TSTP Solution File: SEU775^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU775^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n018.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 : Tue Jul 19 12:14:37 EDT 2022
% Result : Theorem 76.05s 76.25s
% Output : CNFRefutation 76.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 29
% Syntax : Number of formulae : 93 ( 32 unt; 24 typ; 4 def)
% Number of atoms : 415 ( 183 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 917 ( 50 ~; 57 |; 2 &; 802 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 126 ( 126 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 10 con; 0-3 aty)
% Number of variables : 255 ( 197 ^ 58 !; 0 ?; 255 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_breln,type,
breln: $i > $i > $i > $o ).
thf(tp_breln1,type,
breln1: $i > $i > $o ).
thf(tp_breln1invset,type,
breln1invset: $i > $i > $i ).
thf(tp_cartprod,type,
cartprod: $i > $i > $i ).
thf(tp_dpsetconstr,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_sK10_E,type,
sK10_E: ( $i > $i > $o ) > $i ).
thf(tp_sK11_E,type,
sK11_E: ( $i > $i > $o ) > $i ).
thf(tp_sK12_E,type,
sK12_E: $i ).
thf(tp_sK13_E,type,
sK13_E: $i ).
thf(tp_sK14_E,type,
sK14_E: $i ).
thf(tp_sK15_E,type,
sK15_E: $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY450,type,
sK2_SY450: $i ).
thf(tp_sK3_E,type,
sK3_E: ( $i > $i > $o ) > $i ).
thf(tp_sK4_E,type,
sK4_E: ( $i > $i > $o ) > $i ).
thf(tp_sK5_E,type,
sK5_E: ( $i > $i > $o ) > $i ).
thf(tp_sK6_E,type,
sK6_E: ( $i > $i > $o ) > $i ).
thf(tp_sK7_E,type,
sK7_E: $i ).
thf(tp_sK8_E,type,
sK8_E: ( $i > $i > $o ) > $i ).
thf(tp_sK9_E,type,
sK9_E: ( $i > $i > $o ) > $i ).
thf(tp_setOfPairsIsBReln1,type,
setOfPairsIsBReln1: $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(breln,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).
thf(breln1,definition,
( breln1
= ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1) ).
thf(breln1invset,definition,
( breln1invset
= ( ^ [A: $i,R: $i] :
( dpsetconstr @ A @ A
@ ^ [Xx: $i,Xy: $i] : ( in @ ( kpair @ Xy @ Xx ) @ R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1invset) ).
thf(setOfPairsIsBReln1,definition,
( setOfPairsIsBReln1
= ( ! [A: $i,Xphi: $i > $i > $o] :
( breln1 @ A
@ ( dpsetconstr @ A @ A
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setOfPairsIsBReln1) ).
thf(1,conjecture,
( setOfPairsIsBReln1
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1invprop) ).
thf(2,negated_conjecture,
( ( setOfPairsIsBReln1
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
setOfPairsIsBReln1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(5,plain,
( ( ~ ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(6,plain,
( ( ( breln1 @ sK1_A @ sK2_SY450 )
& ~ ( breln1 @ sK1_A @ ( breln1invset @ sK1_A @ sK2_SY450 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(7,plain,
setOfPairsIsBReln1 = $true,
inference(copy,[status(thm)],[3]) ).
thf(8,plain,
( ( ( breln1 @ sK1_A @ sK2_SY450 )
& ~ ( breln1 @ sK1_A @ ( breln1invset @ sK1_A @ sK2_SY450 ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( ~ ( subset @ sK2_SY450 @ ( cartprod @ sK1_A @ sK1_A ) )
| ~ ~ ( subset
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
@ ( cartprod @ sK1_A @ sK1_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,breln,breln1,breln1invset,setOfPairsIsBReln1]) ).
thf(10,plain,
( ( ! [SX0: $i,SX1: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SX0 @ SX0
@ ^ [SX2: $i,SX3: $i] : ( SX1 @ SX2 @ SX3 ) )
@ ( cartprod @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,breln,breln1,breln1invset,setOfPairsIsBReln1]) ).
thf(11,plain,
( ( ~ ( subset @ sK2_SY450 @ ( cartprod @ sK1_A @ sK1_A ) )
| ~ ~ ( subset
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
@ ( cartprod @ sK1_A @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY451: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV1 @ SV1
@ ^ [SX2: $i,SX3: $i] : ( SY451 @ SX2 @ SX3 ) )
@ ( cartprod @ SV1 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ( subset @ sK2_SY450 @ ( cartprod @ sK1_A @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ~ ( subset
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
@ ( cartprod @ sK1_A @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(15,plain,
! [SV2: $i > $i > $o,SV1: $i] :
( ( subset
@ ( dpsetconstr @ SV1 @ SV1
@ ^ [SY454: $i,SY455: $i] : ( SV2 @ SY454 @ SY455 ) )
@ ( cartprod @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
( ( subset @ sK2_SY450 @ ( cartprod @ sK1_A @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(17,plain,
( ( ~ ( subset
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
@ ( cartprod @ sK1_A @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(18,plain,
( ( subset
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
@ ( cartprod @ sK1_A @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(19,plain,
! [SV3: $i > $i > $o,SV4: $i] :
( ( subset
@ ( dpsetconstr @ SV4 @ SV4
@ ^ [SX0: $i,SX1: $i] : ( SV3 @ SX0 @ SX1 ) )
@ ( cartprod @ SV4 @ SV4 ) )
= $true ),
inference(rename,[status(thm)],[15]) ).
thf(20,plain,
! [SV3: $i > $i > $o,SV4: $i] :
( ( ( subset
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
@ ( cartprod @ sK1_A @ sK1_A ) )
= ( subset
@ ( dpsetconstr @ SV4 @ SV4
@ ^ [SX0: $i,SX1: $i] : ( SV3 @ SX0 @ SX1 ) )
@ ( cartprod @ SV4 @ SV4 ) ) )
= $false ),
inference(res,[status(thm)],[18,19]) ).
thf(21,plain,
( ( ( subset
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
@ ( cartprod @ sK1_A @ sK1_A ) )
= ( subset @ sK2_SY450 @ ( cartprod @ sK1_A @ sK1_A ) ) )
= $false ),
inference(res,[status(thm)],[18,16]) ).
thf(22,plain,
( ( ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
= sK2_SY450 )
= $false ),
inference(extuni,[status(esa)],[21]) ).
thf(23,plain,
! [SV3: $i > $i > $o] :
( ( ( in @ ( kpair @ ( sK4_E @ SV3 ) @ ( sK3_E @ SV3 ) ) @ sK2_SY450 )
= $true )
| ( ( SV3 @ ( sK3_E @ SV3 ) @ ( sK4_E @ SV3 ) )
= $true ) ),
inference(extuni,[status(esa)],[20:[bind(SV4,$thf( sK1_A ))]]) ).
thf(24,plain,
! [SV3: $i > $i > $o] :
( ( ( in @ ( kpair @ ( sK4_E @ SV3 ) @ ( sK3_E @ SV3 ) ) @ sK2_SY450 )
= $false )
| ( ( SV3 @ ( sK3_E @ SV3 ) @ ( sK4_E @ SV3 ) )
= $false ) ),
inference(extuni,[status(esa)],[20:[bind(SV4,$thf( sK1_A ))]]) ).
thf(25,plain,
! [SV3: $i > $i > $o] :
( ( ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( SV3 @ SX0 @ SX1 ) ) )
= $false ),
inference(extuni,[status(esa)],[20:[bind(SV4,$thf( sK1_A ))]]) ).
thf(26,plain,
! [SV3: $i > $i > $o,SV4: $i] :
( ( ( ( cartprod @ sK1_A @ sK1_A )
= ( cartprod @ SV4 @ SV4 ) )
= $false )
| ( ( ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
= ( dpsetconstr @ SV4 @ SV4
@ ^ [SX0: $i,SX1: $i] : ( SV3 @ SX0 @ SX1 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[20]) ).
thf(29,plain,
! [SV5: $i > $i > $o] :
( ( ( in @ ( kpair @ ( sK4_E @ SV5 ) @ ( sK3_E @ SV5 ) ) @ sK2_SY450 )
= $true )
| ( ( SV5 @ ( sK3_E @ SV5 ) @ ( sK4_E @ SV5 ) )
= $true ) ),
inference(rename,[status(thm)],[23]) ).
thf(35,plain,
( ( ( in
@ ( kpair
@ ( sK4_E
@ ^ [SX0: $i,SX1: $i] : $false )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] : $false ) )
@ sK2_SY450 )
= $true )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[29:[bind(SV5,$thf( ^ [SV9: $i] : ^ [SV10: $i] : $false ))]]) ).
thf(36,plain,
( ( in
@ ( kpair
@ ( sK4_E
@ ^ [SX0: $i,SX1: $i] : $false )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] : $false ) )
@ sK2_SY450 )
= $true ),
inference(sim,[status(thm)],[35]) ).
thf(37,plain,
! [SV8: $i > $i > $o] :
( ( ( in
@ ( kpair
@ ( sK4_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV8 @ SX0 @ SX1 ) )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV8 @ SX0 @ SX1 ) ) )
@ sK2_SY450 )
= $true )
| ( ( ~ ( SV8
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV8 @ SX0 @ SX1 ) )
@ ( sK4_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV8 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[29:[bind(SV5,$thf( ^ [SV6: $i] : ^ [SV7: $i] : ~ ( SV8 @ SV6 @ SV7 ) ))]]) ).
thf(38,plain,
( ( ( in
@ ( kpair
@ ( sK4_E
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
@ sK2_SY450 )
= $true )
| ( ( ( ( sK3_E
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) )
!= ( sK4_E
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[29:[bind(SV5,$thf( ^ [SY464: $i] : ^ [SY465: $i] : ( SY464 != SY465 ) ))]]) ).
thf(39,plain,
( ( ( in
@ ( kpair
@ ( sK4_E
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
@ sK2_SY450 )
= $true )
| ( ( ( sK3_E
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= ( sK4_E
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[29:[bind(SV5,$thf( ^ [SV14: $i] : ^ [SV13: $i] : ( SV14 = SV13 ) ))]]) ).
thf(41,plain,
! [SV8: $i > $i > $o] :
( ( ( SV8
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV8 @ SX0 @ SX1 ) )
@ ( sK4_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV8 @ SX0 @ SX1 ) ) )
= $false )
| ( ( in
@ ( kpair
@ ( sK4_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV8 @ SX0 @ SX1 ) )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV8 @ SX0 @ SX1 ) ) )
@ sK2_SY450 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(42,plain,
( ( ( ( sK3_E
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) )
= ( sK4_E
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
= $false )
| ( ( in
@ ( kpair
@ ( sK4_E
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
@ sK2_SY450 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV63: $i > $i > $o] :
( ( ( in @ ( kpair @ ( sK4_E @ SV63 ) @ ( sK3_E @ SV63 ) ) @ sK2_SY450 )
= $false )
| ( ( SV63 @ ( sK3_E @ SV63 ) @ ( sK4_E @ SV63 ) )
= $false ) ),
inference(rename,[status(thm)],[24]) ).
thf(47,plain,
! [SV63: $i > $i > $o,SV5: $i > $i > $o] :
( ( ( ( in @ ( kpair @ ( sK4_E @ SV63 ) @ ( sK3_E @ SV63 ) ) @ sK2_SY450 )
= ( in @ ( kpair @ ( sK4_E @ SV5 ) @ ( sK3_E @ SV5 ) ) @ sK2_SY450 ) )
= $false )
| ( ( SV63 @ ( sK3_E @ SV63 ) @ ( sK4_E @ SV63 ) )
= $false )
| ( ( SV5 @ ( sK3_E @ SV5 ) @ ( sK4_E @ SV5 ) )
= $true ) ),
inference(res,[status(thm)],[43,29]) ).
thf(52,plain,
( ( ( in
@ ( kpair
@ ( sK4_E
@ ^ [SX0: $i,SX1: $i] : $true )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] : $true ) )
@ sK2_SY450 )
= $false )
| ( $true = $false ) ),
inference(prim_subst,[status(thm)],[43:[bind(SV63,$thf( ^ [SV69: $i] : ^ [SV70: $i] : $true ))]]) ).
thf(53,plain,
( ( in
@ ( kpair
@ ( sK4_E
@ ^ [SX0: $i,SX1: $i] : $true )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] : $true ) )
@ sK2_SY450 )
= $false ),
inference(sim,[status(thm)],[52]) ).
thf(55,plain,
! [SV66: $i > $i > $o] :
( ( ( in
@ ( kpair
@ ( sK4_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV66 @ SX0 @ SX1 ) )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV66 @ SX0 @ SX1 ) ) )
@ sK2_SY450 )
= $false )
| ( ( ~ ( SV66
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV66 @ SX0 @ SX1 ) )
@ ( sK4_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV66 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[43:[bind(SV63,$thf( ^ [SV64: $i] : ^ [SV65: $i] : ~ ( SV66 @ SV64 @ SV65 ) ))]]) ).
thf(56,plain,
( ( ( in
@ ( kpair
@ ( sK4_E
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
@ sK2_SY450 )
= $false )
| ( ( ( ( sK3_E
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) )
!= ( sK4_E
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[43:[bind(SV63,$thf( ^ [SY500: $i] : ^ [SY501: $i] : ( SY500 != SY501 ) ))]]) ).
thf(61,plain,
! [SV63: $i > $i > $o,SV5: $i > $i > $o] :
( ( ( SV5 @ ( sK3_E @ SV5 ) @ ( sK4_E @ SV5 ) )
= $true )
| ( ( SV63 @ ( sK3_E @ SV63 ) @ ( sK4_E @ SV63 ) )
= $false )
| ( ( ( sK3_E @ SV63 )
= ( sK3_E @ SV5 ) )
= $false )
| ( ( ( sK4_E @ SV63 )
= ( sK4_E @ SV5 ) )
= $false ) ),
inference(extuni,[status(esa)],[47]) ).
thf(62,plain,
! [SV63: $i > $i > $o,SV5: $i > $i > $o] :
( ( ( SV5 @ ( sK3_E @ SV5 ) @ ( sK4_E @ SV5 ) )
= $true )
| ( ( SV63 @ ( sK3_E @ SV63 ) @ ( sK4_E @ SV63 ) )
= $false )
| ( ( ( kpair @ ( sK4_E @ SV63 ) @ ( sK3_E @ SV63 ) )
= ( kpair @ ( sK4_E @ SV5 ) @ ( sK3_E @ SV5 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[47]) ).
thf(63,plain,
! [SV66: $i > $i > $o] :
( ( ( SV66
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV66 @ SX0 @ SX1 ) )
@ ( sK4_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV66 @ SX0 @ SX1 ) ) )
= $true )
| ( ( in
@ ( kpair
@ ( sK4_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV66 @ SX0 @ SX1 ) )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV66 @ SX0 @ SX1 ) ) )
@ sK2_SY450 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(64,plain,
( ( ( ( sK3_E
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) )
= ( sK4_E
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
= $true )
| ( ( in
@ ( kpair
@ ( sK4_E
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
@ sK2_SY450 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(65,plain,
! [SV127: $i > $i > $o] :
( ( ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( SV127 @ SX0 @ SX1 ) ) )
= $false ),
inference(rename,[status(thm)],[25]) ).
thf(70,plain,
! [SV127: $i > $i > $o] :
( ( ( in @ ( kpair @ ( sK6_E @ SV127 ) @ ( sK5_E @ SV127 ) ) @ sK2_SY450 )
= $true )
| ( ( SV127 @ ( sK5_E @ SV127 ) @ ( sK6_E @ SV127 ) )
= $true ) ),
inference(extuni,[status(esa)],[65]) ).
thf(71,plain,
! [SV127: $i > $i > $o] :
( ( ( in @ ( kpair @ ( sK6_E @ SV127 ) @ ( sK5_E @ SV127 ) ) @ sK2_SY450 )
= $false )
| ( ( SV127 @ ( sK5_E @ SV127 ) @ ( sK6_E @ SV127 ) )
= $false ) ),
inference(extuni,[status(esa)],[65]) ).
thf(72,plain,
! [SV128: $i > $i > $o,SV129: $i] :
( ( ( ( cartprod @ sK1_A @ sK1_A )
= ( cartprod @ SV129 @ SV129 ) )
= $false )
| ( ( ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
= ( dpsetconstr @ SV129 @ SV129
@ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
= $false ) ),
inference(rename,[status(thm)],[26]) ).
thf(81,plain,
! [SV128: $i > $i > $o,SV129: $i] :
( ( ( ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
= ( dpsetconstr @ SV129 @ SV129
@ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
= $false )
| ( ( ( ( cartprod @ sK1_A @ sK1_A )
= ( cartprod @ SV129 @ SV129 ) )
= ( ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
= ( dpsetconstr @ SV129 @ SV129
@ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[72]) ).
thf(82,plain,
! [SV128: $i > $i > $o] :
( ( ( ( cartprod @ sK1_A @ sK1_A )
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
= $false )
| ( ( ( cartprod @ sK1_A @ sK1_A )
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) ) )
= $false )
| ( ( in @ ( kpair @ ( sK9_E @ SV128 ) @ ( sK8_E @ SV128 ) ) @ sK2_SY450 )
= $true )
| ( ( SV128 @ ( sK8_E @ SV128 ) @ ( sK9_E @ SV128 ) )
= $true ) ),
inference(extuni,[status(esa)],[81:[bind(SV129,$thf( sK1_A ))]]) ).
thf(83,plain,
! [SV128: $i > $i > $o] :
( ( ( ( cartprod @ sK1_A @ sK1_A )
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
= $false )
| ( ( ( cartprod @ sK1_A @ sK1_A )
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) ) )
= $false )
| ( ( in @ ( kpair @ ( sK9_E @ SV128 ) @ ( sK8_E @ SV128 ) ) @ sK2_SY450 )
= $true )
| ( ( SV128 @ ( sK8_E @ SV128 ) @ ( sK9_E @ SV128 ) )
= $true ) ),
inference(extuni,[status(esa)],[81:[bind(SV129,$thf( sK1_A ))]]) ).
thf(85,plain,
! [SV128: $i > $i > $o] :
( ( ( ( cartprod @ sK1_A @ sK1_A )
= ( cartprod @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
= $false )
| ( ( in @ ( kpair @ ( sK9_E @ SV128 ) @ ( sK8_E @ SV128 ) ) @ sK2_SY450 )
= $true )
| ( ( SV128 @ ( sK8_E @ SV128 ) @ ( sK9_E @ SV128 ) )
= $true ) ),
inference(extuni,[status(esa)],[81:[bind(SV129,$thf( sK1_A ))]]) ).
thf(86,plain,
! [SV128: $i > $i > $o] :
( ( ( ( cartprod @ sK1_A @ sK1_A )
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
= $false )
| ( ( ( cartprod @ sK1_A @ sK1_A )
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) ) )
= $false )
| ( ( in @ ( kpair @ ( sK9_E @ SV128 ) @ ( sK8_E @ SV128 ) ) @ sK2_SY450 )
= $false )
| ( ( SV128 @ ( sK8_E @ SV128 ) @ ( sK9_E @ SV128 ) )
= $false ) ),
inference(extuni,[status(esa)],[81:[bind(SV129,$thf( sK1_A ))]]) ).
thf(87,plain,
! [SV128: $i > $i > $o] :
( ( ( ( cartprod @ sK1_A @ sK1_A )
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
= $false )
| ( ( ( cartprod @ sK1_A @ sK1_A )
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) ) )
= $false )
| ( ( in @ ( kpair @ ( sK9_E @ SV128 ) @ ( sK8_E @ SV128 ) ) @ sK2_SY450 )
= $false )
| ( ( SV128 @ ( sK8_E @ SV128 ) @ ( sK9_E @ SV128 ) )
= $false ) ),
inference(extuni,[status(esa)],[81:[bind(SV129,$thf( sK1_A ))]]) ).
thf(89,plain,
! [SV128: $i > $i > $o] :
( ( ( ( cartprod @ sK1_A @ sK1_A )
= ( cartprod @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
= $false )
| ( ( in @ ( kpair @ ( sK9_E @ SV128 ) @ ( sK8_E @ SV128 ) ) @ sK2_SY450 )
= $false )
| ( ( SV128 @ ( sK8_E @ SV128 ) @ ( sK9_E @ SV128 ) )
= $false ) ),
inference(extuni,[status(esa)],[81:[bind(SV129,$thf( sK1_A ))]]) ).
thf(90,plain,
! [SV128: $i > $i > $o] :
( ( ( in @ ( kpair @ ( sK11_E @ SV128 ) @ ( sK10_E @ SV128 ) ) @ sK2_SY450 )
= $true )
| ( ( SV128 @ ( sK10_E @ SV128 ) @ ( sK11_E @ SV128 ) )
= $true ) ),
inference(extuni,[status(esa)],[72:[bind(SV129,$thf( sK1_A ))]]) ).
thf(91,plain,
! [SV128: $i > $i > $o] :
( ( ( in @ ( kpair @ ( sK11_E @ SV128 ) @ ( sK10_E @ SV128 ) ) @ sK2_SY450 )
= $false )
| ( ( SV128 @ ( sK10_E @ SV128 ) @ ( sK11_E @ SV128 ) )
= $false ) ),
inference(extuni,[status(esa)],[72:[bind(SV129,$thf( sK1_A ))]]) ).
thf(92,plain,
! [SV128: $i > $i > $o] :
( ( ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
= $false ),
inference(extuni,[status(esa)],[72:[bind(SV129,$thf( sK1_A ))]]) ).
thf(93,plain,
! [SV128: $i > $i > $o] :
( ( ( ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
= $false )
| ( ( in @ ( kpair @ ( sK9_E @ SV128 ) @ ( sK8_E @ SV128 ) ) @ sK2_SY450 )
= $false )
| ( ( SV128 @ ( sK8_E @ SV128 ) @ ( sK9_E @ SV128 ) )
= $false ) ),
inference(sim,[status(thm)],[89]) ).
thf(94,plain,
! [SV128: $i > $i > $o] :
( ( ( ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
= $false )
| ( ( in @ ( kpair @ ( sK9_E @ SV128 ) @ ( sK8_E @ SV128 ) ) @ sK2_SY450 )
= $true )
| ( ( SV128 @ ( sK8_E @ SV128 ) @ ( sK9_E @ SV128 ) )
= $true ) ),
inference(sim,[status(thm)],[85]) ).
thf(99,plain,
! [SV63: $i > $i > $o] :
( ( ( ( in
@ ( kpair
@ ( sK4_E
@ ^ [SX0: $i,SX1: $i] : $false )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] : $false ) )
@ sK2_SY450 )
= ( in @ ( kpair @ ( sK4_E @ SV63 ) @ ( sK3_E @ SV63 ) ) @ sK2_SY450 ) )
= $false )
| ( ( SV63 @ ( sK3_E @ SV63 ) @ ( sK4_E @ SV63 ) )
= $false ) ),
inference(res,[status(thm)],[36,43]) ).
thf(104,plain,
! [SV63: $i > $i > $o] :
( ( ( SV63 @ ( sK3_E @ SV63 ) @ ( sK4_E @ SV63 ) )
= $false )
| ( ( ( sK3_E
@ ^ [SX0: $i,SX1: $i] : $false )
= ( sK3_E @ SV63 ) )
= $false )
| ( ( ( sK4_E
@ ^ [SX0: $i,SX1: $i] : $false )
= ( sK4_E @ SV63 ) )
= $false ) ),
inference(extuni,[status(esa)],[99]) ).
thf(105,plain,
! [SV63: $i > $i > $o] :
( ( ( SV63 @ ( sK3_E @ SV63 ) @ ( sK4_E @ SV63 ) )
= $false )
| ( ( ( kpair
@ ( sK4_E
@ ^ [SX0: $i,SX1: $i] : $false )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] : $false ) )
= ( kpair @ ( sK4_E @ SV63 ) @ ( sK3_E @ SV63 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[99]) ).
thf(106,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,105,104,94,93,92,91,90,87,86,83,82,72,71,70,65,64,63,62,61,53,43,42,41,39,36,29,22,19,18]) ).
thf(107,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU775^2 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 03:24:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 0
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 722
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.35 (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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.19/0.40
% 0.19/0.40 Prim_subst applied to clause
% 0.19/0.40
% 0.19/0.40 29:[ 0:<(in@((kpair@(sK4_E@SV5))@(sK3_E@SV5)))@sK2_SY35 = $true>-w(1)-i() 1:<(SV5@(sK3_E@SV5))@(sK4_E@SV5) = $true>-w(1)-i() ]-mln(2)-w(2)-i(rename 23)-o(DERIVED)-fv([ SV5 ])
% 1.16/1.35 .....
% 75.75/75.94 (rf:0,axioms:0,ps:2,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 75.75/75.97
% 75.75/75.97 Prim_subst applied to clause
% 75.75/75.97
% 75.75/75.97 29:[ 0:<(in@((kpair@(sK4_E@SV5))@(sK3_E@SV5)))@sK2_SY450 = $true>-w(1)-i() 1:<(SV5@(sK3_E@SV5))@(sK4_E@SV5) = $true>-w(1)-i() ]-mln(2)-w(2)-i(rename 23)-o(DERIVED)-fv([ SV5 ])
% 75.75/75.99
% 75.75/75.99 Prim_subst applied to clause
% 75.75/75.99
% 75.75/75.99 43:[ 0:<(in@((kpair@(sK4_E@SV63))@(sK3_E@SV63)))@sK2_SY450 = $false>-w(1)-i() 1:<(SV63@(sK3_E@SV63))@(sK4_E@SV63) = $false>-w(1)-i() ]-mln(2)-w(2)-i(rename 24)-o(DERIVED)-fv([ SV63 ])
% 75.75/76.00 ..
% 76.05/76.25
% 76.05/76.25 ********************************
% 76.05/76.25 * All subproblems solved! *
% 76.05/76.25 ********************************
% 76.05/76.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:2,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:106,loop_count:10,foatp_calls:2,translation:fof_full)
% 76.07/76.26
% 76.07/76.26 %**** Beginning of derivation protocol ****
% 76.07/76.26 % SZS output start CNFRefutation
% See solution above
% 76.07/76.26
% 76.07/76.26 %**** End of derivation protocol ****
% 76.07/76.26 %**** no. of clauses in derivation: 65 ****
% 76.07/76.26 %**** clause counter: 106 ****
% 76.07/76.26
% 76.07/76.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:2,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:106,loop_count:10,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------