TSTP Solution File: SCT255_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT255_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 : Fri May 19 11:51:25 EDT 2023
% Result : Theorem 4.76s 2.11s
% Output : Refutation 5.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 37
% Syntax : Number of formulae : 62 ( 34 unt; 14 typ; 0 def)
% Number of atoms : 77 ( 46 equ; 0 cnn)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 456 ( 28 ~; 0 |; 12 &; 399 @)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 6 con; 0-5 aty)
% Number of variables : 134 ( 0 ^; 112 !; 14 ?; 134 :)
% ( 8 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(arrow_411405190le_alt_type,type,
arrow_411405190le_alt: $tType ).
thf(arrow_159774573e_indi_type,type,
arrow_159774573e_indi: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(distinct_type,type,
distinct:
!>[TA: $tType] : ( ( list @ TA ) > $o ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_type,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(list_case_type,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ ( fun @ ( list @ TA ) @ TB ) ) > ( list @ TA ) > TB ) ).
thf(list_ex1_type,type,
list_ex1:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > $o ) ).
thf(splice_type,type,
splice:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(c_type,type,
c: arrow_411405190le_alt ).
thf(d_type,type,
d: arrow_411405190le_alt ).
thf(thesis_type,type,
thesis: $o ).
thf(1,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ thesis,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(25,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_not__Cons__self2) ).
thf(77,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(5,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: TA] :
( ( distinct @ TA @ ( cons @ TA @ C @ ( cons @ TA @ B @ A ) ) )
<=> ( ( C != B )
& ( distinct @ TA @ ( cons @ TA @ C @ A ) )
& ( distinct @ TA @ ( cons @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_distinct__length__2__or__more) ).
thf(32,plain,
! [TA: $tType,A: list @ TA,B: TA,C: TA] :
( ( ( distinct @ TA @ ( cons @ TA @ C @ ( cons @ TA @ B @ A ) ) )
=> ( ( C != B )
& ( distinct @ TA @ ( cons @ TA @ C @ A ) )
& ( distinct @ TA @ ( cons @ TA @ B @ A ) ) ) )
& ( ( ( C != B )
& ( distinct @ TA @ ( cons @ TA @ C @ A ) )
& ( distinct @ TA @ ( cons @ TA @ B @ A ) ) )
=> ( distinct @ TA @ ( cons @ TA @ C @ ( cons @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(14,axiom,
c != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096c_A_126_061_Ad_096) ).
thf(66,plain,
c != d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(17,axiom,
! [TA: $tType] : ( distinct @ TA @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_distinct_Osimps_I1_J) ).
thf(80,plain,
! [TA: $tType] : ( distinct @ TA @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(13,axiom,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_splice__Nil2) ).
thf(63,plain,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_insert__Nil) ).
thf(43,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(18,axiom,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_splice_Osimps_I1_J) ).
thf(82,plain,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_list_Osimps_I3_J) ).
thf(51,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(23,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_not__Cons__self) ).
thf(94,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(21,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct @ TA @ B )
=> ( distinct @ TA @ ( insert @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_distinct__insert) ).
thf(90,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct @ TA @ B )
=> ( distinct @ TA @ ( insert @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(15,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_list_Oinject) ).
thf(69,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(20,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_list__ex1__simps_I1_J) ).
thf(88,plain,
! [TA: $tType,A: fun @ TA @ bool] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(8,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: arrow_411405190le_alt] : ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ B @ ( cons @ arrow_411405190le_alt @ A @ ( cons @ arrow_411405190le_alt @ C @ ( nil @ arrow_411405190le_alt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_third__alt) ).
thf(46,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: arrow_411405190le_alt] : ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ B @ ( cons @ arrow_411405190le_alt @ A @ ( cons @ arrow_411405190le_alt @ C @ ( nil @ arrow_411405190le_alt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( splice @ TA @ ( cons @ TA @ B @ A ) @ ( nil @ TA ) )
= ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_splice_Osimps_I2_J) ).
thf(29,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( splice @ TA @ ( cons @ TA @ B @ A ) @ ( nil @ TA ) )
= ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( splice @ TA @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ D @ ( cons @ TA @ B @ ( splice @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_splice_Osimps_I3_J) ).
thf(60,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( splice @ TA @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ D @ ( cons @ TA @ B @ ( splice @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_list_Osimps_I2_J) ).
thf(85,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(22,axiom,
! [TA: $tType,A: TA] : ( distinct @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_distinct__singleton) ).
thf(92,plain,
! [TA: $tType,A: TA] : ( distinct @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(24,axiom,
! [A: arrow_411405190le_alt] :
( ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ c @ ( cons @ arrow_411405190le_alt @ d @ ( cons @ arrow_411405190le_alt @ A @ ( nil @ arrow_411405190le_alt ) ) ) ) )
=> thesis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(97,plain,
! [A: arrow_411405190le_alt] :
( ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ c @ ( cons @ arrow_411405190le_alt @ d @ ( cons @ arrow_411405190le_alt @ A @ ( nil @ arrow_411405190le_alt ) ) ) ) )
=> thesis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(11,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
<=> ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_neq__Nil__conv) ).
thf(54,plain,
! [TA: $tType,A: list @ TA] :
( ( ( A
!= ( nil @ TA ) )
=> ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) )
& ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
? [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: arrow_411405190le_alt] : ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ A @ ( cons @ arrow_411405190le_alt @ B @ ( cons @ arrow_411405190le_alt @ C @ ( nil @ arrow_411405190le_alt ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_alt3) ).
thf(49,plain,
? [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: arrow_411405190le_alt] : ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ A @ ( cons @ arrow_411405190le_alt @ B @ ( cons @ arrow_411405190le_alt @ C @ ( nil @ arrow_411405190le_alt ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_list_Oexhaust) ).
thf(40,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ TA ),B: TA] :
( ( list_case @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_list_Osimps_I4_J) ).
thf(26,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ TA ),B: TA] :
( ( list_case @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(100,plain,
$false,
inference(e,[status(thm)],[25,77,32,66,80,63,43,82,51,94,90,69,88,46,29,60,85,92,97,54,49,40,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT255_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n017.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 14:57:16 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.84/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.48/1.04 % [INFO] Parsing done (192ms).
% 1.48/1.05 % [INFO] Running in sequential loop mode.
% 2.24/1.25 % [INFO] eprover registered as external prover.
% 2.24/1.26 % [INFO] cvc4 registered as external prover.
% 2.24/1.26 % [INFO] Scanning for conjecture ...
% 2.54/1.36 % [INFO] Found a conjecture and 119 axioms. Running axiom selection ...
% 2.69/1.40 % [INFO] Axiom selection finished. Selected 22 axioms (removed 97 axioms).
% 2.69/1.45 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.99/1.46 % [INFO] Type checking passed.
% 2.99/1.46 % [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 ...
% 4.76/2.10 % External prover 'e' found a proof!
% 4.76/2.10 % [INFO] Killing All external provers ...
% 4.76/2.10 % Time passed: 1577ms (effective reasoning time: 1051ms)
% 4.76/2.10 % 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)>
% 4.76/2.11 % Axioms used in derivation (22): fact_9_list_Osimps_I3_J, fact_4_distinct__singleton, fact_17_distinct__insert, fact_7_alt3, fact_5_list_Oinject, fact_26_splice_Osimps_I3_J, fact_80_list__ex1__simps_I1_J, fact_8_list_Osimps_I2_J, fact_28_splice__Nil2, fact_24_splice_Osimps_I2_J, fact_10_neq__Nil__conv, fact_11_list_Oexhaust, fact_1_third__alt, conj_0, fact_3_distinct_Osimps_I1_J, fact_13_not__Cons__self2, fact_0__096c_A_126_061_Ad_096, fact_27_splice_Osimps_I1_J, fact_6_distinct__length__2__or__more, fact_14_insert__Nil, fact_25_list_Osimps_I4_J, fact_12_not__Cons__self
% 4.76/2.11 % No. of inferences in proof: 48
% 4.76/2.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1577 ms resp. 1051 ms w/o parsing
% 5.01/2.16 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.01/2.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------