%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP009^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:18 AM UTC 2026
% Result : Theorem 42.80s 16.02s
% Output : Refutation 44.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 67 ( 28 unt; 0 typ; 8 def)
% Number of atoms : 365 ( 94 equ; 0 cnn)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1510 ( 60 ~; 47 |; 44 &;1338 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 248 ( 248 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 2 con; 0-8 aty)
% Number of variables : 270 ( 52 ^; 210 !; 0 ?; 270 :)
% ( 0 !>; 0 ?*; 0 @-; 8 @+)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(skt1_type,type,
skt1: $tType ).
thf(skt2_type,type,
skt2: $tType ).
thf(skt3_type,type,
skt3: $tType ).
thf(skt4_type,type,
skt4: $tType ).
thf(c_2Equotient_2E_2D_2D_3E_decl,type,
c_2Equotient_2E_2D_2D_3E:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > TB ) > ( TC > TA ) > ( TB > TC ) > TD > TA ) ).
thf(c_2Equotient_2E_3D_3D_3D_3E_decl,type,
c_2Equotient_2E_3D_3D_3D_3E:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > ( TA > TA > $o ) > ( TB > TA ) > ( TB > TA ) > $o ) ).
thf(c_2Equotient_2EQUOTIENT_decl,type,
c_2Equotient_2EQUOTIENT:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > ( TB > TA ) > ( TA > TB ) > $o ) ).
thf(c_2Ecombin_2EW_decl,type,
c_2Ecombin_2EW:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > TA ) > TB > TA ) ).
thf(c_2Equotient_2Erespects_decl,type,
c_2Equotient_2Erespects:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > TA ) > TB > TA ) ).
thf(sk1_decl,type,
sk1: skt1 > skt1 > $o ).
thf(sk2_decl,type,
sk2: skt1 > skt3 ).
thf(sk3_decl,type,
sk3: skt3 > skt1 ).
thf(sk4_decl,type,
sk4: skt2 > skt2 > $o ).
thf(sk5_decl,type,
sk5: skt2 > skt4 ).
thf(sk6_decl,type,
sk6: skt4 > skt2 ).
thf(sk7_decl,type,
sk7: skt1 > skt2 ).
thf(sk8_decl,type,
sk8: skt1 > skt2 ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1 > skt1 > $o] :
~ ! [B: skt1 > skt3,C: skt3 > skt1] :
( ( c_2Equotient_2EQUOTIENT @ skt1 @ skt3 @ A @ B @ C )
=> ! [D: skt2 > skt2 > $o,E: skt2 > skt4,F: skt4 > skt2] :
( ( c_2Equotient_2EQUOTIENT @ skt2 @ skt4 @ D @ E @ F )
=> ! [G: skt1 > skt2,H: skt1 > skt2] :
( ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ A @ D @ G @ H )
= ( ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ A @ D ) @ G )
& ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ A @ D ) @ H )
& ( ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ C @ E @ G )
= ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ C @ E @ H ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt1 > skt3] :
~ ! [B: skt3 > skt1] :
( ( c_2Equotient_2EQUOTIENT @ skt1 @ skt3 @ sk1 @ A @ B )
=> ! [C: skt2 > skt2 > $o,D: skt2 > skt4,E: skt4 > skt2] :
( ( c_2Equotient_2EQUOTIENT @ skt2 @ skt4 @ C @ D @ E )
=> ! [F: skt1 > skt2,G: skt1 > skt2] :
( ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ C @ F @ G )
= ( ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ C ) @ F )
& ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ C ) @ G )
& ( ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ B @ D @ F )
= ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ B @ D @ G ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: skt3 > skt1] :
~ ( ( c_2Equotient_2EQUOTIENT @ skt1 @ skt3 @ sk1 @ sk2 @ A )
=> ! [B: skt2 > skt2 > $o,C: skt2 > skt4,D: skt4 > skt2] :
( ( c_2Equotient_2EQUOTIENT @ skt2 @ skt4 @ B @ C @ D )
=> ! [E: skt1 > skt2,F: skt1 > skt2] :
( ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ B @ E @ F )
= ( ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ B ) @ E )
& ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ B ) @ F )
& ( ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ A @ C @ E )
= ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ A @ C @ F ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: skt2 > skt2 > $o] :
~ ! [B: skt2 > skt4,C: skt4 > skt2] :
( ( c_2Equotient_2EQUOTIENT @ skt2 @ skt4 @ A @ B @ C )
=> ! [D: skt1 > skt2,E: skt1 > skt2] :
( ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ A @ D @ E )
= ( ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ A ) @ D )
& ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ A ) @ E )
& ( ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ B @ D )
= ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ B @ E ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: skt2 > skt4] :
~ ! [B: skt4 > skt2] :
( ( c_2Equotient_2EQUOTIENT @ skt2 @ skt4 @ sk4 @ A @ B )
=> ! [C: skt1 > skt2,D: skt1 > skt2] :
( ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ C @ D )
= ( ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ C )
& ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ D )
& ( ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ A @ C )
= ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ A @ D ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: skt4 > skt2] :
~ ( ( c_2Equotient_2EQUOTIENT @ skt2 @ skt4 @ sk4 @ sk5 @ A )
=> ! [B: skt1 > skt2,C: skt1 > skt2] :
( ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ B @ C )
= ( ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ B )
& ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ C )
& ( ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ B )
= ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ C ) ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: skt1 > skt2] :
~ ! [B: skt1 > skt2] :
( ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ A @ B )
= ( ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ A )
& ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ B )
& ( ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ A )
= ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ B ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: skt1 > skt2] :
( ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ A )
!= ( ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk7 )
& ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ A )
& ( ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk7 )
= ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ A ) ) ) ) ) ) ).
thf(1,conjecture,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TD > $o,B: TD > TB,C: TB > TD] :
( ( c_2Equotient_2EQUOTIENT @ TD @ TB @ A @ B @ C )
=> ! [D: TC > TC > $o,E: TC > TA,F: TA > TC] :
( ( c_2Equotient_2EQUOTIENT @ TC @ TA @ D @ E @ F )
=> ! [G: TD > TC,H: TD > TC] :
( ( c_2Equotient_2E_3D_3D_3D_3E @ TD @ TC @ A @ D @ G @ H )
= ( ( c_2Equotient_2Erespects @ ( TD > TC ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ TD @ TC @ A @ D ) @ G )
& ( c_2Equotient_2Erespects @ ( TD > TC ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ TD @ TC @ A @ D ) @ H )
& ( ( c_2Equotient_2E_2D_2D_3E @ TB @ TC @ TD @ TA @ C @ E @ G )
= ( c_2Equotient_2E_2D_2D_3E @ TB @ TC @ TD @ TA @ C @ E @ H ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EFUN__REL__EQ__REL) ).
thf(2,negated_conjecture,
~ ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TD > $o,B: TD > TB,C: TB > TD] :
( ( c_2Equotient_2EQUOTIENT @ TD @ TB @ A @ B @ C )
=> ! [D: TC > TC > $o,E: TC > TA,F: TA > TC] :
( ( c_2Equotient_2EQUOTIENT @ TC @ TA @ D @ E @ F )
=> ! [G: TD > TC,H: TD > TC] :
( ( c_2Equotient_2E_3D_3D_3D_3E @ TD @ TC @ A @ D @ G @ H )
= ( ( c_2Equotient_2Erespects @ ( TD > TC ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ TD @ TC @ A @ D ) @ G )
& ( c_2Equotient_2Erespects @ ( TD > TC ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ TD @ TC @ A @ D ) @ H )
& ( ( c_2Equotient_2E_2D_2D_3E @ TB @ TC @ TD @ TA @ C @ E @ G )
= ( c_2Equotient_2E_2D_2D_3E @ TB @ TC @ TD @ TA @ C @ E @ H ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TD > $o,B: TD > TB,C: TB > TD] :
( ( c_2Equotient_2EQUOTIENT @ TD @ TB @ A @ B @ C )
=> ! [D: TC > TC > $o,E: TC > TA,F: TA > TC] :
( ( c_2Equotient_2EQUOTIENT @ TC @ TA @ D @ E @ F )
=> ! [G: TD > TC,H: TD > TC] :
( ( c_2Equotient_2E_3D_3D_3D_3E @ TD @ TC @ A @ D @ G @ H )
= ( ( c_2Equotient_2Erespects @ ( TD > TC ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ TD @ TC @ A @ D ) @ G )
& ( c_2Equotient_2Erespects @ ( TD > TC ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ TD @ TC @ A @ D ) @ H )
& ( ( c_2Equotient_2E_2D_2D_3E @ TB @ TC @ TD @ TA @ C @ E @ G )
= ( c_2Equotient_2E_2D_2D_3E @ TB @ TC @ TD @ TA @ C @ E @ H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
( ( c_2Equotient_2EQUOTIENT @ skt1 @ skt3 @ sk1 @ sk2 @ sk3 )
& ( c_2Equotient_2EQUOTIENT @ skt2 @ skt4 @ sk4 @ sk5 @ sk6 )
& ( ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 )
!= ( ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk7 )
& ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk8 )
& ( ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk7 )
= ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk8 ) ) ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(10,plain,
c_2Equotient_2EQUOTIENT @ skt2 @ skt4 @ sk4 @ sk5 @ sk6,
inference(cnfConj,[status(thm)],[8]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType] :
( ( c_2Equotient_2Erespects @ TB @ TA )
= ( c_2Ecombin_2EW @ TB @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2Erespects__def) ).
thf(21,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Equotient_2Erespects @ TB @ TA )
= ( c_2Ecombin_2EW @ TB @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Equotient_2Erespects @ TA @ TB )
= ( c_2Ecombin_2EW @ TA @ TB ) ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Equotient_2Erespects @ TA @ TB )
= ( c_2Ecombin_2EW @ TA @ TB ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(24,plain,
! [TA: $tType,TB: $tType,A: TA > TA > TB] :
( ( c_2Equotient_2Erespects @ TA @ TB @ A )
= ( c_2Ecombin_2EW @ TA @ TB @ A ) ),
inference(func_ext,[status(esa)],[23]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > TA,B: TB] :
( ( c_2Ecombin_2EW @ TB @ TA @ A @ B )
= ( A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecombin_2EW__THM) ).
thf(13,plain,
! [TA: $tType,TB: $tType,A: TB > TB > TA,B: TB] :
( ( c_2Ecombin_2EW @ TB @ TA @ A @ B )
= ( A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
! [TA: $tType,TB: $tType,B: TA,A: TA > TA > TB] :
( ( c_2Ecombin_2EW @ TA @ TB @ A @ B )
= ( A @ B @ B ) ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
! [TA: $tType,TB: $tType,B: TA,A: TA > TA > TB] :
( ( c_2Ecombin_2EW @ TA @ TB @ A @ B )
= ( A @ B @ B ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(159,plain,
! [TA: $tType,TB: $tType,TC: $tType,B: TC,A: TC > TC > ( TA > TA > TB ) > TA > TB] :
( ( ( c_2Ecombin_2EW @ TA @ TB )
= ( c_2Ecombin_2EW @ TC @ ( ( TA > TA > TB ) > TA > TB ) @ A @ B ) )
| ( ( c_2Equotient_2Erespects @ TA @ TB )
!= ( A @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[23,15]) ).
thf(203,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC] :
( ( c_2Ecombin_2EW @ TA @ TB )
= ( c_2Ecombin_2EW @ TC @ ( ( TA > TA > TB ) > TA > TB )
@ ^ [B: TC,C: TC] : ( c_2Equotient_2Erespects @ TA @ TB )
@ A ) ),
inference(pre_uni,[status(thm)],[159:[bind(A,$thf( ^ [C: TC] : ^ [D: TC] : ( c_2Equotient_2Erespects @ TA @ TB ) )),bind(B,$thf( B ))]]) ).
thf(261,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC] :
( ( c_2Ecombin_2EW @ TA @ TB )
= ( c_2Ecombin_2EW @ TC @ ( ( TA > TA > TB ) > TA > TB )
@ ^ [B: TC,C: TC] : ( c_2Equotient_2Erespects @ TA @ TB )
@ A ) ),
inference(simp,[status(thm)],[203]) ).
thf(9,plain,
c_2Equotient_2EQUOTIENT @ skt1 @ skt3 @ sk1 @ sk2 @ sk3,
inference(cnfConj,[status(thm)],[8]) ).
thf(89,plain,
! [TA: $tType,B: TA,A: TA > TA > skt2 > skt2 > $o] :
( ( c_2Equotient_2EQUOTIENT @ skt2 @ skt4 @ ( c_2Ecombin_2EW @ TA @ ( skt2 > skt2 > $o ) @ A @ B ) @ sk5 @ sk6 )
| ( ( A @ B @ B )
!= sk4 ) ),
inference(paramod_ordered,[status(thm)],[15,10]) ).
thf(186,plain,
! [TA: $tType,A: TA] :
( c_2Equotient_2EQUOTIENT @ skt2 @ skt4
@ ( c_2Ecombin_2EW @ TA @ ( skt2 > skt2 > $o )
@ ^ [B: TA,C: TA] : sk4
@ A )
@ sk5
@ sk6 ),
inference(pre_uni,[status(thm)],[89:[bind(A,$thf( ^ [C: TA] : ^ [D: TA] : sk4 )),bind(B,$thf( B ))]]) ).
thf(244,plain,
! [TA: $tType,A: TA] :
( c_2Equotient_2EQUOTIENT @ skt2 @ skt4
@ ( c_2Ecombin_2EW @ TA @ ( skt2 > skt2 > $o )
@ ^ [B: TA,C: TA] : sk4
@ A )
@ sk5
@ sk6 ),
inference(simp,[status(thm)],[186]) ).
thf(11,plain,
( ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 )
!= ( ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk7 )
& ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk8 )
& ( ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk7 )
= ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk8 ) ) ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(12,plain,
( ( ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk7 )
& ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk8 )
& ( ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk7 )
= ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk8 ) ) )
!= ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(29,plain,
( ( ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk7 )
& ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk8 )
& ( ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk7 )
= ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk8 ) ) )
| ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(32,plain,
( ( ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk7 )
| ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 ) )
& ( ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk8 )
| ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 ) )
& ( ( ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk7 )
= ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk8 ) )
| ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(34,plain,
( ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk8 )
| ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 ) ),
inference(cnfConj,[status(thm)],[32]) ).
thf(28,plain,
( ~ ( ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk7 )
& ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk8 )
& ( ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk7 )
= ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk8 ) ) )
| ~ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(30,plain,
( ~ ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk7 )
| ~ ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk8 )
| ( ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk7 )
!= ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk8 ) )
| ~ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 ) ),
inference(cnf,[status(esa)],[28]) ).
thf(31,plain,
( ( ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk8 )
!= ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk7 ) )
| ~ ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk7 )
| ~ ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk8 )
| ~ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(37,plain,
( ( ( ^ [A: skt3] : sk3 )
!= ( ^ [A: skt3] : sk3 ) )
| ( ( ^ [A: skt3] : sk5 )
!= ( ^ [A: skt3] : sk5 ) )
| ( ( ^ [A: skt3] : sk8 )
!= ( ^ [A: skt3] : sk7 ) )
| ( ( ^ [A: skt3] : A )
!= ( ^ [A: skt3] : A ) )
| ~ ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk7 )
| ~ ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk8 )
| ~ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 ) ),
inference(simp,[status(thm)],[31]) ).
thf(44,plain,
( ( ( ^ [A: skt3] : sk8 )
!= ( ^ [A: skt3] : sk7 ) )
| ~ ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk7 )
| ~ ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk8 )
| ~ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 ) ),
inference(simp,[status(thm)],[37]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA,C: TA > TB] :
( ( c_2Equotient_2EQUOTIENT @ TB @ TA @ A @ B @ C )
=> ! [D: TB,E: TB] :
( ( A @ D @ E )
= ( ( A @ D @ D )
& ( A @ E @ E )
& ( ( B @ D )
= ( B @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EQUOTIENT__REL) ).
thf(16,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA,C: TA > TB] :
( ( c_2Equotient_2EQUOTIENT @ TB @ TA @ A @ B @ C )
=> ! [D: TB,E: TB] :
( ( A @ D @ E )
= ( ( A @ D @ D )
& ( A @ E @ E )
& ( ( B @ D )
= ( B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,plain,
! [TA: $tType,TB: $tType,E: TA,D: TA,C: TB > TA,B: TA > TB,A: TA > TA > $o] :
( ~ ( c_2Equotient_2EQUOTIENT @ TA @ TB @ A @ B @ C )
| ( ( A @ D @ E )
= ( ( A @ D @ D )
& ( A @ E @ E )
& ( ( B @ D )
= ( B @ E ) ) ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(18,plain,
! [TA: $tType,TB: $tType,E: TA,D: TA,C: TB > TA,B: TA > TB,A: TA > TA > $o] :
( ( ( A @ D @ E )
= ( ( A @ D @ D )
& ( A @ E @ E )
& ( ( B @ D )
= ( B @ E ) ) ) )
| ~ ( c_2Equotient_2EQUOTIENT @ TA @ TB @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(292,plain,
! [TC: $tType,TD: $tType,TE: $tType,A: TE] :
( ( ( c_2Ecombin_2EW @ TE @ ( ( TC > TC > TD ) > TC > TD )
@ ^ [B: TE,C: TE] : ( c_2Ecombin_2EW @ TC @ TD )
@ A )
= ( c_2Ecombin_2EW @ TC @ TD ) )
| ( ( c_2Equotient_2Erespects @ TC @ TD )
!= ( c_2Equotient_2Erespects @ TC @ TD ) ) ),
inference(paramod_ordered,[status(thm)],[23,261]) ).
thf(293,plain,
! [TC: $tType,TD: $tType,TE: $tType,A: TE] :
( ( c_2Ecombin_2EW @ TE @ ( ( TC > TC > TD ) > TC > TD )
@ ^ [B: TE,C: TE] : ( c_2Ecombin_2EW @ TC @ TD )
@ A )
= ( c_2Ecombin_2EW @ TC @ TD ) ),
inference(pattern_uni,[status(thm)],[292:[]]) ).
thf(314,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC] :
( ( c_2Ecombin_2EW @ TC @ ( ( TA > TA > TB ) > TA > TB )
@ ^ [B: TC,C: TC] : ( c_2Ecombin_2EW @ TA @ TB )
@ A )
= ( c_2Ecombin_2EW @ TA @ TB ) ),
inference(simp,[status(thm)],[293]) ).
thf(33,plain,
( ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk7 )
| ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 ) ),
inference(cnfConj,[status(thm)],[32]) ).
thf(110,plain,
! [TA: $tType,B: TA,A: TA > TA > skt3 > skt1] :
( ( c_2Equotient_2EQUOTIENT @ skt1 @ skt3 @ sk1 @ sk2 @ ( c_2Ecombin_2EW @ TA @ ( skt3 > skt1 ) @ A @ B ) )
| ( ( A @ B @ B )
!= sk3 ) ),
inference(paramod_ordered,[status(thm)],[15,9]) ).
thf(177,plain,
! [TA: $tType,A: TA] :
( c_2Equotient_2EQUOTIENT @ skt1 @ skt3 @ sk1 @ sk2
@ ( c_2Ecombin_2EW @ TA @ ( skt3 > skt1 )
@ ^ [B: TA,C: TA] : sk3
@ A ) ),
inference(pre_uni,[status(thm)],[110:[bind(A,$thf( ^ [C: TA] : ^ [D: TA] : sk3 )),bind(B,$thf( B ))]]) ).
thf(236,plain,
! [TA: $tType,A: TA] :
( c_2Equotient_2EQUOTIENT @ skt1 @ skt3 @ sk1 @ sk2
@ ( c_2Ecombin_2EW @ TA @ ( skt3 > skt1 )
@ ^ [B: TA,C: TA] : sk3
@ A ) ),
inference(simp,[status(thm)],[177]) ).
thf(158,plain,
! [TA: $tType,TC: $tType,TD: $tType,B: TA,A: TA > TA > ( TC > TC > TD ) > TC > TD] :
( ( ( c_2Ecombin_2EW @ TA @ ( ( TC > TC > TD ) > TC > TD ) @ A @ B )
= ( c_2Ecombin_2EW @ TC @ TD ) )
| ( ( A @ B @ B )
!= ( c_2Equotient_2Erespects @ TC @ TD ) ) ),
inference(paramod_ordered,[status(thm)],[15,23]) ).
thf(219,plain,
! [TA: $tType,TC: $tType,TD: $tType,A: TA] :
( ( c_2Ecombin_2EW @ TA @ ( ( TC > TC > TD ) > TC > TD )
@ ^ [B: TA,C: TA] : ( c_2Equotient_2Erespects @ TC @ TD )
@ A )
= ( c_2Ecombin_2EW @ TC @ TD ) ),
inference(pre_uni,[status(thm)],[158:[bind(A,$thf( ^ [C: TA] : ^ [D: TA] : ( c_2Equotient_2Erespects @ TC @ TD ) )),bind(B,$thf( B ))]]) ).
thf(277,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA] :
( ( c_2Ecombin_2EW @ TA @ ( ( TB > TB > TC ) > TB > TC )
@ ^ [B: TA,C: TA] : ( c_2Equotient_2Erespects @ TB @ TC )
@ A )
= ( c_2Ecombin_2EW @ TB @ TC ) ),
inference(simp,[status(thm)],[219]) ).
thf(339,plain,
! [TC: $tType,TD: $tType,TE: $tType,A: TC] :
( ( ( c_2Ecombin_2EW @ TC @ ( ( TD > TD > TE ) > TD > TE )
@ ^ [B: TC,C: TC] : ( c_2Ecombin_2EW @ TD @ TE )
@ A )
= ( c_2Ecombin_2EW @ TD @ TE ) )
| ( ( c_2Equotient_2Erespects @ TD @ TE )
!= ( c_2Equotient_2Erespects @ TD @ TE ) ) ),
inference(paramod_ordered,[status(thm)],[23,277]) ).
thf(340,plain,
! [TC: $tType,TD: $tType,TE: $tType,A: TC] :
( ( c_2Ecombin_2EW @ TC @ ( ( TD > TD > TE ) > TD > TE )
@ ^ [B: TC,C: TC] : ( c_2Ecombin_2EW @ TD @ TE )
@ A )
= ( c_2Ecombin_2EW @ TD @ TE ) ),
inference(pattern_uni,[status(thm)],[339:[]]) ).
thf(367,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA] :
( ( c_2Ecombin_2EW @ TA @ ( ( TB > TB > TC ) > TB > TC )
@ ^ [B: TA,C: TA] : ( c_2Ecombin_2EW @ TB @ TC )
@ A )
= ( c_2Ecombin_2EW @ TB @ TC ) ),
inference(simp,[status(thm)],[340]) ).
thf(109,plain,
! [TA: $tType,B: TA,A: TA > TA > skt1 > skt3] :
( ( c_2Equotient_2EQUOTIENT @ skt1 @ skt3 @ sk1 @ ( c_2Ecombin_2EW @ TA @ ( skt1 > skt3 ) @ A @ B ) @ sk3 )
| ( ( A @ B @ B )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[15,9]) ).
thf(193,plain,
! [TA: $tType,A: TA] :
( c_2Equotient_2EQUOTIENT @ skt1 @ skt3 @ sk1
@ ( c_2Ecombin_2EW @ TA @ ( skt1 > skt3 )
@ ^ [B: TA,C: TA] : sk2
@ A )
@ sk3 ),
inference(pre_uni,[status(thm)],[109:[bind(A,$thf( ^ [C: TA] : ^ [D: TA] : sk2 )),bind(B,$thf( B ))]]) ).
thf(251,plain,
! [TA: $tType,A: TA] :
( c_2Equotient_2EQUOTIENT @ skt1 @ skt3 @ sk1
@ ( c_2Ecombin_2EW @ TA @ ( skt1 > skt3 )
@ ^ [B: TA,C: TA] : sk2
@ A )
@ sk3 ),
inference(simp,[status(thm)],[193]) ).
thf(35,plain,
( ( ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk7 )
= ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk8 ) )
| ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 ) ),
inference(cnfConj,[status(thm)],[32]) ).
thf(36,plain,
( ( ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk8 )
= ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk7 ) )
| ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TD > $o,B: TD > TB,C: TB > TD] :
( ( c_2Equotient_2EQUOTIENT @ TD @ TB @ A @ B @ C )
=> ! [D: TC > TC > $o,E: TC > TA,F: TA > TC] :
( ( c_2Equotient_2EQUOTIENT @ TC @ TA @ D @ E @ F )
=> ( c_2Equotient_2EQUOTIENT @ ( TD > TC ) @ ( TB > TA ) @ ( c_2Equotient_2E_3D_3D_3D_3E @ TD @ TC @ A @ D ) @ ( c_2Equotient_2E_2D_2D_3E @ TB @ TC @ TD @ TA @ C @ E ) @ ( c_2Equotient_2E_2D_2D_3E @ TD @ TA @ TB @ TC @ B @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EFUN__QUOTIENT) ).
thf(19,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TD > $o,B: TD > TB,C: TB > TD] :
( ( c_2Equotient_2EQUOTIENT @ TD @ TB @ A @ B @ C )
=> ! [D: TC > TC > $o,E: TC > TA,F: TA > TC] :
( ( c_2Equotient_2EQUOTIENT @ TC @ TA @ D @ E @ F )
=> ( c_2Equotient_2EQUOTIENT @ ( TD > TC ) @ ( TB > TA ) @ ( c_2Equotient_2E_3D_3D_3D_3E @ TD @ TC @ A @ D ) @ ( c_2Equotient_2E_2D_2D_3E @ TB @ TC @ TD @ TA @ C @ E ) @ ( c_2Equotient_2E_2D_2D_3E @ TD @ TA @ TB @ TC @ B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(39,plain,
( ( ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk8 )
!= ( c_2Equotient_2E_2D_2D_3E @ skt3 @ skt2 @ skt1 @ skt4 @ sk3 @ sk5 @ sk7 ) )
| ~ ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk7 )
| ~ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 )
| ( ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk8 )
!= ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk7 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[31]) ).
thf(43,plain,
( ( ( ^ [A: skt3] : sk3 )
!= ( ^ [A: skt3] : sk3 ) )
| ( ( ^ [A: skt3] : sk5 )
!= ( ^ [A: skt3] : sk5 ) )
| ( ( ^ [A: skt3] : sk8 )
!= ( ^ [A: skt3] : sk7 ) )
| ( ( ^ [A: skt3] : A )
!= ( ^ [A: skt3] : A ) )
| ~ ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk7 )
| ~ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 )
| ( ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 )
!= ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[39]) ).
thf(47,plain,
( ( ( ^ [A: skt3] : sk8 )
!= ( ^ [A: skt3] : sk7 ) )
| ~ ( c_2Equotient_2Erespects @ ( skt1 > skt2 ) @ $o @ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 ) @ sk7 )
| ~ ( c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk4 @ sk7 @ sk8 )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[43]) ).
thf(1009,plain,
$false,
inference(e,[status(thm)],[10,24,261,9,13,244,34,44,7,18,314,23,21,33,12,236,367,251,16,31,36,19,47,15,277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP009^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.10 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.23/0.30 % Computer : n026.cluster.edu
% 0.23/0.30 % Model : x86_64 x86_64
% 0.23/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.30 % Memory : 8046.5625MB
% 0.23/0.30 % OS : Linux 6.8.0-71-generic
% 0.23/0.30 % CPULimit : 300
% 0.23/0.30 % WCLimit : 300
% 0.23/0.30 % DateTime : Tue Sep 29 19:27:27 UTC 2026
% 0.23/0.30 % CPUTime :
% 0.23/0.30 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.95/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.42/0.93 % [INFO] Parsing done (150ms).
% 1.42/0.93 % [INFO] Running in sequential loop mode.
% 2.12/1.16 % [INFO] eprover registered as external prover.
% 2.12/1.17 % [INFO] Scanning for conjecture ...
% 2.23/1.25 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.23/1.29 % [INFO] Axiom selection finished. Selected 4 axioms (removed 12 axioms).
% 2.55/1.31 % [INFO] Problem is higher-order (TPTP THF).
% 2.55/1.31 % [INFO] Type checking passed.
% 2.55/1.32 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 42.80/16.01 % External prover 'e' found a proof!
% 42.80/16.01 % [INFO] Killing All external provers ...
% 42.80/16.01 % Time passed: 15572ms (effective reasoning time: 15073ms)
% 42.80/16.01 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 42.80/16.01 % Axioms used in derivation (4): thm_2Equotient_2Erespects__def, thm_2Ecombin_2EW__THM, thm_2Equotient_2EQUOTIENT__REL, thm_2Equotient_2EFUN__QUOTIENT
% 42.80/16.01 % No. of inferences in proof: 59
% 42.80/16.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 15572 ms resp. 15073 ms w/o parsing
% 44.60/16.20 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 44.60/16.20 % [INFO] Killing All external provers ...
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