TSTP Solution File: SEV398^5 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEV398^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n010.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 17:36:32 EDT 2022
% Result : Theorem 0.18s 0.41s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 105 ( 62 unt; 8 typ; 0 def)
% Number of atoms : 557 ( 137 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 948 ( 156 ~; 126 |; 17 &; 618 @)
% ( 4 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 140 ( 140 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 225 ( 0 ^ 225 !; 0 ?; 225 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_cF,type,
cF: ( a > $o ) > a > $o ).
thf(tp_cG,type,
cG: ( a > $o ) > a > $o ).
thf(tp_sK1_S,type,
sK1_S: a > $o ).
thf(tp_sK2_SY9,type,
sK2_SY9: a ).
thf(tp_sK3_S,type,
sK3_S: a > $o ).
thf(tp_sK4_SY10,type,
sK4_SY10: a ).
thf(tp_sK5_Xx,type,
sK5_Xx: ( a > $o ) > ( a > $o ) > a ).
thf(1,conjecture,
( ( ! [S: a > $o,T: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( T @ Xx ) )
=> ! [Xx: a] :
( ( cF @ T @ Xx )
=> ( cF @ S @ Xx ) ) )
& ! [S: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( cF @ ( cG @ S ) @ Xx ) )
& ! [Xx: a] :
( ( S @ Xx )
=> ( cG @ ( cF @ S ) @ Xx ) ) ) )
=> ! [S: a > $o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
<=> ( cF @ S @ Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM67A_pme) ).
thf(2,negated_conjecture,
( ( ( ! [S: a > $o,T: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( T @ Xx ) )
=> ! [Xx: a] :
( ( cF @ T @ Xx )
=> ( cF @ S @ Xx ) ) )
& ! [S: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( cF @ ( cG @ S ) @ Xx ) )
& ! [Xx: a] :
( ( S @ Xx )
=> ( cG @ ( cF @ S ) @ Xx ) ) ) )
=> ! [S: a > $o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
<=> ( cF @ S @ Xx ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [S: a > $o,T: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( T @ Xx ) )
=> ! [Xx: a] :
( ( cF @ T @ Xx )
=> ( cF @ S @ Xx ) ) )
& ! [S: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( cF @ ( cG @ S ) @ Xx ) )
& ! [Xx: a] :
( ( S @ Xx )
=> ( cG @ ( cF @ S ) @ Xx ) ) ) )
=> ! [S: a > $o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
<=> ( cF @ S @ Xx ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [S: a > $o,T: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( T @ Xx ) )
=> ! [Xx: a] :
( ( cF @ T @ Xx )
=> ( cF @ S @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [S: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( cF @ ( cG @ S ) @ Xx ) )
& ! [Xx: a] :
( ( S @ Xx )
=> ( cG @ ( cF @ S ) @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [S: a > $o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
<=> ( cF @ S @ Xx ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [S: a > $o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
=> ( cF @ S @ Xx ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[6]) ).
thf(8,plain,
( ( ! [S: a > $o,Xx: a] :
( ( cF @ S @ Xx )
=> ( cF @ ( cG @ ( cF @ S ) ) @ Xx ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[6]) ).
thf(9,plain,
( ( ~ ! [S: a > $o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
=> ( cF @ S @ Xx ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ! [S: a > $o,Xx: a] :
( ( cF @ S @ Xx )
=> ( cF @ ( cG @ ( cF @ S ) ) @ Xx ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(11,plain,
( ( ( cF @ ( cG @ ( cF @ sK1_S ) ) @ sK2_SY9 )
& ~ ( cF @ sK1_S @ sK2_SY9 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(12,plain,
( ( ( cF @ sK3_S @ sK4_SY10 )
& ~ ( cF @ ( cG @ ( cF @ sK3_S ) ) @ sK4_SY10 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(13,plain,
( ( ! [S: a > $o,T: a > $o] :
( ( ( S @ ( sK5_Xx @ T @ S ) )
& ~ ( T @ ( sK5_Xx @ T @ S ) ) )
| ! [Xx: a] :
( ~ ( cF @ T @ Xx )
| ( cF @ S @ Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(14,plain,
( ( ! [S: a > $o,Xx: a] :
( ~ ( S @ Xx )
| ( cF @ ( cG @ S ) @ Xx ) )
& ! [S: a > $o,Xx: a] :
( ~ ( S @ Xx )
| ( cG @ ( cF @ S ) @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(15,plain,
( ( ! [S: a > $o,Xx: a] :
( ~ ( S @ Xx )
| ( cF @ ( cG @ S ) @ Xx ) )
& ! [S: a > $o,Xx: a] :
( ~ ( S @ Xx )
| ( cG @ ( cF @ S ) @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [S: a > $o,T: a > $o] :
( ( ( S @ ( sK5_Xx @ T @ S ) )
& ~ ( T @ ( sK5_Xx @ T @ S ) ) )
| ! [Xx: a] :
( ~ ( cF @ T @ Xx )
| ( cF @ S @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(17,plain,
( ( ( cF @ ( cG @ ( cF @ sK1_S ) ) @ sK2_SY9 )
& ~ ( cF @ sK1_S @ sK2_SY9 ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(18,plain,
( ( ~ ( ~ ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cF @ ( cG @ SX0 ) @ SX1 ) )
| ~ ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cG @ ( cF @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [SX0: a > $o,SX1: a > $o] :
( ~ ( ~ ( SX0 @ ( sK5_Xx @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( sK5_Xx @ SX1 @ SX0 ) ) )
| ! [SX2: a] :
( ~ ( cF @ SX1 @ SX2 )
| ( cF @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( ~ ( cF @ ( cG @ ( cF @ sK1_S ) ) @ sK2_SY9 )
| ~ ~ ( cF @ sK1_S @ sK2_SY9 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cF @ ( cG @ SX0 ) @ SX1 ) )
| ~ ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cG @ ( cF @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV1: a > $o] :
( ( ! [SY11: a > $o] :
( ~ ( ~ ( SV1 @ ( sK5_Xx @ SY11 @ SV1 ) )
| ~ ~ ( SY11 @ ( sK5_Xx @ SY11 @ SV1 ) ) )
| ! [SY12: a] :
( ~ ( cF @ SY11 @ SY12 )
| ( cF @ SV1 @ SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ( cF @ ( cG @ ( cF @ sK1_S ) ) @ sK2_SY9 )
| ~ ~ ( cF @ sK1_S @ sK2_SY9 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cF @ ( cG @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cG @ ( cF @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV2: a > $o,SV1: a > $o] :
( ( ~ ( ~ ( SV1 @ ( sK5_Xx @ SV2 @ SV1 ) )
| ~ ~ ( SV2 @ ( sK5_Xx @ SV2 @ SV1 ) ) )
| ! [SY13: a] :
( ~ ( cF @ SV2 @ SY13 )
| ( cF @ SV1 @ SY13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
( ( ~ ( cF @ ( cG @ ( cF @ sK1_S ) ) @ sK2_SY9 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(28,plain,
( ( ~ ~ ( cF @ sK1_S @ sK2_SY9 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(29,plain,
( ( ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cF @ ( cG @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(30,plain,
( ( ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cG @ ( cF @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(31,plain,
! [SV2: a > $o,SV1: a > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK5_Xx @ SV2 @ SV1 ) )
| ~ ~ ( SV2 @ ( sK5_Xx @ SV2 @ SV1 ) ) ) )
= $true )
| ( ( ! [SY13: a] :
( ~ ( cF @ SV2 @ SY13 )
| ( cF @ SV1 @ SY13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(32,plain,
( ( cF @ ( cG @ ( cF @ sK1_S ) ) @ sK2_SY9 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(33,plain,
( ( ~ ( cF @ sK1_S @ sK2_SY9 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(34,plain,
! [SV3: a > $o] :
( ( ! [SY14: a] :
( ~ ( SV3 @ SY14 )
| ( cF @ ( cG @ SV3 ) @ SY14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(35,plain,
! [SV4: a > $o] :
( ( ! [SY15: a] :
( ~ ( SV4 @ SY15 )
| ( cG @ ( cF @ SV4 ) @ SY15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(36,plain,
! [SV2: a > $o,SV1: a > $o] :
( ( ( ~ ( SV1 @ ( sK5_Xx @ SV2 @ SV1 ) )
| ~ ~ ( SV2 @ ( sK5_Xx @ SV2 @ SV1 ) ) )
= $false )
| ( ( ! [SY13: a] :
( ~ ( cF @ SV2 @ SY13 )
| ( cF @ SV1 @ SY13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(37,plain,
( ( cF @ sK1_S @ sK2_SY9 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV5: a,SV3: a > $o] :
( ( ~ ( SV3 @ SV5 )
| ( cF @ ( cG @ SV3 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV6: a,SV4: a > $o] :
( ( ~ ( SV4 @ SV6 )
| ( cG @ ( cF @ SV4 ) @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV2: a > $o,SV1: a > $o] :
( ( ( ~ ( SV1 @ ( sK5_Xx @ SV2 @ SV1 ) ) )
= $false )
| ( ( ! [SY13: a] :
( ~ ( cF @ SV2 @ SY13 )
| ( cF @ SV1 @ SY13 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(41,plain,
! [SV1: a > $o,SV2: a > $o] :
( ( ( ~ ~ ( SV2 @ ( sK5_Xx @ SV2 @ SV1 ) ) )
= $false )
| ( ( ! [SY13: a] :
( ~ ( cF @ SV2 @ SY13 )
| ( cF @ SV1 @ SY13 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(42,plain,
! [SV5: a,SV3: a > $o] :
( ( ( ~ ( SV3 @ SV5 ) )
= $true )
| ( ( cF @ ( cG @ SV3 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV6: a,SV4: a > $o] :
( ( ( ~ ( SV4 @ SV6 ) )
= $true )
| ( ( cG @ ( cF @ SV4 ) @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV2: a > $o,SV1: a > $o] :
( ( ( SV1 @ ( sK5_Xx @ SV2 @ SV1 ) )
= $true )
| ( ( ! [SY13: a] :
( ~ ( cF @ SV2 @ SY13 )
| ( cF @ SV1 @ SY13 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(45,plain,
! [SV1: a > $o,SV2: a > $o] :
( ( ( ~ ( SV2 @ ( sK5_Xx @ SV2 @ SV1 ) ) )
= $true )
| ( ( ! [SY13: a] :
( ~ ( cF @ SV2 @ SY13 )
| ( cF @ SV1 @ SY13 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(46,plain,
! [SV5: a,SV3: a > $o] :
( ( ( SV3 @ SV5 )
= $false )
| ( ( cF @ ( cG @ SV3 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV6: a,SV4: a > $o] :
( ( ( SV4 @ SV6 )
= $false )
| ( ( cG @ ( cF @ SV4 ) @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV1: a > $o,SV7: a,SV2: a > $o] :
( ( ( ~ ( cF @ SV2 @ SV7 )
| ( cF @ SV1 @ SV7 ) )
= $true )
| ( ( SV1 @ ( sK5_Xx @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV1: a > $o,SV2: a > $o] :
( ( ( SV2 @ ( sK5_Xx @ SV2 @ SV1 ) )
= $false )
| ( ( ! [SY13: a] :
( ~ ( cF @ SV2 @ SY13 )
| ( cF @ SV1 @ SY13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV1: a > $o,SV7: a,SV2: a > $o] :
( ( ( ~ ( cF @ SV2 @ SV7 ) )
= $true )
| ( ( cF @ SV1 @ SV7 )
= $true )
| ( ( SV1 @ ( sK5_Xx @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(51,plain,
! [SV1: a > $o,SV8: a,SV2: a > $o] :
( ( ( ~ ( cF @ SV2 @ SV8 )
| ( cF @ SV1 @ SV8 ) )
= $true )
| ( ( SV2 @ ( sK5_Xx @ SV2 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV1: a > $o,SV7: a,SV2: a > $o] :
( ( ( cF @ SV2 @ SV7 )
= $false )
| ( ( cF @ SV1 @ SV7 )
= $true )
| ( ( SV1 @ ( sK5_Xx @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(53,plain,
! [SV1: a > $o,SV8: a,SV2: a > $o] :
( ( ( ~ ( cF @ SV2 @ SV8 ) )
= $true )
| ( ( cF @ SV1 @ SV8 )
= $true )
| ( ( SV2 @ ( sK5_Xx @ SV2 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(54,plain,
! [SV1: a > $o,SV8: a,SV2: a > $o] :
( ( ( cF @ SV2 @ SV8 )
= $false )
| ( ( cF @ SV1 @ SV8 )
= $true )
| ( ( SV2 @ ( sK5_Xx @ SV2 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(55,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[32,54,52,47,46,37]) ).
thf(56,plain,
( ( ! [S: a > $o,Xx: a] :
( ~ ( S @ Xx )
| ( cF @ ( cG @ S ) @ Xx ) )
& ! [S: a > $o,Xx: a] :
( ~ ( S @ Xx )
| ( cG @ ( cF @ S ) @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(57,plain,
( ( ! [S: a > $o,T: a > $o] :
( ( ( S @ ( sK5_Xx @ T @ S ) )
& ~ ( T @ ( sK5_Xx @ T @ S ) ) )
| ! [Xx: a] :
( ~ ( cF @ T @ Xx )
| ( cF @ S @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(58,plain,
( ( ( cF @ sK3_S @ sK4_SY10 )
& ~ ( cF @ ( cG @ ( cF @ sK3_S ) ) @ sK4_SY10 ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(59,plain,
( ( ! [SX0: a > $o,SX1: a > $o] :
( ~ ( ~ ( SX0 @ ( sK5_Xx @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( sK5_Xx @ SX1 @ SX0 ) ) )
| ! [SX2: a] :
( ~ ( cF @ SX1 @ SX2 )
| ( cF @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(60,plain,
( ( ~ ( ~ ( cF @ sK3_S @ sK4_SY10 )
| ~ ~ ( cF @ ( cG @ ( cF @ sK3_S ) ) @ sK4_SY10 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(61,plain,
( ( ~ ( ~ ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cF @ ( cG @ SX0 ) @ SX1 ) )
| ~ ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cG @ ( cF @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(62,plain,
! [SV9: a > $o] :
( ( ! [SY16: a > $o] :
( ~ ( ~ ( SV9 @ ( sK5_Xx @ SY16 @ SV9 ) )
| ~ ~ ( SY16 @ ( sK5_Xx @ SY16 @ SV9 ) ) )
| ! [SY17: a] :
( ~ ( cF @ SY16 @ SY17 )
| ( cF @ SV9 @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(63,plain,
( ( ~ ( cF @ sK3_S @ sK4_SY10 )
| ~ ~ ( cF @ ( cG @ ( cF @ sK3_S ) ) @ sK4_SY10 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(64,plain,
( ( ~ ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cF @ ( cG @ SX0 ) @ SX1 ) )
| ~ ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cG @ ( cF @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(65,plain,
! [SV10: a > $o,SV9: a > $o] :
( ( ~ ( ~ ( SV9 @ ( sK5_Xx @ SV10 @ SV9 ) )
| ~ ~ ( SV10 @ ( sK5_Xx @ SV10 @ SV9 ) ) )
| ! [SY18: a] :
( ~ ( cF @ SV10 @ SY18 )
| ( cF @ SV9 @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(66,plain,
( ( ~ ( cF @ sK3_S @ sK4_SY10 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(67,plain,
( ( ~ ~ ( cF @ ( cG @ ( cF @ sK3_S ) ) @ sK4_SY10 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(68,plain,
( ( ~ ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cF @ ( cG @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(69,plain,
( ( ~ ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cG @ ( cF @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(70,plain,
! [SV10: a > $o,SV9: a > $o] :
( ( ( ~ ( ~ ( SV9 @ ( sK5_Xx @ SV10 @ SV9 ) )
| ~ ~ ( SV10 @ ( sK5_Xx @ SV10 @ SV9 ) ) ) )
= $true )
| ( ( ! [SY18: a] :
( ~ ( cF @ SV10 @ SY18 )
| ( cF @ SV9 @ SY18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(71,plain,
( ( cF @ sK3_S @ sK4_SY10 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(72,plain,
( ( ~ ( cF @ ( cG @ ( cF @ sK3_S ) ) @ sK4_SY10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(73,plain,
( ( ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cF @ ( cG @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(74,plain,
( ( ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cG @ ( cF @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(75,plain,
! [SV10: a > $o,SV9: a > $o] :
( ( ( ~ ( SV9 @ ( sK5_Xx @ SV10 @ SV9 ) )
| ~ ~ ( SV10 @ ( sK5_Xx @ SV10 @ SV9 ) ) )
= $false )
| ( ( ! [SY18: a] :
( ~ ( cF @ SV10 @ SY18 )
| ( cF @ SV9 @ SY18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(76,plain,
( ( cF @ ( cG @ ( cF @ sK3_S ) ) @ sK4_SY10 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV11: a > $o] :
( ( ! [SY19: a] :
( ~ ( SV11 @ SY19 )
| ( cF @ ( cG @ SV11 ) @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV12: a > $o] :
( ( ! [SY20: a] :
( ~ ( SV12 @ SY20 )
| ( cG @ ( cF @ SV12 ) @ SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV10: a > $o,SV9: a > $o] :
( ( ( ~ ( SV9 @ ( sK5_Xx @ SV10 @ SV9 ) ) )
= $false )
| ( ( ! [SY18: a] :
( ~ ( cF @ SV10 @ SY18 )
| ( cF @ SV9 @ SY18 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(80,plain,
! [SV9: a > $o,SV10: a > $o] :
( ( ( ~ ~ ( SV10 @ ( sK5_Xx @ SV10 @ SV9 ) ) )
= $false )
| ( ( ! [SY18: a] :
( ~ ( cF @ SV10 @ SY18 )
| ( cF @ SV9 @ SY18 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(81,plain,
! [SV13: a,SV11: a > $o] :
( ( ~ ( SV11 @ SV13 )
| ( cF @ ( cG @ SV11 ) @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV14: a,SV12: a > $o] :
( ( ~ ( SV12 @ SV14 )
| ( cG @ ( cF @ SV12 ) @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(83,plain,
! [SV10: a > $o,SV9: a > $o] :
( ( ( SV9 @ ( sK5_Xx @ SV10 @ SV9 ) )
= $true )
| ( ( ! [SY18: a] :
( ~ ( cF @ SV10 @ SY18 )
| ( cF @ SV9 @ SY18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(84,plain,
! [SV9: a > $o,SV10: a > $o] :
( ( ( ~ ( SV10 @ ( sK5_Xx @ SV10 @ SV9 ) ) )
= $true )
| ( ( ! [SY18: a] :
( ~ ( cF @ SV10 @ SY18 )
| ( cF @ SV9 @ SY18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(85,plain,
! [SV13: a,SV11: a > $o] :
( ( ( ~ ( SV11 @ SV13 ) )
= $true )
| ( ( cF @ ( cG @ SV11 ) @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV14: a,SV12: a > $o] :
( ( ( ~ ( SV12 @ SV14 ) )
= $true )
| ( ( cG @ ( cF @ SV12 ) @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV9: a > $o,SV15: a,SV10: a > $o] :
( ( ( ~ ( cF @ SV10 @ SV15 )
| ( cF @ SV9 @ SV15 ) )
= $true )
| ( ( SV9 @ ( sK5_Xx @ SV10 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(88,plain,
! [SV9: a > $o,SV10: a > $o] :
( ( ( SV10 @ ( sK5_Xx @ SV10 @ SV9 ) )
= $false )
| ( ( ! [SY18: a] :
( ~ ( cF @ SV10 @ SY18 )
| ( cF @ SV9 @ SY18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(89,plain,
! [SV13: a,SV11: a > $o] :
( ( ( SV11 @ SV13 )
= $false )
| ( ( cF @ ( cG @ SV11 ) @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(90,plain,
! [SV14: a,SV12: a > $o] :
( ( ( SV12 @ SV14 )
= $false )
| ( ( cG @ ( cF @ SV12 ) @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(91,plain,
! [SV9: a > $o,SV15: a,SV10: a > $o] :
( ( ( ~ ( cF @ SV10 @ SV15 ) )
= $true )
| ( ( cF @ SV9 @ SV15 )
= $true )
| ( ( SV9 @ ( sK5_Xx @ SV10 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(92,plain,
! [SV9: a > $o,SV16: a,SV10: a > $o] :
( ( ( ~ ( cF @ SV10 @ SV16 )
| ( cF @ SV9 @ SV16 ) )
= $true )
| ( ( SV10 @ ( sK5_Xx @ SV10 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(93,plain,
! [SV9: a > $o,SV15: a,SV10: a > $o] :
( ( ( cF @ SV10 @ SV15 )
= $false )
| ( ( cF @ SV9 @ SV15 )
= $true )
| ( ( SV9 @ ( sK5_Xx @ SV10 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(94,plain,
! [SV9: a > $o,SV16: a,SV10: a > $o] :
( ( ( ~ ( cF @ SV10 @ SV16 ) )
= $true )
| ( ( cF @ SV9 @ SV16 )
= $true )
| ( ( SV10 @ ( sK5_Xx @ SV10 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(95,plain,
! [SV9: a > $o,SV16: a,SV10: a > $o] :
( ( ( cF @ SV10 @ SV16 )
= $false )
| ( ( cF @ SV9 @ SV16 )
= $true )
| ( ( SV10 @ ( sK5_Xx @ SV10 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(96,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[71,95,93,90,89,76]) ).
thf(97,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[96,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV398^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 28 17:17:19 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 0
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.34 (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)....
% 0.18/0.41
% 0.18/0.41 ********************************
% 0.18/0.41 * All subproblems solved! *
% 0.18/0.41 ********************************
% 0.18/0.41 % SZS status Theorem for /export/starexec/sandbox/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:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:96,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.42
% 0.18/0.42 %**** Beginning of derivation protocol ****
% 0.18/0.42 % SZS output start CNFRefutation
% See solution above
% 0.18/0.42
% 0.18/0.42 %**** End of derivation protocol ****
% 0.18/0.42 %**** no. of clauses in derivation: 97 ****
% 0.18/0.42 %**** clause counter: 96 ****
% 0.18/0.42
% 0.18/0.42 % SZS status Theorem for /export/starexec/sandbox/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:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:96,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------