%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM651^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n017.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 10:34:47 AM UTC 2026
% Result : Theorem 0.11s 0.27s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 5
% Syntax : Number of formulae : 114 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 833 ( 566 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 1294 ( 549 ~; 219 |; 0 &; 498 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 13 con; 0-2 aty)
% Number of variables : 179 ( 0 ^; 179 !; 0 ?; 179 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_nat,type,
nat: $tType ).
thf(tp_pl,type,
pl: nat > nat > nat ).
thf(tp_sK1_SX0,type,
sK1_SX0: nat ).
thf(tp_sK2_SX0,type,
sK2_SX0: nat ).
thf(tp_sK3_SX0,type,
sK3_SX0: nat ).
thf(tp_sK4_SX0,type,
sK4_SX0: nat ).
thf(tp_sK5_SX0,type,
sK5_SX0: nat ).
thf(tp_sK6_SX0,type,
sK6_SX0: nat ).
thf(tp_sK7_SX0,type,
sK7_SX0: nat ).
thf(tp_sK8_SX0,type,
sK8_SX0: nat ).
thf(tp_sK9_SX0,type,
sK9_SX0: nat ).
thf(tp_x,type,
x: nat ).
thf(tp_y,type,
y: nat ).
thf(1,axiom,
! [Xx: nat,Xy: nat,Xz: nat] :
( ( pl @ ( pl @ Xx @ Xy ) @ Xz )
= ( pl @ Xx @ ( pl @ Xy @ Xz ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz5) ).
thf(2,axiom,
! [Xa: $o] :
( ~ ~ Xa
=> Xa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',et) ).
thf(3,axiom,
! [Xx: nat,Xy: nat] :
( ( pl @ Xx @ Xy )
= ( pl @ Xy @ Xx ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz6) ).
thf(4,axiom,
! [Xx: nat,Xy: nat] :
( Xy
!= ( pl @ Xx @ Xy ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz7) ).
thf(5,conjecture,
~ ( ( ( x = y )
=> ~ ~ ! [Xx_0: nat] :
( x
!= ( pl @ y @ Xx_0 ) ) )
=> ~ ~ ( ( ~ ! [Xx_0: nat] :
( x
!= ( pl @ y @ Xx_0 ) )
=> ~ ~ ! [Xx_0: nat] :
( y
!= ( pl @ x @ Xx_0 ) ) )
=> ~ ( ~ ! [Xx_0: nat] :
( y
!= ( pl @ x @ Xx_0 ) )
=> ( x != y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz9b) ).
thf(6,negated_conjecture,
( ( ~ ( ( ( x = y )
=> ~ ~ ! [Xx_0: nat] :
( x
!= ( pl @ y @ Xx_0 ) ) )
=> ~ ~ ( ( ~ ! [Xx_0: nat] :
( x
!= ( pl @ y @ Xx_0 ) )
=> ~ ~ ! [Xx_0: nat] :
( y
!= ( pl @ x @ Xx_0 ) ) )
=> ~ ( ~ ! [Xx_0: nat] :
( y
!= ( pl @ x @ Xx_0 ) )
=> ( x != y ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( ~ ( ( ( x = y )
=> ~ ~ ! [Xx_0: nat] :
( x
!= ( pl @ y @ Xx_0 ) ) )
=> ~ ~ ( ( ~ ! [Xx_0: nat] :
( x
!= ( pl @ y @ Xx_0 ) )
=> ~ ~ ! [Xx_0: nat] :
( y
!= ( pl @ x @ Xx_0 ) ) )
=> ~ ( ~ ! [Xx_0: nat] :
( y
!= ( pl @ x @ Xx_0 ) )
=> ( x != y ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat] :
( ( pl @ ( pl @ Xx @ Xy ) @ Xz )
= ( pl @ Xx @ ( pl @ Xy @ Xz ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( ! [Xa: $o] :
( ~ ~ Xa
=> Xa ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( pl @ Xx @ Xy )
= ( pl @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [Xx: nat,Xy: nat] :
( Xy
!= ( pl @ Xx @ Xy ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(12,plain,
( ( ( ( x = y )
=> ~ ~ ! [Xx_0: nat] :
( x
!= ( pl @ y @ Xx_0 ) ) )
=> ~ ~ ( ( ~ ! [Xx_0: nat] :
( x
!= ( pl @ y @ Xx_0 ) )
=> ~ ~ ! [Xx_0: nat] :
( y
!= ( pl @ x @ Xx_0 ) ) )
=> ~ ( ~ ! [Xx_0: nat] :
( y
!= ( pl @ x @ Xx_0 ) )
=> ( x != y ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [Xx: nat,Xy: nat] :
( Xy
!= ( pl @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( pl @ Xx @ Xy )
= ( pl @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
( ( ! [Xa: $o] :
( ~ ~ Xa
=> Xa ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(16,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat] :
( ( pl @ ( pl @ Xx @ Xy ) @ Xz )
= ( pl @ Xx @ ( pl @ Xy @ Xz ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(17,plain,
( ( ( ( x = y )
=> ~ ~ ! [Xx_0: nat] :
( x
!= ( pl @ y @ Xx_0 ) ) )
=> ~ ~ ( ( ~ ! [Xx_0: nat] :
( x
!= ( pl @ y @ Xx_0 ) )
=> ~ ~ ! [Xx_0: nat] :
( y
!= ( pl @ x @ Xx_0 ) ) )
=> ~ ( ~ ! [Xx_0: nat] :
( y
!= ( pl @ x @ Xx_0 ) )
=> ( x != y ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(18,plain,
( ( ! [SX0: nat,SX1: nat] :
( SX1
!= ( pl @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(19,plain,
( ( ! [SX0: $o] :
( ~ ~ ~ SX0
| SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(20,plain,
( ( ~ ( ( x != y )
| ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) ) )
| ~ ~ ( ~ ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) )
| ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
| ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(21,plain,
! [SV1: nat] :
( ( ! [SY12: nat] :
( ( pl @ SV1 @ SY12 )
= ( pl @ SY12 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(22,plain,
! [SV2: nat] :
( ( ! [SY13: nat,SY14: nat] :
( ( pl @ ( pl @ SV2 @ SY13 ) @ SY14 )
= ( pl @ SV2 @ ( pl @ SY13 @ SY14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(23,plain,
! [SV3: nat] :
( ( ! [SY15: nat] :
( SY15
!= ( pl @ SV3 @ SY15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(24,plain,
! [SV4: $o] :
( ( ~ ~ ~ SV4
| SV4 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[19]) ).
thf(25,plain,
( ( ~ ~ ~ $true
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[19]) ).
thf(26,plain,
( ( ~ ~ ~ $false
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[19]) ).
thf(27,plain,
( ( ( ~ ( ( x != y )
| ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) )
| ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
| ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(28,plain,
! [SV5: nat,SV1: nat] :
( ( ( pl @ SV1 @ SV5 )
= ( pl @ SV5 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(29,plain,
! [SV6: nat,SV2: nat] :
( ( ! [SY16: nat] :
( ( pl @ ( pl @ SV2 @ SV6 ) @ SY16 )
= ( pl @ SV2 @ ( pl @ SV6 @ SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(30,plain,
! [SV3: nat,SV7: nat] :
( ( SV7
!= ( pl @ SV3 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(31,plain,
! [SV4: $o] :
( ( ( ~ ~ ~ SV4 )
= $true )
| ( SV4 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(32,plain,
( ( ( ~ ~ ~ $true )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(33,plain,
( ( ( ~ ~ ~ $false )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(34,plain,
( ( ( ( x != y )
| ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) )
| ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
| ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(35,plain,
! [SV8: nat,SV6: nat,SV2: nat] :
( ( ( pl @ ( pl @ SV2 @ SV6 ) @ SV8 )
= ( pl @ SV2 @ ( pl @ SV6 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV3: nat,SV7: nat] :
( ( SV7
= ( pl @ SV3 @ SV7 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV4: $o] :
( ( ( ~ ~ SV4 )
= $false )
| ( SV4 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(38,plain,
( ( ( ~ ~ $true )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(39,plain,
( ( ( ~ ~ $false )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(40,plain,
( ( ( x != y )
= $false )
| ( ( ~ ~ ( ~ ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) )
| ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
| ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(41,plain,
( ( ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) )
| ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
| ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(42,plain,
! [SV4: $o] :
( ( ( ~ SV4 ) = $true )
| ( SV4 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(43,plain,
( ( ( ~ $true ) = $true )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(44,plain,
( ( ( ~ $false ) = $true )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(45,plain,
( ( ( x = y )
= $true )
| ( ( ~ ~ ( ~ ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) )
| ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
| ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(46,plain,
( ( ( ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) )
| ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
| ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(47,plain,
! [SV4: $o] :
( ( SV4 = $false )
| ( SV4 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(48,plain,
( ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(49,plain,
( ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(50,plain,
( ( ( ~ ( ~ ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) )
| ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
| ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) ) )
= $false )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(51,plain,
( ( ( ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) )
| ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
| ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(52,plain,
( ( ( ~ ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) )
| ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
| ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(53,plain,
( ( ( x
!= ( pl @ y @ sK1_SX0 ) )
= $false )
| ( ( ~ ~ ( ~ ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) )
| ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
| ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[51]) ).
thf(54,plain,
( ( ( ~ ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) )
| ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(55,plain,
( ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true )
| ( ( ~ ~ ( ~ ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) )
| ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
| ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(56,plain,
( ( ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) )
| ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(57,plain,
( ( ( ~ ( ~ ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) )
| ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
| ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) ) )
= $false )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(58,plain,
( ( ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(59,plain,
( ( ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(60,plain,
( ( ( ~ ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) )
| ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
| ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(61,plain,
( ( ( ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(62,plain,
( ( ( ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(63,plain,
( ( ( ~ ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) )
| ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(64,plain,
( ( ( ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(65,plain,
( ( ( ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(66,plain,
( ( ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) )
| ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(67,plain,
( ( ( x
!= ( pl @ y @ sK2_SX0 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[64]) ).
thf(68,plain,
( ( ( y
!= ( pl @ x @ sK3_SX0 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[65]) ).
thf(69,plain,
( ( ( ~ ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(70,plain,
( ( ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(71,plain,
( ( ( x
= ( pl @ y @ sK2_SX0 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(72,plain,
( ( ( y
= ( pl @ x @ sK3_SX0 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(73,plain,
( ( ( ~ ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(74,plain,
( ( ( ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(75,plain,
( ( ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) )
= $false )
| ( ( x
= ( pl @ y @ sK2_SX0 ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(76,plain,
( ( ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) )
= $false )
| ( ( y
= ( pl @ x @ sK3_SX0 ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(77,plain,
( ( ( ! [SX0: nat] :
( x
!= ( pl @ y @ SX0 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(78,plain,
( ( ( ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(79,plain,
( ( ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
= $false )
| ( ( x
= ( pl @ y @ sK2_SX0 ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(80,plain,
( ( ( x != y )
= $false )
| ( ( x
= ( pl @ y @ sK2_SX0 ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(81,plain,
( ( ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
= $false )
| ( ( y
= ( pl @ x @ sK3_SX0 ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(82,plain,
( ( ( x != y )
= $false )
| ( ( y
= ( pl @ x @ sK3_SX0 ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(83,plain,
( ( ( x
!= ( pl @ y @ sK4_SX0 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[77]) ).
thf(84,plain,
( ( ( y
!= ( pl @ x @ sK5_SX0 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[78]) ).
thf(85,plain,
( ( ( ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
= $true )
| ( ( x
= ( pl @ y @ sK2_SX0 ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(86,plain,
( ( ( x = y )
= $true )
| ( ( x
= ( pl @ y @ sK2_SX0 ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(87,plain,
( ( ( ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
= $true )
| ( ( y
= ( pl @ x @ sK3_SX0 ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(88,plain,
( ( ( x = y )
= $true )
| ( ( y
= ( pl @ x @ sK3_SX0 ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(89,plain,
( ( ( x
= ( pl @ y @ sK4_SX0 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(90,plain,
( ( ( y
= ( pl @ x @ sK5_SX0 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(91,plain,
( ( ( ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
= $false )
| ( ( x
= ( pl @ y @ sK2_SX0 ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(92,plain,
( ( ( ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
= $false )
| ( ( y
= ( pl @ x @ sK3_SX0 ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(93,plain,
( ( ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) )
= $false )
| ( ( x
= ( pl @ y @ sK4_SX0 ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(94,plain,
( ( ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) )
| ( x != y ) )
= $false )
| ( ( y
= ( pl @ x @ sK5_SX0 ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(95,plain,
( ( ( y
!= ( pl @ x @ sK6_SX0 ) )
= $false )
| ( ( x
= ( pl @ y @ sK2_SX0 ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[91]) ).
thf(96,plain,
( ( ( y
!= ( pl @ x @ sK7_SX0 ) )
= $false )
| ( ( y
= ( pl @ x @ sK3_SX0 ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[92]) ).
thf(97,plain,
( ( ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
= $false )
| ( ( x
= ( pl @ y @ sK4_SX0 ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(98,plain,
( ( ( x != y )
= $false )
| ( ( x
= ( pl @ y @ sK4_SX0 ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(99,plain,
( ( ( ~ ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
= $false )
| ( ( y
= ( pl @ x @ sK5_SX0 ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(100,plain,
( ( ( x != y )
= $false )
| ( ( y
= ( pl @ x @ sK5_SX0 ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(101,plain,
( ( ( y
= ( pl @ x @ sK6_SX0 ) )
= $true )
| ( ( x
= ( pl @ y @ sK2_SX0 ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(102,plain,
( ( ( y
= ( pl @ x @ sK7_SX0 ) )
= $true )
| ( ( y
= ( pl @ x @ sK3_SX0 ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(103,plain,
( ( ( ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
= $true )
| ( ( x
= ( pl @ y @ sK4_SX0 ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(104,plain,
( ( ( x = y )
= $true )
| ( ( x
= ( pl @ y @ sK4_SX0 ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(105,plain,
( ( ( ~ ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
= $true )
| ( ( y
= ( pl @ x @ sK5_SX0 ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(106,plain,
( ( ( x = y )
= $true )
| ( ( y
= ( pl @ x @ sK5_SX0 ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(107,plain,
( ( ( ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
= $false )
| ( ( x
= ( pl @ y @ sK4_SX0 ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(108,plain,
( ( ( ! [SX0: nat] :
( y
!= ( pl @ x @ SX0 ) ) )
= $false )
| ( ( y
= ( pl @ x @ sK5_SX0 ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(109,plain,
( ( ( y
!= ( pl @ x @ sK8_SX0 ) )
= $false )
| ( ( x
= ( pl @ y @ sK4_SX0 ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[107]) ).
thf(110,plain,
( ( ( y
!= ( pl @ x @ sK9_SX0 ) )
= $false )
| ( ( y
= ( pl @ x @ sK5_SX0 ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[108]) ).
thf(111,plain,
( ( ( y
= ( pl @ x @ sK8_SX0 ) )
= $true )
| ( ( x
= ( pl @ y @ sK4_SX0 ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(112,plain,
( ( ( y
= ( pl @ x @ sK9_SX0 ) )
= $true )
| ( ( y
= ( pl @ x @ sK5_SX0 ) )
= $true )
| ( ( x
= ( pl @ y @ sK1_SX0 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(113,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,112,111,106,104,102,101,88,86,49,48,47,36,35]) ).
thf(114,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM651^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.11/0.18 % Computer : n017.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Oct 6 13:27:45 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.27
% 0.11/0.27 No.of.Axioms: 4
% 0.11/0.27
% 0.11/0.27 Length.of.Defs: 0
% 0.11/0.27
% 0.11/0.27 Contains.Choice.Funs: false
% 0.11/0.27 ..
% 0.11/0.27
% 0.11/0.27 ********************************
% 0.11/0.27 * All subproblems solved! *
% 0.11/0.27 ********************************
% 0.11/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:4,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:113,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.27
% 0.11/0.27 %**** Beginning of derivation protocol ****
% 0.11/0.27 % SZS output start CNFRefutation
% See solution above
% 0.11/0.27
% 0.11/0.27 %**** End of derivation protocol ****
% 0.11/0.27 %**** no. of clauses in derivation: 114 ****
% 0.11/0.27 %**** clause counter: 113 ****
% 0.11/0.27
% 0.11/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:4,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:113,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------