TSTP Solution File: SEU815^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU815^2 : 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 : n029.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 12:14:58 EDT 2022
% Result : Theorem 0.14s 0.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 21
% Syntax : Number of formulae : 125 ( 44 unt; 15 typ; 5 def)
% Number of atoms : 777 ( 216 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 1142 ( 160 ~; 233 |; 2 &; 719 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 260 ( 1 ^ 259 !; 0 ?; 260 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_SY8,type,
sK2_SY8: $i > $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY14,type,
sK4_SY14: $i > $i > $i ).
thf(tp_sK5_SY16,type,
sK5_SY16: $o > $i > $i > $i ).
thf(tp_sK6_SX0,type,
sK6_SX0: $i > $i > $i ).
thf(tp_sK7_SX0,type,
sK7_SX0: $i > $i > $i ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(tp_setunionE,type,
setunionE: $o ).
thf(tp_setunionI,type,
setunionI: $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subsetI1,type,
subsetI1: $o ).
thf(tp_transitiveset,type,
transitiveset: $i > $o ).
thf(tp_transitivesetOp2,type,
transitivesetOp2: $o ).
thf(setunionE,definition,
( setunionE
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(setunionI,definition,
( setunionI
= ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(subsetI1,definition,
( subsetI1
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(transitiveset,definition,
( transitiveset
= ( ^ [A: $i] :
! [X: $i] :
( ( in @ X @ A )
=> ( subset @ X @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitiveset) ).
thf(transitivesetOp2,definition,
( transitivesetOp2
= ( ! [X: $i] :
( ( transitiveset @ X )
=> ! [A: $i,Xx: $i] :
( ( in @ A @ X )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivesetOp2) ).
thf(1,conjecture,
( setunionI
=> ( setunionE
=> ( subsetI1
=> ( transitivesetOp2
=> ! [X: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( transitiveset @ Xx ) )
=> ( transitiveset @ ( setunion @ X ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionTransitive) ).
thf(2,negated_conjecture,
( ( setunionI
=> ( setunionE
=> ( subsetI1
=> ( transitivesetOp2
=> ! [X: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( transitiveset @ Xx ) )
=> ( transitiveset @ ( setunion @ X ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
setunionI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(4,plain,
setunionE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(5,plain,
subsetI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(6,plain,
transitivesetOp2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(7,plain,
( ( ! [X: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( transitiveset @ Xx ) )
=> ( transitiveset @ ( setunion @ X ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(8,plain,
( ( ~ ! [X: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( transitiveset @ Xx ) )
=> ( transitiveset @ ( setunion @ X ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [SY0: $i] :
( ~ ( in @ SY0 @ sK1_X )
| ( transitiveset @ SY0 ) )
& ~ ( transitiveset @ ( setunion @ sK1_X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
transitivesetOp2 = $true,
inference(copy,[status(thm)],[6]) ).
thf(11,plain,
subsetI1 = $true,
inference(copy,[status(thm)],[5]) ).
thf(12,plain,
setunionE = $true,
inference(copy,[status(thm)],[4]) ).
thf(13,plain,
setunionI = $true,
inference(copy,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [SY0: $i] :
( ~ ( in @ SY0 @ sK1_X )
| ( transitiveset @ SY0 ) )
& ~ ( transitiveset @ ( setunion @ sK1_X ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(15,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_X )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) )
| ~ ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ ( setunion @ sK1_X ) )
| ( subset @ SX0 @ ( setunion @ sK1_X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,setunionE,setunionI,subsetI1,transitiveset,transitivesetOp2]) ).
thf(16,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,setunionE,setunionI,subsetI1,transitiveset,transitivesetOp2]) ).
thf(17,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ! [SX2: $o] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX1 @ SX3 )
| ~ ( in @ SX3 @ SX0 )
| SX2 )
| SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,setunionE,setunionI,subsetI1,transitiveset,transitivesetOp2]) ).
thf(18,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,setunionE,setunionI,subsetI1,transitiveset,transitivesetOp2]) ).
thf(19,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,setunionE,setunionI,subsetI1,transitiveset,transitivesetOp2]) ).
thf(20,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_X )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) )
| ~ ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ ( setunion @ sK1_X ) )
| ( subset @ SX0 @ ( setunion @ sK1_X ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(21,plain,
! [SV1: $i] :
( ( ! [SY1: $i,SY2: $i] :
( ~ ( in @ SY1 @ SY2 )
| ~ ( in @ SY2 @ SV1 )
| ( in @ SY1 @ ( setunion @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(22,plain,
! [SV2: $i] :
( ( ! [SY3: $i] :
( ~ ( in @ SY3 @ ( setunion @ SV2 ) )
| ! [SY4: $o] :
( ~ ! [SY5: $i] :
( ~ ( in @ SY3 @ SY5 )
| ~ ( in @ SY5 @ SV2 )
| SY4 )
| SY4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(23,plain,
! [SV3: $i] :
( ( ! [SY6: $i] :
( ~ ! [SY7: $i] :
( ~ ( in @ SY7 @ SV3 )
| ( in @ SY7 @ SY6 ) )
| ( subset @ SV3 @ SY6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(24,plain,
! [SV4: $i] :
( ( ~ ! [SY8: $i] :
( ~ ( in @ SY8 @ SV4 )
| ( subset @ SY8 @ SV4 ) )
| ! [SY9: $i,SY10: $i] :
( ~ ( in @ SY9 @ SV4 )
| ~ ( in @ SY10 @ SY9 )
| ( in @ SY10 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(25,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_X )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(26,plain,
( ( ~ ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ ( setunion @ sK1_X ) )
| ( subset @ SX0 @ ( setunion @ sK1_X ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(27,plain,
! [SV1: $i,SV5: $i] :
( ( ! [SY11: $i] :
( ~ ( in @ SV5 @ SY11 )
| ~ ( in @ SY11 @ SV1 )
| ( in @ SV5 @ ( setunion @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(28,plain,
! [SV2: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ ( setunion @ SV2 ) )
| ! [SY12: $o] :
( ~ ! [SY13: $i] :
( ~ ( in @ SV6 @ SY13 )
| ~ ( in @ SY13 @ SV2 )
| SY12 )
| SY12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(29,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ! [SY14: $i] :
( ~ ( in @ SY14 @ SV3 )
| ( in @ SY14 @ SV7 ) )
| ( subset @ SV3 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(30,plain,
! [SV4: $i] :
( ( ( ~ ! [SY8: $i] :
( ~ ( in @ SY8 @ SV4 )
| ( subset @ SY8 @ SV4 ) ) )
= $true )
| ( ( ! [SY9: $i,SY10: $i] :
( ~ ( in @ SY9 @ SV4 )
| ~ ( in @ SY10 @ SY9 )
| ( in @ SY10 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(31,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_X )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(32,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ ( setunion @ sK1_X ) )
| ( subset @ SX0 @ ( setunion @ sK1_X ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(33,plain,
! [SV1: $i,SV8: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ SV8 )
| ~ ( in @ SV8 @ SV1 )
| ( in @ SV5 @ ( setunion @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(34,plain,
! [SV2: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ ( setunion @ SV2 ) ) )
= $true )
| ( ( ! [SY12: $o] :
( ~ ! [SY13: $i] :
( ~ ( in @ SV6 @ SY13 )
| ~ ( in @ SY13 @ SV2 )
| SY12 )
| SY12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ! [SY14: $i] :
( ~ ( in @ SY14 @ SV3 )
| ( in @ SY14 @ SV7 ) ) )
= $true )
| ( ( subset @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV4: $i] :
( ( ( ! [SY8: $i] :
( ~ ( in @ SY8 @ SV4 )
| ( subset @ SY8 @ SV4 ) ) )
= $false )
| ( ( ! [SY9: $i,SY10: $i] :
( ~ ( in @ SY9 @ SV4 )
| ~ ( in @ SY10 @ SY9 )
| ( in @ SY10 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV9: $i] :
( ( ~ ( in @ SV9 @ sK1_X )
| ! [SY15: $i] :
( ~ ( in @ SY15 @ SV9 )
| ( subset @ SY15 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(38,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( setunion @ sK1_X ) )
| ( subset @ SX0 @ ( setunion @ sK1_X ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(39,plain,
! [SV1: $i,SV8: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV8 ) )
= $true )
| ( ( ~ ( in @ SV8 @ SV1 )
| ( in @ SV5 @ ( setunion @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV2: $i,SV6: $i] :
( ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false )
| ( ( ! [SY12: $o] :
( ~ ! [SY13: $i] :
( ~ ( in @ SV6 @ SY13 )
| ~ ( in @ SY13 @ SV2 )
| SY12 )
| SY12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV7: $i,SV3: $i] :
( ( ( ! [SY14: $i] :
( ~ ( in @ SY14 @ SV3 )
| ( in @ SY14 @ SV7 ) ) )
= $false )
| ( ( subset @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(42,plain,
! [SV4: $i] :
( ( ( ~ ( in @ ( sK2_SY8 @ SV4 ) @ SV4 )
| ( subset @ ( sK2_SY8 @ SV4 ) @ SV4 ) )
= $false )
| ( ( ! [SY9: $i,SY10: $i] :
( ~ ( in @ SY9 @ SV4 )
| ~ ( in @ SY10 @ SY9 )
| ( in @ SY10 @ SV4 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[36]) ).
thf(43,plain,
! [SV9: $i] :
( ( ( ~ ( in @ SV9 @ sK1_X ) )
= $true )
| ( ( ! [SY15: $i] :
( ~ ( in @ SY15 @ SV9 )
| ( subset @ SY15 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(44,plain,
( ( ~ ( in @ sK3_SX0 @ ( setunion @ sK1_X ) )
| ( subset @ sK3_SX0 @ ( setunion @ sK1_X ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(45,plain,
! [SV1: $i,SV8: $i,SV5: $i] :
( ( ( in @ SV5 @ SV8 )
= $false )
| ( ( ~ ( in @ SV8 @ SV1 )
| ( in @ SV5 @ ( setunion @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(46,plain,
! [SV10: $o,SV2: $i,SV6: $i] :
( ( ( ~ ! [SY16: $i] :
( ~ ( in @ SV6 @ SY16 )
| ~ ( in @ SY16 @ SV2 )
| SV10 )
| SV10 )
= $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV2: $i,SV6: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV6 @ SX0 )
| ~ ( in @ SX0 @ SV2 )
| $true )
| $true )
= $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[40]) ).
thf(48,plain,
! [SV2: $i,SV6: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV6 @ SX0 )
| ~ ( in @ SX0 @ SV2 )
| $false )
| $false )
= $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[40]) ).
thf(49,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK4_SY14 @ SV7 @ SV3 ) @ SV3 )
| ( in @ ( sK4_SY14 @ SV7 @ SV3 ) @ SV7 ) )
= $false )
| ( ( subset @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(50,plain,
! [SV4: $i] :
( ( ( ~ ( in @ ( sK2_SY8 @ SV4 ) @ SV4 ) )
= $false )
| ( ( ! [SY9: $i,SY10: $i] :
( ~ ( in @ SY9 @ SV4 )
| ~ ( in @ SY10 @ SY9 )
| ( in @ SY10 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(51,plain,
! [SV4: $i] :
( ( ( subset @ ( sK2_SY8 @ SV4 ) @ SV4 )
= $false )
| ( ( ! [SY9: $i,SY10: $i] :
( ~ ( in @ SY9 @ SV4 )
| ~ ( in @ SY10 @ SY9 )
| ( in @ SY10 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(52,plain,
! [SV9: $i] :
( ( ( in @ SV9 @ sK1_X )
= $false )
| ( ( ! [SY15: $i] :
( ~ ( in @ SY15 @ SV9 )
| ( subset @ SY15 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(53,plain,
( ( ~ ( in @ sK3_SX0 @ ( setunion @ sK1_X ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(54,plain,
( ( subset @ sK3_SX0 @ ( setunion @ sK1_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(55,plain,
! [SV5: $i,SV1: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV1 ) )
= $true )
| ( ( in @ SV5 @ ( setunion @ SV1 ) )
= $true )
| ( ( in @ SV5 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(56,plain,
! [SV10: $o,SV2: $i,SV6: $i] :
( ( ( ~ ! [SY16: $i] :
( ~ ( in @ SV6 @ SY16 )
| ~ ( in @ SY16 @ SV2 )
| SV10 ) )
= $true )
| ( SV10 = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(57,plain,
! [SV2: $i,SV6: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV6 @ SX0 )
| ~ ( in @ SX0 @ SV2 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(58,plain,
! [SV2: $i,SV6: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV6 @ SX0 )
| ~ ( in @ SX0 @ SV2 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(59,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK4_SY14 @ SV7 @ SV3 ) @ SV3 ) )
= $false )
| ( ( subset @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(60,plain,
! [SV3: $i,SV7: $i] :
( ( ( in @ ( sK4_SY14 @ SV7 @ SV3 ) @ SV7 )
= $false )
| ( ( subset @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(61,plain,
! [SV4: $i] :
( ( ( in @ ( sK2_SY8 @ SV4 ) @ SV4 )
= $true )
| ( ( ! [SY9: $i,SY10: $i] :
( ~ ( in @ SY9 @ SV4 )
| ~ ( in @ SY10 @ SY9 )
| ( in @ SY10 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(62,plain,
! [SV4: $i,SV11: $i] :
( ( ( ! [SY17: $i] :
( ~ ( in @ SV11 @ SV4 )
| ~ ( in @ SY17 @ SV11 )
| ( in @ SY17 @ SV4 ) ) )
= $true )
| ( ( subset @ ( sK2_SY8 @ SV4 ) @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(63,plain,
! [SV9: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV9 )
| ( subset @ SV12 @ SV9 ) )
= $true )
| ( ( in @ SV9 @ sK1_X )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(64,plain,
( ( in @ sK3_SX0 @ ( setunion @ sK1_X ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(65,plain,
! [SV5: $i,SV1: $i,SV8: $i] :
( ( ( in @ SV8 @ SV1 )
= $false )
| ( ( in @ SV5 @ ( setunion @ SV1 ) )
= $true )
| ( ( in @ SV5 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(66,plain,
! [SV10: $o,SV2: $i,SV6: $i] :
( ( ( ! [SY16: $i] :
( ~ ( in @ SV6 @ SY16 )
| ~ ( in @ SY16 @ SV2 )
| SV10 ) )
= $false )
| ( SV10 = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(67,plain,
! [SV2: $i,SV6: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV6 @ SX0 )
| ~ ( in @ SX0 @ SV2 )
| $true ) )
= $false )
| ( $true = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(68,plain,
! [SV2: $i,SV6: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV6 @ SX0 )
| ~ ( in @ SX0 @ SV2 )
| $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(69,plain,
! [SV3: $i,SV7: $i] :
( ( ( in @ ( sK4_SY14 @ SV7 @ SV3 ) @ SV3 )
= $true )
| ( ( subset @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(70,plain,
! [SV4: $i,SV13: $i] :
( ( ( ! [SY18: $i] :
( ~ ( in @ SV13 @ SV4 )
| ~ ( in @ SY18 @ SV13 )
| ( in @ SY18 @ SV4 ) ) )
= $true )
| ( ( in @ ( sK2_SY8 @ SV4 ) @ SV4 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(71,plain,
! [SV14: $i,SV4: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV4 )
| ~ ( in @ SV14 @ SV11 )
| ( in @ SV14 @ SV4 ) )
= $true )
| ( ( subset @ ( sK2_SY8 @ SV4 ) @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(72,plain,
! [SV9: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV9 ) )
= $true )
| ( ( subset @ SV12 @ SV9 )
= $true )
| ( ( in @ SV9 @ sK1_X )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(73,plain,
! [SV2: $i,SV10: $o,SV6: $i] :
( ( ( ~ ( in @ SV6 @ ( sK5_SY16 @ SV10 @ SV2 @ SV6 ) )
| ~ ( in @ ( sK5_SY16 @ SV10 @ SV2 @ SV6 ) @ SV2 )
| SV10 )
= $false )
| ( SV10 = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[66]) ).
thf(74,plain,
! [SV2: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ ( sK6_SX0 @ SV2 @ SV6 ) )
| ~ ( in @ ( sK6_SX0 @ SV2 @ SV6 ) @ SV2 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[67]) ).
thf(75,plain,
! [SV2: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ ( sK7_SX0 @ SV2 @ SV6 ) )
| ~ ( in @ ( sK7_SX0 @ SV2 @ SV6 ) @ SV2 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[68]) ).
thf(76,plain,
! [SV15: $i,SV4: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV4 )
| ~ ( in @ SV15 @ SV13 )
| ( in @ SV15 @ SV4 ) )
= $true )
| ( ( in @ ( sK2_SY8 @ SV4 ) @ SV4 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(77,plain,
! [SV14: $i,SV4: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV4 ) )
= $true )
| ( ( ~ ( in @ SV14 @ SV11 )
| ( in @ SV14 @ SV4 ) )
= $true )
| ( ( subset @ ( sK2_SY8 @ SV4 ) @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(78,plain,
! [SV9: $i,SV12: $i] :
( ( ( in @ SV12 @ SV9 )
= $false )
| ( ( subset @ SV12 @ SV9 )
= $true )
| ( ( in @ SV9 @ sK1_X )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(79,plain,
! [SV2: $i,SV10: $o,SV6: $i] :
( ( ( ~ ( in @ SV6 @ ( sK5_SY16 @ SV10 @ SV2 @ SV6 ) ) )
= $false )
| ( SV10 = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(80,plain,
! [SV6: $i,SV2: $i,SV10: $o] :
( ( ( ~ ( in @ ( sK5_SY16 @ SV10 @ SV2 @ SV6 ) @ SV2 )
| SV10 )
= $false )
| ( SV10 = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(81,plain,
! [SV2: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ ( sK6_SX0 @ SV2 @ SV6 ) ) )
= $false )
| ( $true = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(82,plain,
! [SV6: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK6_SX0 @ SV2 @ SV6 ) @ SV2 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(83,plain,
! [SV2: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ ( sK7_SX0 @ SV2 @ SV6 ) ) )
= $false )
| ( $false = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(84,plain,
! [SV6: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK7_SX0 @ SV2 @ SV6 ) @ SV2 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(85,plain,
! [SV15: $i,SV4: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV4 ) )
= $true )
| ( ( ~ ( in @ SV15 @ SV13 )
| ( in @ SV15 @ SV4 ) )
= $true )
| ( ( in @ ( sK2_SY8 @ SV4 ) @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(86,plain,
! [SV14: $i,SV4: $i,SV11: $i] :
( ( ( in @ SV11 @ SV4 )
= $false )
| ( ( ~ ( in @ SV14 @ SV11 )
| ( in @ SV14 @ SV4 ) )
= $true )
| ( ( subset @ ( sK2_SY8 @ SV4 ) @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV2: $i,SV10: $o,SV6: $i] :
( ( ( in @ SV6 @ ( sK5_SY16 @ SV10 @ SV2 @ SV6 ) )
= $true )
| ( SV10 = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(88,plain,
! [SV6: $i,SV2: $i,SV10: $o] :
( ( ( ~ ( in @ ( sK5_SY16 @ SV10 @ SV2 @ SV6 ) @ SV2 ) )
= $false )
| ( SV10 = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(89,plain,
! [SV2: $i,SV6: $i,SV10: $o] :
( ( SV10 = $false )
| ( SV10 = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(90,plain,
! [SV2: $i,SV6: $i] :
( ( ( in @ SV6 @ ( sK6_SX0 @ SV2 @ SV6 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(91,plain,
! [SV6: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK6_SX0 @ SV2 @ SV6 ) @ SV2 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(92,plain,
! [SV2: $i,SV6: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(93,plain,
! [SV2: $i,SV6: $i] :
( ( ( in @ SV6 @ ( sK7_SX0 @ SV2 @ SV6 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(94,plain,
! [SV6: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK7_SX0 @ SV2 @ SV6 ) @ SV2 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(95,plain,
! [SV2: $i,SV6: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(96,plain,
! [SV15: $i,SV4: $i,SV13: $i] :
( ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ~ ( in @ SV15 @ SV13 )
| ( in @ SV15 @ SV4 ) )
= $true )
| ( ( in @ ( sK2_SY8 @ SV4 ) @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(97,plain,
! [SV4: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV11 ) )
= $true )
| ( ( in @ SV14 @ SV4 )
= $true )
| ( ( in @ SV11 @ SV4 )
= $false )
| ( ( subset @ ( sK2_SY8 @ SV4 ) @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(98,plain,
! [SV6: $i,SV2: $i,SV10: $o] :
( ( ( in @ ( sK5_SY16 @ SV10 @ SV2 @ SV6 ) @ SV2 )
= $true )
| ( SV10 = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(99,plain,
! [SV6: $i,SV2: $i] :
( ( ( in @ ( sK6_SX0 @ SV2 @ SV6 ) @ SV2 )
= $true )
| ( $true = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(100,plain,
! [SV6: $i,SV2: $i] :
( ( ( in @ ( sK7_SX0 @ SV2 @ SV6 ) @ SV2 )
= $true )
| ( $false = $true )
| ( ( in @ SV6 @ ( setunion @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(101,plain,
! [SV4: $i,SV13: $i,SV15: $i] :
( ( ( ~ ( in @ SV15 @ SV13 ) )
= $true )
| ( ( in @ SV15 @ SV4 )
= $true )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( in @ ( sK2_SY8 @ SV4 ) @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(102,plain,
! [SV4: $i,SV11: $i,SV14: $i] :
( ( ( in @ SV14 @ SV11 )
= $false )
| ( ( in @ SV14 @ SV4 )
= $true )
| ( ( in @ SV11 @ SV4 )
= $false )
| ( ( subset @ ( sK2_SY8 @ SV4 ) @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(103,plain,
! [SV4: $i,SV13: $i,SV15: $i] :
( ( ( in @ SV15 @ SV13 )
= $false )
| ( ( in @ SV15 @ SV4 )
= $true )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( in @ ( sK2_SY8 @ SV4 ) @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(104,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[54,103,102,100,99,98,95,93,92,90,89,87,78,69,65,64,60]) ).
thf(105,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU815^2 : TPTP v8.1.0. Released v3.7.0.
% 0.00/0.10 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.09/0.30 % Computer : n029.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 600
% 0.09/0.30 % DateTime : Mon Jun 20 07:28:15 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30
% 0.09/0.30 No.of.Axioms: 0
% 0.09/0.30
% 0.09/0.30 Length.of.Defs: 1002
% 0.09/0.30
% 0.09/0.30 Contains.Choice.Funs: false
% 0.09/0.30 (rf:0,axioms:0,ps:3,u:6,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)....
% 0.14/0.47
% 0.14/0.47 ********************************
% 0.14/0.47 * All subproblems solved! *
% 0.14/0.47 ********************************
% 0.14/0.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,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:104,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.14/0.48
% 0.14/0.48 %**** Beginning of derivation protocol ****
% 0.14/0.48 % SZS output start CNFRefutation
% See solution above
% 0.14/0.48
% 0.14/0.48 %**** End of derivation protocol ****
% 0.14/0.48 %**** no. of clauses in derivation: 105 ****
% 0.14/0.48 %**** clause counter: 104 ****
% 0.14/0.48
% 0.14/0.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,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:104,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------