TSTP Solution File: SEV107^5 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEV107^5 : 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 : n024.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 17:35:07 EDT 2022
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of formulae : 178 ( 111 unt; 13 typ; 0 def)
% Number of atoms : 1021 ( 243 equ; 0 cnn)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 1749 ( 301 ~; 275 |; 71 &;1078 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 416 ( 0 ^ 400 !; 16 ?; 416 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_cR,type,
cR: a > a > $o ).
thf(tp_cS,type,
cS: $i > $i > $o ).
thf(tp_f,type,
f: a > $i > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: a ).
thf(tp_sK2_Xw,type,
sK2_Xw: $i > a ).
thf(tp_sK3_Xy,type,
sK3_Xy: $i ).
thf(tp_sK4_SY26,type,
sK4_SY26: a ).
thf(tp_sK5_SY30,type,
sK5_SY30: a ).
thf(tp_sK6_Xy,type,
sK6_Xy: $i ).
thf(tp_sK7_SY35,type,
sK7_SY35: a ).
thf(tp_sK8_Xy,type,
sK8_Xy: a > $i ).
thf(tp_z,type,
z: a ).
thf(1,conjecture,
( ( ! [Xu: a,Xv: a,Xw: a] :
( ( ( cR @ Xu @ Xv )
& ( cR @ Xw @ Xv ) )
=> ( cR @ Xu @ Xw ) )
& ! [Xx: a] : ( cR @ Xx @ Xx ) )
=> ( ( ! [Xx: a] :
? [Xy: $i] : ( f @ Xx @ Xy )
& ! [Xx: a,Xy1: $i,Xy2: $i] :
( ( ( f @ Xx @ Xy1 )
& ( f @ Xx @ Xy2 ) )
=> ( cS @ Xy1 @ Xy2 ) )
& ! [Xx1: a,Xx2: a,Xy: $i] :
( ( ( f @ Xx1 @ Xy )
& ( f @ Xx2 @ Xy ) )
=> ( cR @ Xx1 @ Xx2 ) ) )
=> ( ! [Xx: a] :
? [Xy: $i] :
! [Xw: a] :
( ( f @ Xx @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx @ z ) ) )
& ! [Xy: $i,Xx1: a,Xx2: a] :
( ( ! [Xw: a] :
( ( f @ Xx1 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx1 @ z ) ) )
& ! [Xw: a] :
( ( f @ Xx2 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx2 @ z ) ) ) )
=> ( cR @ Xx1 @ Xx2 ) )
& ! [Xy: $i] :
? [Xx: a] :
! [Xw: a] :
( ( f @ Xx @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx @ z ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM552B_pme) ).
thf(2,negated_conjecture,
( ( ( ! [Xu: a,Xv: a,Xw: a] :
( ( ( cR @ Xu @ Xv )
& ( cR @ Xw @ Xv ) )
=> ( cR @ Xu @ Xw ) )
& ! [Xx: a] : ( cR @ Xx @ Xx ) )
=> ( ( ! [Xx: a] :
? [Xy: $i] : ( f @ Xx @ Xy )
& ! [Xx: a,Xy1: $i,Xy2: $i] :
( ( ( f @ Xx @ Xy1 )
& ( f @ Xx @ Xy2 ) )
=> ( cS @ Xy1 @ Xy2 ) )
& ! [Xx1: a,Xx2: a,Xy: $i] :
( ( ( f @ Xx1 @ Xy )
& ( f @ Xx2 @ Xy ) )
=> ( cR @ Xx1 @ Xx2 ) ) )
=> ( ! [Xx: a] :
? [Xy: $i] :
! [Xw: a] :
( ( f @ Xx @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx @ z ) ) )
& ! [Xy: $i,Xx1: a,Xx2: a] :
( ( ! [Xw: a] :
( ( f @ Xx1 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx1 @ z ) ) )
& ! [Xw: a] :
( ( f @ Xx2 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx2 @ z ) ) ) )
=> ( cR @ Xx1 @ Xx2 ) )
& ! [Xy: $i] :
? [Xx: a] :
! [Xw: a] :
( ( f @ Xx @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx @ z ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [Xu: a,Xv: a,Xw: a] :
( ( ( cR @ Xu @ Xv )
& ( cR @ Xw @ Xv ) )
=> ( cR @ Xu @ Xw ) )
& ! [Xx: a] : ( cR @ Xx @ Xx ) )
=> ( ( ! [Xx: a] :
? [Xy: $i] : ( f @ Xx @ Xy )
& ! [Xx: a,Xy1: $i,Xy2: $i] :
( ( ( f @ Xx @ Xy1 )
& ( f @ Xx @ Xy2 ) )
=> ( cS @ Xy1 @ Xy2 ) )
& ! [Xx1: a,Xx2: a,Xy: $i] :
( ( ( f @ Xx1 @ Xy )
& ( f @ Xx2 @ Xy ) )
=> ( cR @ Xx1 @ Xx2 ) ) )
=> ( ! [Xx: a] :
? [Xy: $i] :
! [Xw: a] :
( ( f @ Xx @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx @ z ) ) )
& ! [Xy: $i,Xx1: a,Xx2: a] :
( ( ! [Xw: a] :
( ( f @ Xx1 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx1 @ z ) ) )
& ! [Xw: a] :
( ( f @ Xx2 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx2 @ z ) ) ) )
=> ( cR @ Xx1 @ Xx2 ) )
& ! [Xy: $i] :
? [Xx: a] :
! [Xw: a] :
( ( f @ Xx @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx @ z ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xu: a,Xv: a,Xw: a] :
( ( ( cR @ Xu @ Xv )
& ( cR @ Xw @ Xv ) )
=> ( cR @ Xu @ Xw ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: a] : ( cR @ Xx @ Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: a] :
? [Xy: $i] : ( f @ Xx @ Xy ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [Xx: a,Xy1: $i,Xy2: $i] :
( ( ( f @ Xx @ Xy1 )
& ( f @ Xx @ Xy2 ) )
=> ( cS @ Xy1 @ Xy2 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [Xx1: a,Xx2: a,Xy: $i] :
( ( ( f @ Xx1 @ Xy )
& ( f @ Xx2 @ Xy ) )
=> ( cR @ Xx1 @ Xx2 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ! [Xx: a] :
? [Xy: $i] :
! [Xw: a] :
( ( f @ Xx @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx @ z ) ) )
& ! [Xy: $i,Xx1: a,Xx2: a] :
( ( ! [Xw: a] :
( ( f @ Xx1 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx1 @ z ) ) )
& ! [Xw: a] :
( ( f @ Xx2 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx2 @ z ) ) ) )
=> ( cR @ Xx1 @ Xx2 ) )
& ! [Xy: $i] :
? [Xx: a] :
! [Xw: a] :
( ( f @ Xx @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx @ z ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [Xx: a] :
? [Xy: $i] :
! [Xw: a] :
( ( f @ Xx @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx @ z ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[9]) ).
thf(11,plain,
( ( ! [Xy: $i,Xx1: a,Xx2: a] :
( ( ! [Xw: a] :
( ( f @ Xx1 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx1 @ z ) ) )
& ! [Xw: a] :
( ( f @ Xx2 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx2 @ z ) ) ) )
=> ( cR @ Xx1 @ Xx2 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[9]) ).
thf(12,plain,
( ( ! [Xy: $i] :
? [Xx: a] :
! [Xw: a] :
( ( f @ Xx @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx @ z ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[9]) ).
thf(13,plain,
( ( ~ ! [Xx: a] :
? [Xy: $i] :
! [Xw: a] :
( ( f @ Xx @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx @ z ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(14,plain,
( ( ~ ! [Xy: $i,Xx1: a,Xx2: a] :
( ( ! [Xw: a] :
( ( f @ Xx1 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx1 @ z ) ) )
& ! [Xw: a] :
( ( f @ Xx2 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx2 @ z ) ) ) )
=> ( cR @ Xx1 @ Xx2 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(15,plain,
( ( ~ ! [Xy: $i] :
? [Xx: a] :
! [Xw: a] :
( ( f @ Xx @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx @ z ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(16,plain,
( ( ( ! [Xy: $i] : ( f @ ( sK2_Xw @ Xy ) @ Xy )
| ~ ( cR @ sK1_Xx @ z ) )
& ! [SY25: $i] :
~ ( f @ sK1_Xx @ SY25 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(17,plain,
( ( ( ! [SY28: a] :
~ ( f @ SY28 @ sK3_Xy )
| ( f @ sK4_SY26 @ sK3_Xy ) )
& ( ( cR @ sK4_SY26 @ z )
| ( f @ sK4_SY26 @ sK3_Xy ) )
& ( ! [SY29: a] :
~ ( f @ SY29 @ sK3_Xy )
| ( f @ sK5_SY30 @ sK3_Xy ) )
& ( ( cR @ sK5_SY30 @ z )
| ( f @ sK5_SY30 @ sK3_Xy ) )
& ~ ( cR @ sK4_SY26 @ sK5_SY30 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(18,plain,
( ( ( ( f @ sK7_SY35 @ sK6_Xy )
| ! [Xx: a] :
~ ( cR @ Xx @ z ) )
& ! [SY37: a] :
~ ( f @ SY37 @ sK6_Xy ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(19,plain,
( ( ! [Xu: a,Xv: a,Xw: a] :
( ~ ( cR @ Xu @ Xv )
| ~ ( cR @ Xw @ Xv )
| ( cR @ Xu @ Xw ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(20,plain,
( ( ! [Xx: a] : ( f @ Xx @ ( sK8_Xy @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(21,plain,
( ( ! [Xx: a,Xy1: $i,Xy2: $i] :
( ~ ( f @ Xx @ Xy1 )
| ~ ( f @ Xx @ Xy2 )
| ( cS @ Xy1 @ Xy2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(22,plain,
( ( ! [Xx1: a,Xx2: a] :
( ! [Xy: $i] :
( ~ ( f @ Xx1 @ Xy )
| ~ ( f @ Xx2 @ Xy ) )
| ( cR @ Xx1 @ Xx2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(23,plain,
( ( ! [Xx1: a,Xx2: a] :
( ! [Xy: $i] :
( ~ ( f @ Xx1 @ Xy )
| ~ ( f @ Xx2 @ Xy ) )
| ( cR @ Xx1 @ Xx2 ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(24,plain,
( ( ! [Xx: a,Xy1: $i,Xy2: $i] :
( ~ ( f @ Xx @ Xy1 )
| ~ ( f @ Xx @ Xy2 )
| ( cS @ Xy1 @ Xy2 ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(25,plain,
( ( ! [Xx: a] : ( f @ Xx @ ( sK8_Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(26,plain,
( ( ! [Xx: a] : ( cR @ Xx @ Xx ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(27,plain,
( ( ! [Xu: a,Xv: a,Xw: a] :
( ~ ( cR @ Xu @ Xv )
| ~ ( cR @ Xw @ Xv )
| ( cR @ Xu @ Xw ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(28,plain,
( ( ( ! [Xy: $i] : ( f @ ( sK2_Xw @ Xy ) @ Xy )
| ~ ( cR @ sK1_Xx @ z ) )
& ! [SY25: $i] :
~ ( f @ sK1_Xx @ SY25 ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(29,plain,
( ( ~ ( ~ ( ! [SX0: $i] : ( f @ ( sK2_Xw @ SX0 ) @ SX0 )
| ~ ( cR @ sK1_Xx @ z ) )
| ~ ! [SX0: $i] :
~ ( f @ sK1_Xx @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(30,plain,
! [SV1: a] :
( ( ! [SY38: a] :
( ! [SY39: $i] :
( ~ ( f @ SV1 @ SY39 )
| ~ ( f @ SY38 @ SY39 ) )
| ( cR @ SV1 @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(31,plain,
! [SV2: a] :
( ( ! [SY40: $i,SY41: $i] :
( ~ ( f @ SV2 @ SY40 )
| ~ ( f @ SV2 @ SY41 )
| ( cS @ SY40 @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(32,plain,
! [SV3: a] :
( ( f @ SV3 @ ( sK8_Xy @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(33,plain,
! [SV4: a] :
( ( cR @ SV4 @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(34,plain,
! [SV5: a] :
( ( ! [SY42: a,SY43: a] :
( ~ ( cR @ SV5 @ SY42 )
| ~ ( cR @ SY43 @ SY42 )
| ( cR @ SV5 @ SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(35,plain,
( ( ~ ( ! [SX0: $i] : ( f @ ( sK2_Xw @ SX0 ) @ SX0 )
| ~ ( cR @ sK1_Xx @ z ) )
| ~ ! [SX0: $i] :
~ ( f @ sK1_Xx @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV6: a,SV1: a] :
( ( ! [SY44: $i] :
( ~ ( f @ SV1 @ SY44 )
| ~ ( f @ SV6 @ SY44 ) )
| ( cR @ SV1 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV7: $i,SV2: a] :
( ( ! [SY45: $i] :
( ~ ( f @ SV2 @ SV7 )
| ~ ( f @ SV2 @ SY45 )
| ( cS @ SV7 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV8: a,SV5: a] :
( ( ! [SY46: a] :
( ~ ( cR @ SV5 @ SV8 )
| ~ ( cR @ SY46 @ SV8 )
| ( cR @ SV5 @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(39,plain,
( ( ~ ( ! [SX0: $i] : ( f @ ( sK2_Xw @ SX0 ) @ SX0 )
| ~ ( cR @ sK1_Xx @ z ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(40,plain,
( ( ~ ! [SX0: $i] :
~ ( f @ sK1_Xx @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(41,plain,
! [SV6: a,SV1: a] :
( ( ( ! [SY44: $i] :
( ~ ( f @ SV1 @ SY44 )
| ~ ( f @ SV6 @ SY44 ) ) )
= $true )
| ( ( cR @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV9: $i,SV7: $i,SV2: a] :
( ( ~ ( f @ SV2 @ SV7 )
| ~ ( f @ SV2 @ SV9 )
| ( cS @ SV7 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV10: a,SV8: a,SV5: a] :
( ( ~ ( cR @ SV5 @ SV8 )
| ~ ( cR @ SV10 @ SV8 )
| ( cR @ SV5 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(44,plain,
( ( ! [SX0: $i] : ( f @ ( sK2_Xw @ SX0 ) @ SX0 )
| ~ ( cR @ sK1_Xx @ z ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(45,plain,
( ( ! [SX0: $i] :
~ ( f @ sK1_Xx @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(46,plain,
! [SV6: a,SV11: $i,SV1: a] :
( ( ( ~ ( f @ SV1 @ SV11 )
| ~ ( f @ SV6 @ SV11 ) )
= $true )
| ( ( cR @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV9: $i,SV7: $i,SV2: a] :
( ( ( ~ ( f @ SV2 @ SV7 )
| ~ ( f @ SV2 @ SV9 ) )
= $true )
| ( ( cS @ SV7 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV10: a,SV8: a,SV5: a] :
( ( ( ~ ( cR @ SV5 @ SV8 )
| ~ ( cR @ SV10 @ SV8 ) )
= $true )
| ( ( cR @ SV5 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(49,plain,
( ( ( ! [SX0: $i] : ( f @ ( sK2_Xw @ SX0 ) @ SX0 ) )
= $true )
| ( ( ~ ( cR @ sK1_Xx @ z ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(50,plain,
! [SV12: $i] :
( ( ~ ( f @ sK1_Xx @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV6: a,SV11: $i,SV1: a] :
( ( ( ~ ( f @ SV1 @ SV11 ) )
= $true )
| ( ( ~ ( f @ SV6 @ SV11 ) )
= $true )
| ( ( cR @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV9: $i,SV7: $i,SV2: a] :
( ( ( ~ ( f @ SV2 @ SV7 ) )
= $true )
| ( ( ~ ( f @ SV2 @ SV9 ) )
= $true )
| ( ( cS @ SV7 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV10: a,SV8: a,SV5: a] :
( ( ( ~ ( cR @ SV5 @ SV8 ) )
= $true )
| ( ( ~ ( cR @ SV10 @ SV8 ) )
= $true )
| ( ( cR @ SV5 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV13: $i] :
( ( ( f @ ( sK2_Xw @ SV13 ) @ SV13 )
= $true )
| ( ( ~ ( cR @ sK1_Xx @ z ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(55,plain,
! [SV12: $i] :
( ( f @ sK1_Xx @ SV12 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(56,plain,
! [SV6: a,SV11: $i,SV1: a] :
( ( ( f @ SV1 @ SV11 )
= $false )
| ( ( ~ ( f @ SV6 @ SV11 ) )
= $true )
| ( ( cR @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV9: $i,SV7: $i,SV2: a] :
( ( ( f @ SV2 @ SV7 )
= $false )
| ( ( ~ ( f @ SV2 @ SV9 ) )
= $true )
| ( ( cS @ SV7 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV10: a,SV8: a,SV5: a] :
( ( ( cR @ SV5 @ SV8 )
= $false )
| ( ( ~ ( cR @ SV10 @ SV8 ) )
= $true )
| ( ( cR @ SV5 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV13: $i] :
( ( ( cR @ sK1_Xx @ z )
= $false )
| ( ( f @ ( sK2_Xw @ SV13 ) @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV1: a,SV11: $i,SV6: a] :
( ( ( f @ SV6 @ SV11 )
= $false )
| ( ( f @ SV1 @ SV11 )
= $false )
| ( ( cR @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV7: $i,SV9: $i,SV2: a] :
( ( ( f @ SV2 @ SV9 )
= $false )
| ( ( f @ SV2 @ SV7 )
= $false )
| ( ( cS @ SV7 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV5: a,SV8: a,SV10: a] :
( ( ( cR @ SV10 @ SV8 )
= $false )
| ( ( cR @ SV5 @ SV8 )
= $false )
| ( ( cR @ SV5 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(63,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[32,62,61,60,59,55,33]) ).
thf(64,plain,
( ( ! [Xx1: a,Xx2: a] :
( ! [Xy: $i] :
( ~ ( f @ Xx1 @ Xy )
| ~ ( f @ Xx2 @ Xy ) )
| ( cR @ Xx1 @ Xx2 ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(65,plain,
( ( ! [Xx: a,Xy1: $i,Xy2: $i] :
( ~ ( f @ Xx @ Xy1 )
| ~ ( f @ Xx @ Xy2 )
| ( cS @ Xy1 @ Xy2 ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(66,plain,
( ( ! [Xx: a] : ( f @ Xx @ ( sK8_Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(67,plain,
( ( ! [Xx: a] : ( cR @ Xx @ Xx ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(68,plain,
( ( ! [Xu: a,Xv: a,Xw: a] :
( ~ ( cR @ Xu @ Xv )
| ~ ( cR @ Xw @ Xv )
| ( cR @ Xu @ Xw ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(69,plain,
( ( ( ! [SY28: a] :
~ ( f @ SY28 @ sK3_Xy )
| ( f @ sK4_SY26 @ sK3_Xy ) )
& ( ( cR @ sK4_SY26 @ z )
| ( f @ sK4_SY26 @ sK3_Xy ) )
& ( ! [SY29: a] :
~ ( f @ SY29 @ sK3_Xy )
| ( f @ sK5_SY30 @ sK3_Xy ) )
& ( ( cR @ sK5_SY30 @ z )
| ( f @ sK5_SY30 @ sK3_Xy ) )
& ~ ( cR @ sK4_SY26 @ sK5_SY30 ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(70,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy )
| ( f @ sK4_SY26 @ sK3_Xy ) )
| ~ ( ( cR @ sK4_SY26 @ z )
| ( f @ sK4_SY26 @ sK3_Xy ) ) )
| ~ ~ ( ~ ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy )
| ( f @ sK5_SY30 @ sK3_Xy ) )
| ~ ( ( cR @ sK5_SY30 @ z )
| ( f @ sK5_SY30 @ sK3_Xy ) ) ) )
| ~ ~ ( cR @ sK4_SY26 @ sK5_SY30 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(71,plain,
! [SV14: a] :
( ( ! [SY47: a] :
( ! [SY48: $i] :
( ~ ( f @ SV14 @ SY48 )
| ~ ( f @ SY47 @ SY48 ) )
| ( cR @ SV14 @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(72,plain,
! [SV15: a] :
( ( ! [SY49: $i,SY50: $i] :
( ~ ( f @ SV15 @ SY49 )
| ~ ( f @ SV15 @ SY50 )
| ( cS @ SY49 @ SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(73,plain,
! [SV16: a] :
( ( f @ SV16 @ ( sK8_Xy @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(74,plain,
! [SV17: a] :
( ( cR @ SV17 @ SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(75,plain,
! [SV18: a] :
( ( ! [SY51: a,SY52: a] :
( ~ ( cR @ SV18 @ SY51 )
| ~ ( cR @ SY52 @ SY51 )
| ( cR @ SV18 @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(76,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy )
| ( f @ sK4_SY26 @ sK3_Xy ) )
| ~ ( ( cR @ sK4_SY26 @ z )
| ( f @ sK4_SY26 @ sK3_Xy ) ) )
| ~ ~ ( ~ ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy )
| ( f @ sK5_SY30 @ sK3_Xy ) )
| ~ ( ( cR @ sK5_SY30 @ z )
| ( f @ sK5_SY30 @ sK3_Xy ) ) ) )
| ~ ~ ( cR @ sK4_SY26 @ sK5_SY30 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(77,plain,
! [SV19: a,SV14: a] :
( ( ! [SY53: $i] :
( ~ ( f @ SV14 @ SY53 )
| ~ ( f @ SV19 @ SY53 ) )
| ( cR @ SV14 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(78,plain,
! [SV20: $i,SV15: a] :
( ( ! [SY54: $i] :
( ~ ( f @ SV15 @ SV20 )
| ~ ( f @ SV15 @ SY54 )
| ( cS @ SV20 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(79,plain,
! [SV21: a,SV18: a] :
( ( ! [SY55: a] :
( ~ ( cR @ SV18 @ SV21 )
| ~ ( cR @ SY55 @ SV21 )
| ( cR @ SV18 @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(80,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy )
| ( f @ sK4_SY26 @ sK3_Xy ) )
| ~ ( ( cR @ sK4_SY26 @ z )
| ( f @ sK4_SY26 @ sK3_Xy ) ) )
| ~ ~ ( ~ ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy )
| ( f @ sK5_SY30 @ sK3_Xy ) )
| ~ ( ( cR @ sK5_SY30 @ z )
| ( f @ sK5_SY30 @ sK3_Xy ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(81,plain,
( ( ~ ~ ( cR @ sK4_SY26 @ sK5_SY30 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(82,plain,
! [SV19: a,SV14: a] :
( ( ( ! [SY53: $i] :
( ~ ( f @ SV14 @ SY53 )
| ~ ( f @ SV19 @ SY53 ) ) )
= $true )
| ( ( cR @ SV14 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(83,plain,
! [SV22: $i,SV20: $i,SV15: a] :
( ( ~ ( f @ SV15 @ SV20 )
| ~ ( f @ SV15 @ SV22 )
| ( cS @ SV20 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(84,plain,
! [SV23: a,SV21: a,SV18: a] :
( ( ~ ( cR @ SV18 @ SV21 )
| ~ ( cR @ SV23 @ SV21 )
| ( cR @ SV18 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(85,plain,
( ( ~ ( ~ ~ ( ~ ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy )
| ( f @ sK4_SY26 @ sK3_Xy ) )
| ~ ( ( cR @ sK4_SY26 @ z )
| ( f @ sK4_SY26 @ sK3_Xy ) ) )
| ~ ~ ( ~ ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy )
| ( f @ sK5_SY30 @ sK3_Xy ) )
| ~ ( ( cR @ sK5_SY30 @ z )
| ( f @ sK5_SY30 @ sK3_Xy ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(86,plain,
( ( ~ ( cR @ sK4_SY26 @ sK5_SY30 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(87,plain,
! [SV19: a,SV24: $i,SV14: a] :
( ( ( ~ ( f @ SV14 @ SV24 )
| ~ ( f @ SV19 @ SV24 ) )
= $true )
| ( ( cR @ SV14 @ SV19 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(88,plain,
! [SV22: $i,SV20: $i,SV15: a] :
( ( ( ~ ( f @ SV15 @ SV20 )
| ~ ( f @ SV15 @ SV22 ) )
= $true )
| ( ( cS @ SV20 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(89,plain,
! [SV23: a,SV21: a,SV18: a] :
( ( ( ~ ( cR @ SV18 @ SV21 )
| ~ ( cR @ SV23 @ SV21 ) )
= $true )
| ( ( cR @ SV18 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(90,plain,
( ( ~ ~ ( ~ ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy )
| ( f @ sK4_SY26 @ sK3_Xy ) )
| ~ ( ( cR @ sK4_SY26 @ z )
| ( f @ sK4_SY26 @ sK3_Xy ) ) )
| ~ ~ ( ~ ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy )
| ( f @ sK5_SY30 @ sK3_Xy ) )
| ~ ( ( cR @ sK5_SY30 @ z )
| ( f @ sK5_SY30 @ sK3_Xy ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(91,plain,
( ( cR @ sK4_SY26 @ sK5_SY30 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(92,plain,
! [SV19: a,SV24: $i,SV14: a] :
( ( ( ~ ( f @ SV14 @ SV24 ) )
= $true )
| ( ( ~ ( f @ SV19 @ SV24 ) )
= $true )
| ( ( cR @ SV14 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(93,plain,
! [SV22: $i,SV20: $i,SV15: a] :
( ( ( ~ ( f @ SV15 @ SV20 ) )
= $true )
| ( ( ~ ( f @ SV15 @ SV22 ) )
= $true )
| ( ( cS @ SV20 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(94,plain,
! [SV23: a,SV21: a,SV18: a] :
( ( ( ~ ( cR @ SV18 @ SV21 ) )
= $true )
| ( ( ~ ( cR @ SV23 @ SV21 ) )
= $true )
| ( ( cR @ SV18 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(95,plain,
( ( ~ ~ ( ~ ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy )
| ( f @ sK4_SY26 @ sK3_Xy ) )
| ~ ( ( cR @ sK4_SY26 @ z )
| ( f @ sK4_SY26 @ sK3_Xy ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(96,plain,
( ( ~ ~ ( ~ ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy )
| ( f @ sK5_SY30 @ sK3_Xy ) )
| ~ ( ( cR @ sK5_SY30 @ z )
| ( f @ sK5_SY30 @ sK3_Xy ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(97,plain,
! [SV19: a,SV24: $i,SV14: a] :
( ( ( f @ SV14 @ SV24 )
= $false )
| ( ( ~ ( f @ SV19 @ SV24 ) )
= $true )
| ( ( cR @ SV14 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(98,plain,
! [SV22: $i,SV20: $i,SV15: a] :
( ( ( f @ SV15 @ SV20 )
= $false )
| ( ( ~ ( f @ SV15 @ SV22 ) )
= $true )
| ( ( cS @ SV20 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(99,plain,
! [SV23: a,SV21: a,SV18: a] :
( ( ( cR @ SV18 @ SV21 )
= $false )
| ( ( ~ ( cR @ SV23 @ SV21 ) )
= $true )
| ( ( cR @ SV18 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(100,plain,
( ( ~ ( ~ ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy )
| ( f @ sK4_SY26 @ sK3_Xy ) )
| ~ ( ( cR @ sK4_SY26 @ z )
| ( f @ sK4_SY26 @ sK3_Xy ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(101,plain,
( ( ~ ( ~ ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy )
| ( f @ sK5_SY30 @ sK3_Xy ) )
| ~ ( ( cR @ sK5_SY30 @ z )
| ( f @ sK5_SY30 @ sK3_Xy ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(102,plain,
! [SV14: a,SV24: $i,SV19: a] :
( ( ( f @ SV19 @ SV24 )
= $false )
| ( ( f @ SV14 @ SV24 )
= $false )
| ( ( cR @ SV14 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(103,plain,
! [SV20: $i,SV22: $i,SV15: a] :
( ( ( f @ SV15 @ SV22 )
= $false )
| ( ( f @ SV15 @ SV20 )
= $false )
| ( ( cS @ SV20 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(104,plain,
! [SV18: a,SV21: a,SV23: a] :
( ( ( cR @ SV23 @ SV21 )
= $false )
| ( ( cR @ SV18 @ SV21 )
= $false )
| ( ( cR @ SV18 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(105,plain,
( ( ~ ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy )
| ( f @ sK4_SY26 @ sK3_Xy ) )
| ~ ( ( cR @ sK4_SY26 @ z )
| ( f @ sK4_SY26 @ sK3_Xy ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(106,plain,
( ( ~ ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy )
| ( f @ sK5_SY30 @ sK3_Xy ) )
| ~ ( ( cR @ sK5_SY30 @ z )
| ( f @ sK5_SY30 @ sK3_Xy ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(107,plain,
( ( ~ ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy )
| ( f @ sK4_SY26 @ sK3_Xy ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(108,plain,
( ( ~ ( ( cR @ sK4_SY26 @ z )
| ( f @ sK4_SY26 @ sK3_Xy ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(109,plain,
( ( ~ ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy )
| ( f @ sK5_SY30 @ sK3_Xy ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(110,plain,
( ( ~ ( ( cR @ sK5_SY30 @ z )
| ( f @ sK5_SY30 @ sK3_Xy ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(111,plain,
( ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy )
| ( f @ sK4_SY26 @ sK3_Xy ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(112,plain,
( ( ( cR @ sK4_SY26 @ z )
| ( f @ sK4_SY26 @ sK3_Xy ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(113,plain,
( ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy )
| ( f @ sK5_SY30 @ sK3_Xy ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(114,plain,
( ( ( cR @ sK5_SY30 @ z )
| ( f @ sK5_SY30 @ sK3_Xy ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(115,plain,
( ( ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy ) )
= $true )
| ( ( f @ sK4_SY26 @ sK3_Xy )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(116,plain,
( ( ( cR @ sK4_SY26 @ z )
= $true )
| ( ( f @ sK4_SY26 @ sK3_Xy )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(117,plain,
( ( ( ! [SX0: a] :
~ ( f @ SX0 @ sK3_Xy ) )
= $true )
| ( ( f @ sK5_SY30 @ sK3_Xy )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(118,plain,
( ( ( cR @ sK5_SY30 @ z )
= $true )
| ( ( f @ sK5_SY30 @ sK3_Xy )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(119,plain,
! [SV25: a] :
( ( ( ~ ( f @ SV25 @ sK3_Xy ) )
= $true )
| ( ( f @ sK4_SY26 @ sK3_Xy )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(120,plain,
! [SV26: a] :
( ( ( ~ ( f @ SV26 @ sK3_Xy ) )
= $true )
| ( ( f @ sK5_SY30 @ sK3_Xy )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(121,plain,
! [SV25: a] :
( ( ( f @ SV25 @ sK3_Xy )
= $false )
| ( ( f @ sK4_SY26 @ sK3_Xy )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(122,plain,
! [SV26: a] :
( ( ( f @ SV26 @ sK3_Xy )
= $false )
| ( ( f @ sK5_SY30 @ sK3_Xy )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(123,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[73,122,121,118,116,104,103,102,91,74]) ).
thf(124,plain,
( ( ! [Xx1: a,Xx2: a] :
( ! [Xy: $i] :
( ~ ( f @ Xx1 @ Xy )
| ~ ( f @ Xx2 @ Xy ) )
| ( cR @ Xx1 @ Xx2 ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(125,plain,
( ( ! [Xx: a,Xy1: $i,Xy2: $i] :
( ~ ( f @ Xx @ Xy1 )
| ~ ( f @ Xx @ Xy2 )
| ( cS @ Xy1 @ Xy2 ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(126,plain,
( ( ! [Xx: a] : ( f @ Xx @ ( sK8_Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(127,plain,
( ( ! [Xx: a] : ( cR @ Xx @ Xx ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(128,plain,
( ( ! [Xu: a,Xv: a,Xw: a] :
( ~ ( cR @ Xu @ Xv )
| ~ ( cR @ Xw @ Xv )
| ( cR @ Xu @ Xw ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(129,plain,
( ( ( ( f @ sK7_SY35 @ sK6_Xy )
| ! [Xx: a] :
~ ( cR @ Xx @ z ) )
& ! [SY37: a] :
~ ( f @ SY37 @ sK6_Xy ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(130,plain,
( ( ~ ( ~ ( ( f @ sK7_SY35 @ sK6_Xy )
| ! [SX0: a] :
~ ( cR @ SX0 @ z ) )
| ~ ! [SX0: a] :
~ ( f @ SX0 @ sK6_Xy ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(131,plain,
! [SV27: a] :
( ( ! [SY56: a] :
( ! [SY57: $i] :
( ~ ( f @ SV27 @ SY57 )
| ~ ( f @ SY56 @ SY57 ) )
| ( cR @ SV27 @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(132,plain,
! [SV28: a] :
( ( ! [SY58: $i,SY59: $i] :
( ~ ( f @ SV28 @ SY58 )
| ~ ( f @ SV28 @ SY59 )
| ( cS @ SY58 @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(133,plain,
! [SV29: a] :
( ( f @ SV29 @ ( sK8_Xy @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(134,plain,
! [SV30: a] :
( ( cR @ SV30 @ SV30 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(135,plain,
! [SV31: a] :
( ( ! [SY60: a,SY61: a] :
( ~ ( cR @ SV31 @ SY60 )
| ~ ( cR @ SY61 @ SY60 )
| ( cR @ SV31 @ SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(136,plain,
( ( ~ ( ( f @ sK7_SY35 @ sK6_Xy )
| ! [SX0: a] :
~ ( cR @ SX0 @ z ) )
| ~ ! [SX0: a] :
~ ( f @ SX0 @ sK6_Xy ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(137,plain,
! [SV32: a,SV27: a] :
( ( ! [SY62: $i] :
( ~ ( f @ SV27 @ SY62 )
| ~ ( f @ SV32 @ SY62 ) )
| ( cR @ SV27 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(138,plain,
! [SV33: $i,SV28: a] :
( ( ! [SY63: $i] :
( ~ ( f @ SV28 @ SV33 )
| ~ ( f @ SV28 @ SY63 )
| ( cS @ SV33 @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(139,plain,
! [SV34: a,SV31: a] :
( ( ! [SY64: a] :
( ~ ( cR @ SV31 @ SV34 )
| ~ ( cR @ SY64 @ SV34 )
| ( cR @ SV31 @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(140,plain,
( ( ~ ( ( f @ sK7_SY35 @ sK6_Xy )
| ! [SX0: a] :
~ ( cR @ SX0 @ z ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(141,plain,
( ( ~ ! [SX0: a] :
~ ( f @ SX0 @ sK6_Xy ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(142,plain,
! [SV32: a,SV27: a] :
( ( ( ! [SY62: $i] :
( ~ ( f @ SV27 @ SY62 )
| ~ ( f @ SV32 @ SY62 ) ) )
= $true )
| ( ( cR @ SV27 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(143,plain,
! [SV35: $i,SV33: $i,SV28: a] :
( ( ~ ( f @ SV28 @ SV33 )
| ~ ( f @ SV28 @ SV35 )
| ( cS @ SV33 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(144,plain,
! [SV36: a,SV34: a,SV31: a] :
( ( ~ ( cR @ SV31 @ SV34 )
| ~ ( cR @ SV36 @ SV34 )
| ( cR @ SV31 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(145,plain,
( ( ( f @ sK7_SY35 @ sK6_Xy )
| ! [SX0: a] :
~ ( cR @ SX0 @ z ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(146,plain,
( ( ! [SX0: a] :
~ ( f @ SX0 @ sK6_Xy ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(147,plain,
! [SV32: a,SV37: $i,SV27: a] :
( ( ( ~ ( f @ SV27 @ SV37 )
| ~ ( f @ SV32 @ SV37 ) )
= $true )
| ( ( cR @ SV27 @ SV32 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(148,plain,
! [SV35: $i,SV33: $i,SV28: a] :
( ( ( ~ ( f @ SV28 @ SV33 )
| ~ ( f @ SV28 @ SV35 ) )
= $true )
| ( ( cS @ SV33 @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(149,plain,
! [SV36: a,SV34: a,SV31: a] :
( ( ( ~ ( cR @ SV31 @ SV34 )
| ~ ( cR @ SV36 @ SV34 ) )
= $true )
| ( ( cR @ SV31 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(150,plain,
( ( ( f @ sK7_SY35 @ sK6_Xy )
= $true )
| ( ( ! [SX0: a] :
~ ( cR @ SX0 @ z ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(151,plain,
! [SV38: a] :
( ( ~ ( f @ SV38 @ sK6_Xy ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(152,plain,
! [SV32: a,SV37: $i,SV27: a] :
( ( ( ~ ( f @ SV27 @ SV37 ) )
= $true )
| ( ( ~ ( f @ SV32 @ SV37 ) )
= $true )
| ( ( cR @ SV27 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(153,plain,
! [SV35: $i,SV33: $i,SV28: a] :
( ( ( ~ ( f @ SV28 @ SV33 ) )
= $true )
| ( ( ~ ( f @ SV28 @ SV35 ) )
= $true )
| ( ( cS @ SV33 @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(154,plain,
! [SV36: a,SV34: a,SV31: a] :
( ( ( ~ ( cR @ SV31 @ SV34 ) )
= $true )
| ( ( ~ ( cR @ SV36 @ SV34 ) )
= $true )
| ( ( cR @ SV31 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(155,plain,
! [SV39: a] :
( ( ( ~ ( cR @ SV39 @ z ) )
= $true )
| ( ( f @ sK7_SY35 @ sK6_Xy )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(156,plain,
! [SV38: a] :
( ( f @ SV38 @ sK6_Xy )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(157,plain,
! [SV32: a,SV37: $i,SV27: a] :
( ( ( f @ SV27 @ SV37 )
= $false )
| ( ( ~ ( f @ SV32 @ SV37 ) )
= $true )
| ( ( cR @ SV27 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(158,plain,
! [SV35: $i,SV33: $i,SV28: a] :
( ( ( f @ SV28 @ SV33 )
= $false )
| ( ( ~ ( f @ SV28 @ SV35 ) )
= $true )
| ( ( cS @ SV33 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(159,plain,
! [SV36: a,SV34: a,SV31: a] :
( ( ( cR @ SV31 @ SV34 )
= $false )
| ( ( ~ ( cR @ SV36 @ SV34 ) )
= $true )
| ( ( cR @ SV31 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(160,plain,
! [SV39: a] :
( ( ( cR @ SV39 @ z )
= $false )
| ( ( f @ sK7_SY35 @ sK6_Xy )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(161,plain,
! [SV27: a,SV37: $i,SV32: a] :
( ( ( f @ SV32 @ SV37 )
= $false )
| ( ( f @ SV27 @ SV37 )
= $false )
| ( ( cR @ SV27 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(162,plain,
! [SV33: $i,SV35: $i,SV28: a] :
( ( ( f @ SV28 @ SV35 )
= $false )
| ( ( f @ SV28 @ SV33 )
= $false )
| ( ( cS @ SV33 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(163,plain,
! [SV31: a,SV34: a,SV36: a] :
( ( ( cR @ SV36 @ SV34 )
= $false )
| ( ( cR @ SV31 @ SV34 )
= $false )
| ( ( cR @ SV31 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(164,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[133,163,162,161,160,156,134]) ).
thf(165,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[164,63,123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEV107^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 27 21:07:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 0
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 (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)........
% 0.18/0.47
% 0.18/0.47 ********************************
% 0.18/0.47 * All subproblems solved! *
% 0.18/0.47 ********************************
% 0.18/0.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:164,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.48
% 0.18/0.48 %**** Beginning of derivation protocol ****
% 0.18/0.48 % SZS output start CNFRefutation
% See solution above
% 0.18/0.48
% 0.18/0.48 %**** End of derivation protocol ****
% 0.18/0.48 %**** no. of clauses in derivation: 165 ****
% 0.18/0.48 %**** clause counter: 164 ****
% 0.18/0.48
% 0.18/0.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:164,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------