77: a,SY78: a] :
( ~ ~ ( ~ ( sK5_SX0 @ SY76 @ SY77 )
| ~ ( sK5_SX0 @ SY77 @ SY78 ) )
| ( sK5_SX0 @ SY76 @ SY78 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(35,plain,
( ( ~ ( sK1_S @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(36,plain,
! [SV1: a > a > $o] :
( ( ( ! [SY70: a,SY71: a,SY72: a] :
( ~ ~ ( ~ ( SV1 @ SY70 @ SY71 )
| ~ ( SV1 @ SY71 @ SY72 ) )
| ( SV1 @ SY70 @ SY72 ) ) )
= $false )
| ( ( ~ ( sK1_S @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SY16 @ sK3_SY31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV2: a > a > $o] :
( ( ( ! [SY73: a,SY74: a,SY75: a] :
( ~ ~ ( ~ ( SV2 @ SY73 @ SY74 )
| ~ ( SV2 @ SY74 @ SY75 ) )
| ( SV2 @ SY73 @ SY75 ) ) )
= $false )
| ( ( ~ ( sK1_S @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY31 @ sK4_SY45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(38,plain,
( ( ! [SY76: a,SY77: a,SY78: a] :
( ~ ~ ( ~ ( sK5_SX0 @ SY76 @ SY77 )
| ~ ( sK5_SX0 @ SY77 @ SY78 ) )
| ( sK5_SX0 @ SY76 @ SY78 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(39,plain,
( ( sK1_S @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(40,plain,
! [SV1: a > a > $o] :
( ( ( ! [SY79: a,SY80: a] :
( ~ ~ ( ~ ( SV1 @ ( sK6_SY70 @ SV1 ) @ SY79 )
| ~ ( SV1 @ SY79 @ SY80 ) )
| ( SV1 @ ( sK6_SY70 @ SV1 ) @ SY80 ) ) )
= $false )
| ( ( ~ ( sK1_S @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SY16 @ sK3_SY31 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[36]) ).
thf(41,plain,
! [SV2: a > a > $o] :
( ( ( ! [SY81: a,SY82: a] :
( ~ ~ ( ~ ( SV2 @ ( sK7_SY73 @ SV2 ) @ SY81 )
| ~ ( SV2 @ SY81 @ SY82 ) )
| ( SV2 @ ( sK7_SY73 @ SV2 ) @ SY82 ) ) )
= $false )
| ( ( ~ ( sK1_S @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY31 @ sK4_SY45 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[37]) ).
thf(42,plain,
! [SV3: a] :
( ( ! [SY83: a,SY84: a] :
( ~ ~ ( ~ ( sK5_SX0 @ SV3 @ SY83 )
| ~ ( sK5_SX0 @ SY83 @ SY84 ) )
| ( sK5_SX0 @ SV3 @ SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV1: a > a > $o] :
( ( ( ! [SY85: a] :
( ~ ~ ( ~ ( SV1 @ ( sK6_SY70 @ SV1 ) @ ( sK8_SY79 @ SV1 ) )
| ~ ( SV1 @ ( sK8_SY79 @ SV1 ) @ SY85 ) )
| ( SV1 @ ( sK6_SY70 @ SV1 ) @ SY85 ) ) )
= $false )
| ( ( ~ ( sK1_S @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SY16 @ sK3_SY31 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(44,plain,
! [SV2: a > a > $o] :
( ( ( ! [SY86: a] :
( ~ ~ ( ~ ( SV2 @ ( sK7_SY73 @ SV2 ) @ ( sK9_SY81 @ SV2 ) )
| ~ ( SV2 @ ( sK9_SY81 @ SV2 ) @ SY86 ) )
| ( SV2 @ ( sK7_SY73 @ SV2 ) @ SY86 ) ) )
= $false )
| ( ( ~ ( sK1_S @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY31 @ sK4_SY45 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(45,plain,
! [SV4: a,SV3: a] :
( ( ! [SY87: a] :
( ~ ~ ( ~ ( sK5_SX0 @ SV3 @ SV4 )
| ~ ( sK5_SX0 @ SV4 @ SY87 ) )
| ( sK5_SX0 @ SV3 @ SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(46,plain,
! [SV1: a > a > $o] :
( ( ( ~ ~ ( ~ ( SV1 @ ( sK6_SY70 @ SV1 ) @ ( sK8_SY79 @ SV1 ) )
| ~ ( SV1 @ ( sK8_SY79 @ SV1 ) @ ( sK10_SY85 @ SV1 ) ) )
| ( SV1 @ ( sK6_SY70 @ SV1 ) @ ( sK10_SY85 @ SV1 ) ) )
= $false )
| ( ( ~ ( sK1_S @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SY16 @ sK3_SY31 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[43]) ).
thf(47,plain,
! [SV2: a > a > $o] :
( ( ( ~ ~ ( ~ ( SV2 @ ( sK7_SY73 @ SV2 ) @ ( sK9_SY81 @ SV2 ) )
| ~ ( SV2 @ ( sK9_SY81 @ SV2 ) @ ( sK11_SY86 @ SV2 ) ) )
| ( SV2 @ ( sK7_SY73 @ SV2 ) @ ( sK11_SY86 @ SV2 ) ) )
= $false )
| ( ( ~ ( sK1_S @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY31 @ sK4_SY45 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(48,plain,
! [SV5: a,SV4: a,SV3: a] :
( ( ~ ~ ( ~ ( sK5_SX0 @ SV3 @ SV4 )
| ~ ( sK5_SX0 @ SV4 @ SV5 ) )
| ( sK5_SX0 @ SV3 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV1: a > a > $o] :
( ( ( ~ ~ ( ~ ( SV1 @ ( sK6_SY70 @ SV1 ) @ ( sK8_SY79 @ SV1 ) )
| ~ ( SV1 @ ( sK8_SY79 @ SV1 ) @ ( sK10_SY85 @ SV1 ) ) ) )
= $false )
| ( ( ~ ( sK1_S @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SY16 @ sK3_SY31 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(50,plain,
! [SV1: a > a > $o] :
( ( ( SV1 @ ( sK6_SY70 @ SV1 ) @ ( sK10_SY85 @ SV1 ) )
= $false )
| ( ( ~ ( sK1_S @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SY16 @ sK3_SY31 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(51,plain,
! [SV2: a > a > $o] :
( ( ( ~ ~ ( ~ ( SV2 @ ( sK7_SY73 @ SV2 ) @ ( sK9_SY81 @ SV2 ) )
| ~ ( SV2 @ ( sK9_SY81 @ SV2 ) @ ( sK11_SY86 @ SV2 ) ) ) )
= $false )
| ( ( ~ ( sK1_S @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY31 @ sK4_SY45 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(52,plain,
! [SV2: a > a > $o] :
( ( ( SV2 @ ( sK7_SY73 @ SV2 ) @ ( sK11_SY86 @ SV2 ) )
= $false )
| ( ( ~ ( sK1_S @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY31 @ sK4_SY45 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(53,plain,
! [SV5: a,SV4: a,SV3: a] :
( ( ( ~ ~ ( ~ ( sK5_SX0 @ SV3 @ SV4 )
| ~ ( sK5_SX0 @ SV4 @ SV5 ) ) )
= $true )
| ( ( sK5_SX0 @ SV3 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV1: a > a > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK6_SY70 @ SV1 ) @ ( sK8_SY79 @ SV1 ) )
| ~ ( SV1 @ ( sK8_SY79 @ SV1 ) @ ( sK10_SY85 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( sK1_S @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SY16 @ sK3_SY31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(55,plain,
! [SV1: a > a > $o] :
( ( ( sK1_S @ SV1 )
= $false )
| ( ( SV1 @ ( sK6_SY70 @ SV1 ) @ ( sK10_SY85 @ SV1 ) )
= $false )
| ( ( SV1 @ sK2_SY16 @ sK3_SY31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(56,plain,
! [SV2: a > a > $o] :
( ( ( ~ ( ~ ( SV2 @ ( sK7_SY73 @ SV2 ) @ ( sK9_SY81 @ SV2 ) )
| ~ ( SV2 @ ( sK9_SY81 @ SV2 ) @ ( sK11_SY86 @ SV2 ) ) ) )
= $true )
| ( ( ~ ( sK1_S @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY31 @ sK4_SY45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(57,plain,
! [SV2: a > a > $o] :
( ( ( sK1_S @ SV2 )
= $false )
| ( ( SV2 @ ( sK7_SY73 @ SV2 ) @ ( sK11_SY86 @ SV2 ) )
= $false )
| ( ( SV2 @ sK3_SY31 @ sK4_SY45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV5: a,SV4: a,SV3: a] :
( ( ( ~ ( ~ ( sK5_SX0 @ SV3 @ SV4 )
| ~ ( sK5_SX0 @ SV4 @ SV5 ) ) )
= $false )
| ( ( sK5_SX0 @ SV3 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV1: a > a > $o] :
( ( ( ~ ( SV1 @ ( sK6_SY70 @ SV1 ) @ ( sK8_SY79 @ SV1 ) )
| ~ ( SV1 @ ( sK8_SY79 @ SV1 ) @ ( sK10_SY85 @ SV1 ) ) )
= $false )
| ( ( ~ ( sK1_S @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SY16 @ sK3_SY31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV2: a > a > $o] :
( ( ( ~ ( SV2 @ ( sK7_SY73 @ SV2 ) @ ( sK9_SY81 @ SV2 ) )
| ~ ( SV2 @ ( sK9_SY81 @ SV2 ) @ ( sK11_SY86 @ SV2 ) ) )
= $false )
| ( ( ~ ( sK1_S @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY31 @ sK4_SY45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV5: a,SV4: a,SV3: a] :
( ( ( ~ ( sK5_SX0 @ SV3 @ SV4 )
| ~ ( sK5_SX0 @ SV4 @ SV5 ) )
= $true )
| ( ( sK5_SX0 @ SV3 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(62,plain,
! [SV1: a > a > $o] :
( ( ( ~ ( SV1 @ ( sK6_SY70 @ SV1 ) @ ( sK8_SY79 @ SV1 ) ) )
= $false )
| ( ( ~ ( sK1_S @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SY16 @ sK3_SY31 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(63,plain,
! [SV1: a > a > $o] :
( ( ( ~ ( SV1 @ ( sK8_SY79 @ SV1 ) @ ( sK10_SY85 @ SV1 ) ) )
= $false )
| ( ( ~ ( sK1_S @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SY16 @ sK3_SY31 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(64,plain,
! [SV2: a > a > $o] :
( ( ( ~ ( SV2 @ ( sK7_SY73 @ SV2 ) @ ( sK9_SY81 @ SV2 ) ) )
= $false )
| ( ( ~ ( sK1_S @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY31 @ sK4_SY45 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(65,plain,
! [SV2: a > a > $o] :
( ( ( ~ ( SV2 @ ( sK9_SY81 @ SV2 ) @ ( sK11_SY86 @ SV2 ) ) )
= $false )
| ( ( ~ ( sK1_S @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY31 @ sK4_SY45 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(66,plain,
! [SV5: a,SV4: a,SV3: a] :
( ( ( ~ ( sK5_SX0 @ SV3 @ SV4 ) )
= $true )
| ( ( ~ ( sK5_SX0 @ SV4 @ SV5 ) )
= $true )
| ( ( sK5_SX0 @ SV3 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(67,plain,
! [SV1: a > a > $o] :
( ( ( SV1 @ ( sK6_SY70 @ SV1 ) @ ( sK8_SY79 @ SV1 ) )
= $true )
| ( ( ~ ( sK1_S @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SY16 @ sK3_SY31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(68,plain,
! [SV1: a > a > $o] :
( ( ( SV1 @ ( sK8_SY79 @ SV1 ) @ ( sK10_SY85 @ SV1 ) )
= $true )
| ( ( ~ ( sK1_S @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SY16 @ sK3_SY31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(69,plain,
! [SV2: a > a > $o] :
( ( ( SV2 @ ( sK7_SY73 @ SV2 ) @ ( sK9_SY81 @ SV2 ) )
= $true )
| ( ( ~ ( sK1_S @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY31 @ sK4_SY45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(70,plain,
! [SV2: a > a > $o] :
( ( ( SV2 @ ( sK9_SY81 @ SV2 ) @ ( sK11_SY86 @ SV2 ) )
= $true )
| ( ( ~ ( sK1_S @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY31 @ sK4_SY45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(71,plain,
! [SV5: a,SV4: a,SV3: a] :
( ( ( sK5_SX0 @ SV3 @ SV4 )
= $false )
| ( ( ~ ( sK5_SX0 @ SV4 @ SV5 ) )
= $true )
| ( ( sK5_SX0 @ SV3 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(72,plain,
! [SV1: a > a > $o] :
( ( ( sK1_S @ SV1 )
= $false )
| ( ( SV1 @ ( sK6_SY70 @ SV1 ) @ ( sK8_SY79 @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SY16 @ sK3_SY31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(73,plain,
! [SV1: a > a > $o] :
( ( ( sK1_S @ SV1 )
= $false )
| ( ( SV1 @ ( sK8_SY79 @ SV1 ) @ ( sK10_SY85 @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SY16 @ sK3_SY31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(74,plain,
! [SV2: a > a > $o] :
( ( ( sK1_S @ SV2 )
= $false )
| ( ( SV2 @ ( sK7_SY73 @ SV2 ) @ ( sK9_SY81 @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY31 @ sK4_SY45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(75,plain,
! [SV2: a > a > $o] :
( ( ( sK1_S @ SV2 )
= $false )
| ( ( SV2 @ ( sK9_SY81 @ SV2 ) @ ( sK11_SY86 @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY31 @ sK4_SY45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(76,plain,
! [SV3: a,SV5: a,SV4: a] :
( ( ( sK5_SX0 @ SV4 @ SV5 )
= $false )
| ( ( sK5_SX0 @ SV3 @ SV4 )
= $false )
| ( ( sK5_SX0 @ SV3 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(77,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,76,75,74,73,72,57,55,39]) ).
thf(78,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV120^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n026.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 15:43:47 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.23
% 0.08/0.23 No.of.Axioms: 0
% 0.08/0.23
% 0.08/0.23 Length.of.Defs: 0
% 0.08/0.23
% 0.08/0.23 Contains.Choice.Funs: false
% 0.08/0.23 ..
% 0.08/0.23
% 0.08/0.23 ********************************
% 0.08/0.23 * All subproblems solved! *
% 0.08/0.23 ********************************
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:77,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.23
% 0.08/0.23 %**** Beginning of derivation protocol ****
% 0.08/0.23 % SZS output start CNFRefutation
% See solution above
% 0.08/0.23
% 0.08/0.23 %**** End of derivation protocol ****
% 0.08/0.23 %**** no. of clauses in derivation: 78 ****
% 0.08/0.23 %**** clause counter: 77 ****
% 0.08/0.23
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:77,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------