TSTP Solution File: SWC118+1 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SWC118+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% 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 : 300s
% DateTime : Tue May 21 04:30:55 EDT 2024
% Result : Theorem 7.71s 3.44s
% Output : Refutation 8.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 120
% Syntax : Number of formulae : 218 ( 19 unt; 24 typ; 0 def)
% Number of atoms : 993 ( 204 equ; 0 cnn)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 2387 ( 72 ~; 46 |; 162 &;1516 @)
% ( 26 <=>; 565 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 2 con; 0-2 aty)
% Number of variables : 489 ( 0 ^ 432 !; 57 ?; 489 :)
% Comments :
%------------------------------------------------------------------------------
thf(ssList_type,type,
ssList: $i > $o ).
thf(app_type,type,
app: $i > $i > $i ).
thf(totalorderedP_type,type,
totalorderedP: $i > $o ).
thf(ssItem_type,type,
ssItem: $i > $o ).
thf(cons_type,type,
cons: $i > $i > $i ).
thf(nil_type,type,
nil: $i ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(neq_type,type,
neq: $i > $i > $o ).
thf(segmentP_type,type,
segmentP: $i > $i > $o ).
thf(strictorderedP_type,type,
strictorderedP: $i > $o ).
thf(lt_type,type,
lt: $i > $i > $o ).
thf(frontsegP_type,type,
frontsegP: $i > $i > $o ).
thf(gt_type,type,
gt: $i > $i > $o ).
thf(hd_type,type,
hd: $i > $i ).
thf(cyclefreeP_type,type,
cyclefreeP: $i > $o ).
thf(strictorderP_type,type,
strictorderP: $i > $o ).
thf(duplicatefreeP_type,type,
duplicatefreeP: $i > $o ).
thf(singletonP_type,type,
singletonP: $i > $o ).
thf(memberP_type,type,
memberP: $i > $i > $o ).
thf(tl_type,type,
tl: $i > $i ).
thf(totalorderP_type,type,
totalorderP: $i > $o ).
thf(rearsegP_type,type,
rearsegP: $i > $i > $o ).
thf(equalelemsP_type,type,
equalelemsP: $i > $o ).
thf(geq_type,type,
geq: $i > $i > $o ).
thf(46,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( equalelemsP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73) ).
thf(295,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( equalelemsP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(96,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( memberP @ A @ B )
<=> ? [C: $i] :
( ( ssList @ C )
& ? [D: $i] :
( ( ssList @ D )
& ( ( app @ C @ ( cons @ B @ D ) )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
thf(501,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( ( memberP @ A @ B )
=> ? [C: $i] :
( ( ssList @ C )
& ? [D: $i] :
( ( ssList @ D )
& ( ( app @ C @ ( cons @ B @ D ) )
= A ) ) ) )
& ( ? [C: $i] :
( ( ssList @ C )
& ? [D: $i] :
( ( ssList @ D )
& ( ( app @ C @ ( cons @ B @ D ) )
= A ) ) )
=> ( memberP @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(10,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( hd @ ( cons @ B @ A ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
thf(138,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( hd @ ( cons @ B @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(89,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( lt @ A @ B )
=> ~ ( lt @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax33) ).
thf(481,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( lt @ A @ B )
=> ~ ( lt @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(80,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( equalelemsP @ A )
<=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ( ( ( app @ D @ ( cons @ B @ ( cons @ C @ E ) ) )
= A )
=> ( B = C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax14) ).
thf(440,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( equalelemsP @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ( ( ( app @ D @ ( cons @ B @ ( cons @ C @ E ) ) )
= A )
=> ( B = C ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ( ( ( app @ D @ ( cons @ B @ ( cons @ C @ E ) ) )
= A )
=> ( B = C ) ) ) ) ) )
=> ( equalelemsP @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(26,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( ( gt @ A @ B )
& ( gt @ B @ C ) )
=> ( gt @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax95) ).
thf(202,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( ( gt @ A @ B )
& ( gt @ B @ C ) )
=> ( gt @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(95,axiom,
totalorderP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62) ).
thf(500,plain,
totalorderP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(86,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( segmentP @ A @ B )
& ( segmentP @ B @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax54) ).
thf(472,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( segmentP @ A @ B )
& ( segmentP @ B @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(55,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( segmentP @ A @ B )
<=> ? [C: $i] :
( ( ssList @ C )
& ? [D: $i] :
( ( ssList @ D )
& ( ( app @ ( app @ C @ B ) @ D )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
thf(340,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( segmentP @ A @ B )
=> ? [C: $i] :
( ( ssList @ C )
& ? [D: $i] :
( ( ssList @ D )
& ( ( app @ ( app @ C @ B ) @ D )
= A ) ) ) )
& ( ? [C: $i] :
( ( ssList @ C )
& ? [D: $i] :
( ( ssList @ D )
& ( ( app @ ( app @ C @ B ) @ D )
= A ) ) )
=> ( segmentP @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(74,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( rearsegP @ A @ B )
<=> ? [C: $i] :
( ( ssList @ C )
& ( ( app @ C @ B )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
thf(417,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( rearsegP @ A @ B )
=> ? [C: $i] :
( ( ssList @ C )
& ( ( app @ C @ B )
= A ) ) )
& ( ? [C: $i] :
( ( ssList @ C )
& ( ( app @ C @ B )
= A ) )
=> ( rearsegP @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(19,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( strictorderP @ A )
<=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( ( lt @ B @ C )
| ( lt @ C @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).
thf(174,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( strictorderP @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( ( lt @ B @ C )
| ( lt @ C @ B ) ) ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( ( lt @ B @ C )
| ( lt @ C @ B ) ) ) ) ) ) ) )
=> ( strictorderP @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(70,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( singletonP @ A )
<=> ? [B: $i] :
( ( ssItem @ B )
& ( ( cons @ B @ nil )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
thf(404,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( singletonP @ A )
=> ? [B: $i] :
( ( ssItem @ B )
& ( ( cons @ B @ nil )
= A ) ) )
& ( ? [B: $i] :
( ( ssItem @ B )
& ( ( cons @ B @ nil )
= A ) )
=> ( singletonP @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(63,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( ( geq @ A @ B )
& ( geq @ B @ C ) )
=> ( geq @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax88) ).
thf(389,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( ( geq @ A @ B )
& ( geq @ B @ C ) )
=> ( geq @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(5,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( strictorderedP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax68) ).
thf(125,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( strictorderedP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( app @ nil @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(216,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( app @ nil @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(87,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( cons @ C @ ( app @ B @ A ) )
= ( app @ ( cons @ C @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax27) ).
thf(475,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( cons @ C @ ( app @ B @ A ) )
= ( app @ ( cons @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(91,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( rearsegP @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
thf(485,plain,
! [A: $i] :
( ( ssList @ A )
=> ( rearsegP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(56,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( nil
= ( app @ A @ B ) )
<=> ( ( nil = B )
& ( nil = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax83) ).
thf(348,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( nil
= ( app @ A @ B ) )
=> ( ( nil = B )
& ( nil = A ) ) )
& ( ( ( nil = B )
& ( nil = A ) )
=> ( nil
= ( app @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(12,axiom,
cyclefreeP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).
thf(147,plain,
cyclefreeP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(33,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( strictorderedP @ A )
<=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( lt @ B @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax12) ).
thf(221,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( strictorderedP @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( lt @ B @ C ) ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( lt @ B @ C ) ) ) ) ) ) )
=> ( strictorderedP @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(45,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( rearsegP @ A @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
thf(293,plain,
! [A: $i] :
( ( ssList @ A )
=> ( rearsegP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(66,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( ( leq @ A @ B )
& ( leq @ B @ C ) )
=> ( leq @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax30) ).
thf(396,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( ( leq @ A @ B )
& ( leq @ B @ C ) )
=> ( leq @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(7,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( gt @ A @ B )
=> ~ ( gt @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax94) ).
thf(133,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( gt @ A @ B )
=> ~ ( gt @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(71,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ssList @ ( app @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
thf(411,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ssList @ ( app @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(49,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( frontsegP @ ( cons @ A @ C ) @ ( cons @ B @ D ) )
<=> ( ( A = B )
& ( frontsegP @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax44) ).
thf(307,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( ( frontsegP @ ( cons @ A @ C ) @ ( cons @ B @ D ) )
=> ( ( A = B )
& ( frontsegP @ C @ D ) ) )
& ( ( ( A = B )
& ( frontsegP @ C @ D ) )
=> ( frontsegP @ ( cons @ A @ C ) @ ( cons @ B @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(34,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ~ ( memberP @ nil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
thf(233,plain,
! [A: $i] :
( ( ssItem @ A )
=> ~ ( memberP @ nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(81,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( tl @ ( cons @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
thf(452,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( tl @ ( cons @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(48,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ssItem @ B )
& ( ( hd @ A )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax75) ).
thf(302,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ssItem @ B )
& ( ( hd @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(47,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssItem @ D )
=> ( ( ( cons @ C @ A )
= ( cons @ D @ B ) )
=> ( ( C = D )
& ( B = A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19) ).
thf(297,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssItem @ D )
=> ( ( ( cons @ C @ A )
= ( cons @ D @ B ) )
=> ( ( C = D )
& ( B = A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(75,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( rearsegP @ nil @ A )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
thf(424,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( rearsegP @ nil @ A )
=> ( nil = A ) )
& ( ( nil = A )
=> ( rearsegP @ nil @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(22,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( app @ C @ B )
= ( app @ A @ B ) )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax79) ).
thf(192,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( app @ C @ B )
= ( app @ A @ B ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(24,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( totalorderedP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax65) ).
thf(197,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(78,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( frontsegP @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
thf(435,plain,
! [A: $i] :
( ( ssList @ A )
=> ( frontsegP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(51,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( neq @ A @ B )
<=> ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
thf(317,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( neq @ A @ B )
=> ( A != B ) )
& ( ( A != B )
=> ( neq @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(16,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( app @ ( app @ A @ B ) @ C )
= ( app @ A @ ( app @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax82) ).
thf(156,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( app @ ( app @ A @ B ) @ C )
= ( app @ A @ ( app @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(57,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( totalorderP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61) ).
thf(356,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( totalorderP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(11,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( segmentP @ nil @ A )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
thf(141,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( segmentP @ nil @ A )
=> ( nil = A ) )
& ( ( nil = A )
=> ( segmentP @ nil @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(65,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( app @ B @ C )
= ( app @ B @ A ) )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax80) ).
thf(393,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( app @ B @ C )
= ( app @ B @ A ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(83,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( totalorderedP @ A )
<=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( leq @ B @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).
thf(457,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( totalorderedP @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( leq @ B @ C ) ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( leq @ B @ C ) ) ) ) ) ) )
=> ( totalorderedP @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(36,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( frontsegP @ A @ B )
<=> ? [C: $i] :
( ( ssList @ C )
& ( ( app @ B @ C )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
thf(237,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( frontsegP @ A @ B )
=> ? [C: $i] :
( ( ssList @ C )
& ( ( app @ B @ C )
= A ) ) )
& ( ? [C: $i] :
( ( ssList @ C )
& ( ( app @ B @ C )
= A ) )
=> ( frontsegP @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(37,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( segmentP @ A @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
thf(244,plain,
! [A: $i] :
( ( ssList @ A )
=> ( segmentP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(28,axiom,
~ ( singletonP @ nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
thf(205,plain,
~ ( singletonP @ nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(67,axiom,
strictorderP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax64) ).
thf(398,plain,
strictorderP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(76,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( nil != A )
=> ( ( hd @ ( app @ A @ B ) )
= ( hd @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax85) ).
thf(430,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( nil != A )
=> ( ( hd @ ( app @ A @ B ) )
= ( hd @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(13,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( frontsegP @ A @ B )
& ( frontsegP @ B @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).
thf(148,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( frontsegP @ A @ B )
& ( frontsegP @ B @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(40,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil = A )
| ? [B: $i] :
( ( ssList @ B )
& ? [C: $i] :
( ( ssItem @ C )
& ( ( cons @ C @ B )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
thf(264,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil = A )
| ? [B: $i] :
( ( ssList @ B )
& ? [C: $i] :
( ( ssItem @ C )
& ( ( cons @ C @ B )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(69,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( cyclefreeP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax59) ).
thf(402,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( cyclefreeP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(27,axiom,
duplicatefreeP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax72) ).
thf(204,plain,
duplicatefreeP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(72,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( leq @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
thf(413,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( leq @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(64,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( duplicatefreeP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax71) ).
thf(391,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( duplicatefreeP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(62,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( memberP @ ( cons @ B @ C ) @ A )
<=> ( ( A = B )
| ( memberP @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).
thf(382,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( memberP @ ( cons @ B @ C ) @ A )
=> ( ( A = B )
| ( memberP @ C @ A ) ) )
& ( ( ( A = B )
| ( memberP @ C @ A ) )
=> ( memberP @ ( cons @ B @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(17,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( cyclefreeP @ A )
<=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ~ ( ( leq @ B @ C )
& ( leq @ C @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
thf(159,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( cyclefreeP @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ~ ( ( leq @ B @ C )
& ( leq @ C @ B ) ) ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ~ ( ( leq @ B @ C )
& ( leq @ C @ B ) ) ) ) ) ) ) )
=> ( cyclefreeP @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(20,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( app @ A @ nil )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
thf(187,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( app @ A @ nil )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(18,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ssList @ ( cons @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
thf(172,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ssList @ ( cons @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(32,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ~ ( lt @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax90) ).
thf(219,plain,
! [A: $i] :
( ( ssItem @ A )
=> ~ ( lt @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(42,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( strictorderedP @ ( cons @ A @ B ) )
<=> ( ( nil = B )
| ( ( nil != B )
& ( strictorderedP @ B )
& ( lt @ A @ ( hd @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax70) ).
thf(274,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( strictorderedP @ ( cons @ A @ B ) )
=> ( ( nil = B )
| ( ( nil != B )
& ( strictorderedP @ B )
& ( lt @ A @ ( hd @ B ) ) ) ) )
& ( ( ( nil = B )
| ( ( nil != B )
& ( strictorderedP @ B )
& ( lt @ A @ ( hd @ B ) ) ) )
=> ( strictorderedP @ ( cons @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(61,axiom,
? [A: $i] :
( ( ssItem @ A )
& ? [B: $i] :
( ( ssItem @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(377,plain,
? [A: $i] :
( ( ssItem @ A )
& ? [B: $i] :
( ( ssItem @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(59,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( frontsegP @ A @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
thf(362,plain,
! [A: $i] :
( ( ssList @ A )
=> ( frontsegP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(97,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( geq @ A @ B )
<=> ( leq @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax32) ).
thf(509,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( ( geq @ A @ B )
=> ( leq @ B @ A ) )
& ( ( leq @ B @ A )
=> ( geq @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(1,conjecture,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( B != D )
| ( A != C )
| ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ E @ C ) @ F )
!= D )
| ~ ( totalorderedP @ C )
| ? [G: $i] :
( ( ssItem @ G )
& ? [H: $i] :
( ( ssList @ H )
& ( ( app @ H @ ( cons @ G @ nil ) )
= E )
& ? [I: $i] :
( ( ssItem @ I )
& ? [J: $i] :
( ( ssList @ J )
& ( ( app @ ( cons @ I @ nil ) @ J )
= C )
& ( leq @ G @ I ) ) ) ) )
| ? [G: $i] :
( ( ssItem @ G )
& ? [H: $i] :
( ( ssList @ H )
& ( ( app @ ( cons @ G @ nil ) @ H )
= F )
& ? [I: $i] :
( ( ssItem @ I )
& ? [J: $i] :
( ( ssList @ J )
& ( ( app @ J @ ( cons @ I @ nil ) )
= C )
& ( leq @ I @ G ) ) ) ) ) ) ) )
| ( ( nil != D )
& ( nil = C ) )
| ( ( nil = B )
& ( nil = A ) )
| ( ( neq @ A @ nil )
& ( segmentP @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( B != D )
| ( A != C )
| ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ E @ C ) @ F )
!= D )
| ~ ( totalorderedP @ C )
| ? [G: $i] :
( ( ssItem @ G )
& ? [H: $i] :
( ( ssList @ H )
& ( ( app @ H @ ( cons @ G @ nil ) )
= E )
& ? [I: $i] :
( ( ssItem @ I )
& ? [J: $i] :
( ( ssList @ J )
& ( ( app @ ( cons @ I @ nil ) @ J )
= C )
& ( leq @ G @ I ) ) ) ) )
| ? [G: $i] :
( ( ssItem @ G )
& ? [H: $i] :
( ( ssList @ H )
& ( ( app @ ( cons @ G @ nil ) @ H )
= F )
& ? [I: $i] :
( ( ssItem @ I )
& ? [J: $i] :
( ( ssList @ J )
& ( ( app @ J @ ( cons @ I @ nil ) )
= C )
& ( leq @ I @ G ) ) ) ) ) ) ) )
| ( ( nil != D )
& ( nil = C ) )
| ( ( nil = B )
& ( nil = A ) )
| ( ( neq @ A @ nil )
& ( segmentP @ B @ A ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(98,plain,
~ ! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( B != D )
| ( A != C )
| ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ E @ C ) @ F )
!= D )
| ~ ( totalorderedP @ C )
| ? [G: $i] :
( ( ssItem @ G )
& ? [H: $i] :
( ( ssList @ H )
& ( ( app @ H @ ( cons @ G @ nil ) )
= E )
& ? [I: $i] :
( ( ssItem @ I )
& ? [J: $i] :
( ( ssList @ J )
& ( ( app @ ( cons @ I @ nil ) @ J )
= C )
& ( leq @ G @ I ) ) ) ) )
| ? [G: $i] :
( ( ssItem @ G )
& ? [H: $i] :
( ( ssList @ H )
& ( ( app @ ( cons @ G @ nil ) @ H )
= F )
& ? [I: $i] :
( ( ssItem @ I )
& ? [J: $i] :
( ( ssList @ J )
& ( ( app @ J @ ( cons @ I @ nil ) )
= C )
& ( leq @ I @ G ) ) ) ) ) ) ) )
| ( ( nil != D )
& ( nil = C ) )
| ( ( nil = B )
& ( nil = A ) )
| ( ( neq @ A @ nil )
& ( segmentP @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(41,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( cons @ B @ A )
!= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(271,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( cons @ B @ A )
!= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(52,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( totalorderedP @ ( cons @ A @ B ) )
<=> ( ( nil = B )
| ( ( nil != B )
& ( totalorderedP @ B )
& ( leq @ A @ ( hd @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax67) ).
thf(323,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( totalorderedP @ ( cons @ A @ B ) )
=> ( ( nil = B )
| ( ( nil != B )
& ( totalorderedP @ B )
& ( leq @ A @ ( hd @ B ) ) ) ) )
& ( ( ( nil = B )
| ( ( nil != B )
& ( totalorderedP @ B )
& ( leq @ A @ ( hd @ B ) ) ) )
=> ( totalorderedP @ ( cons @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(90,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( rearsegP @ A @ B )
=> ( rearsegP @ ( app @ C @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax50) ).
thf(483,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( rearsegP @ A @ B )
=> ( rearsegP @ ( app @ C @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(39,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( totalorderP @ A )
<=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( ( leq @ B @ C )
| ( leq @ C @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9) ).
thf(251,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( totalorderP @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( ( leq @ B @ C )
| ( leq @ C @ B ) ) ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( ( leq @ B @ C )
| ( leq @ C @ B ) ) ) ) ) ) ) )
=> ( totalorderP @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(68,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).
thf(399,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(82,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( rearsegP @ A @ B )
& ( rearsegP @ B @ C ) )
=> ( rearsegP @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47) ).
thf(455,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( rearsegP @ A @ B )
& ( rearsegP @ B @ C ) )
=> ( rearsegP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(8,axiom,
totalorderedP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).
thf(135,plain,
totalorderedP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(93,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( lt @ A @ B )
<=> ( ( A != B )
& ( leq @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax93) ).
thf(490,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( ( lt @ A @ B )
=> ( ( A != B )
& ( leq @ A @ B ) ) )
& ( ( ( A != B )
& ( leq @ A @ B ) )
=> ( lt @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(92,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( nil
!= ( cons @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
thf(487,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( nil
!= ( cons @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(4,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( ( lt @ A @ B )
& ( lt @ B @ C ) )
=> ( lt @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax34) ).
thf(123,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( ( lt @ A @ B )
& ( lt @ B @ C ) )
=> ( lt @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(25,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( leq @ A @ B )
=> ( ( A = B )
| ( lt @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax92) ).
thf(199,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( leq @ A @ B )
=> ( ( A = B )
| ( lt @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(6,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( frontsegP @ nil @ A )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
thf(127,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( frontsegP @ nil @ A )
=> ( nil = A ) )
& ( ( nil = A )
=> ( frontsegP @ nil @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(85,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( geq @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax89) ).
thf(470,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( geq @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(53,axiom,
ssList @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
thf(336,plain,
ssList @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(15,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( frontsegP @ A @ B )
=> ( frontsegP @ ( app @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax43) ).
thf(154,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( frontsegP @ A @ B )
=> ( frontsegP @ ( app @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(50,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( ( geq @ A @ B )
& ( geq @ B @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax87) ).
thf(314,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( ( geq @ A @ B )
& ( geq @ B @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(94,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( rearsegP @ A @ B )
& ( rearsegP @ B @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48) ).
thf(497,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( rearsegP @ A @ B )
& ( rearsegP @ B @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(44,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ssList @ ( tl @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
thf(290,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ssList @ ( tl @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(77,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( ( leq @ A @ B )
& ( lt @ B @ C ) )
=> ( lt @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax91) ).
thf(433,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( ( leq @ A @ B )
& ( lt @ B @ C ) )
=> ( lt @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(29,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( gt @ A @ B )
<=> ( lt @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax35) ).
thf(207,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( ( gt @ A @ B )
=> ( lt @ B @ A ) )
& ( ( lt @ B @ A )
=> ( gt @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(88,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( ( leq @ A @ B )
& ( leq @ B @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).
thf(478,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( ( leq @ A @ B )
& ( leq @ B @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(43,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ssItem @ ( hd @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(287,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ssItem @ ( hd @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(35,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( segmentP @ A @ B )
=> ( segmentP @ ( app @ ( app @ C @ A ) @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax56) ).
thf(235,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( segmentP @ A @ B )
=> ( segmentP @ ( app @ ( app @ C @ A ) @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(38,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ssList @ B )
& ( ( tl @ A )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax76) ).
thf(246,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ssList @ B )
& ( ( tl @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(14,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( cons @ B @ A )
= ( app @ ( cons @ B @ nil ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax81) ).
thf(151,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( cons @ B @ A )
= ( app @ ( cons @ B @ nil ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(21,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( segmentP @ A @ B )
& ( segmentP @ B @ C ) )
=> ( segmentP @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
thf(190,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( segmentP @ A @ B )
& ( segmentP @ B @ C ) )
=> ( segmentP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(30,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( neq @ A @ B )
<=> ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(210,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( ( neq @ A @ B )
=> ( A != B ) )
& ( ( A != B )
=> ( neq @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(9,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( frontsegP @ A @ B )
& ( frontsegP @ B @ C ) )
=> ( frontsegP @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).
thf(136,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( frontsegP @ A @ B )
& ( frontsegP @ B @ C ) )
=> ( frontsegP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(58,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( memberP @ ( app @ B @ C ) @ A )
<=> ( ( memberP @ B @ A )
| ( memberP @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
thf(358,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( memberP @ ( app @ B @ C ) @ A )
=> ( ( memberP @ B @ A )
| ( memberP @ C @ A ) ) )
& ( ( ( memberP @ B @ A )
| ( memberP @ C @ A ) )
=> ( memberP @ ( app @ B @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(23,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( segmentP @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
thf(195,plain,
! [A: $i] :
( ( ssList @ A )
=> ( segmentP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(79,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( nil != A )
=> ( ( tl @ ( app @ A @ B ) )
= ( app @ ( tl @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax86) ).
thf(437,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( nil != A )
=> ( ( tl @ ( app @ A @ B ) )
= ( app @ ( tl @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(73,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( strictorderP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax63) ).
thf(415,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( strictorderP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(84,axiom,
equalelemsP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax74) ).
thf(469,plain,
equalelemsP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(60,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( duplicatefreeP @ A )
<=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( B != C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13) ).
thf(364,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( duplicatefreeP @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( B != C ) ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( B != C ) ) ) ) ) ) )
=> ( duplicatefreeP @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(54,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( nil != B )
& ( nil != A )
& ( ( hd @ B )
= ( hd @ A ) )
& ( ( tl @ B )
= ( tl @ A ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax77) ).
thf(337,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( nil != B )
& ( nil != A )
& ( ( hd @ B )
= ( hd @ A ) )
& ( ( tl @ B )
= ( tl @ A ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(3,axiom,
strictorderedP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69) ).
thf(122,plain,
strictorderedP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(512,plain,
$false,
inference(e,[status(thm)],[295,501,138,481,440,202,500,472,340,417,174,404,389,125,216,475,485,348,147,221,293,396,133,411,307,233,452,302,297,424,192,197,435,317,156,356,141,393,457,237,244,205,398,430,148,264,402,204,413,391,382,159,187,172,219,274,377,362,509,98,271,323,483,251,399,455,135,490,487,123,199,127,470,336,154,314,497,290,433,207,478,287,235,246,151,190,210,136,358,195,437,415,469,364,337,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWC118+1 : TPTP v8.2.0. Released v2.4.0.
% 0.10/0.11 % Command : run_Leo-III %s %d
% 0.10/0.30 % Computer : n029.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sun May 19 03:49:39 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.91/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.56/1.14 % [INFO] Parsing done (234ms).
% 1.56/1.15 % [INFO] Running in sequential loop mode.
% 1.95/1.49 % [INFO] eprover registered as external prover.
% 1.95/1.49 % [INFO] cvc4 registered as external prover.
% 1.95/1.50 % [INFO] Scanning for conjecture ...
% 2.30/1.64 % [INFO] Found a conjecture (or negated_conjecture) and 95 axioms. Running axiom selection ...
% 2.68/1.74 % [INFO] Axiom selection finished. Selected 95 axioms (removed 0 axioms).
% 2.90/1.86 % [INFO] Problem is first-order (TPTP FOF).
% 2.90/1.88 % [INFO] Type checking passed.
% 2.90/1.89 % [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 ...
% 7.71/3.44 % External prover 'e' found a proof!
% 7.71/3.44 % [INFO] Killing All external provers ...
% 7.71/3.44 % Time passed: 2993ms (effective reasoning time: 2286ms)
% 7.71/3.44 % 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)>
% 7.71/3.44 % Axioms used in derivation (95): ax74, ax13, ax37, ax14, ax12, ax79, ax20, ax52, ax67, ax24, ax63, ax56, ax4, ax47, ax41, ax90, ax31, ax28, ax9, ax17, ax6, ax45, ax40, ax85, ax35, ax58, ax69, ax78, ax39, ax89, ax27, ax66, ax8, ax91, ax73, ax51, ax48, ax21, ax88, ax62, ax10, ax55, ax32, ax95, ax16, ax80, ax59, ax1, ax7, ax77, ax38, ax44, ax84, ax92, ax94, ax33, ax26, ax61, ax11, ax50, ax87, ax72, ax65, ax22, ax15, ax81, ax76, ax43, ax83, ax19, ax2, ax70, ax54, ax49, ax46, ax34, ax23, ax86, ax25, ax60, ax71, ax57, ax68, ax30, ax42, ax82, ax18, ax3, ax5, ax36, ax64, ax29, ax75, ax53, ax93
% 7.71/3.44 % No. of inferences in proof: 194
% 7.71/3.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2993 ms resp. 2286 ms w/o parsing
% 8.01/3.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.01/3.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------