%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT214_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n010.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 : Sun Sep 27 08:27:34 AM UTC 2026
% Result : Theorem 7.90s 2.66s
% Output : Refutation 8.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 42
% Syntax : Number of formulae : 86 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 209 ( 178 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 1069 ( 28 ~; 9 |; 51 &; 918 @)
% ( 15 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 6 con; 0-5 aty)
% Number of variables : 281 ( 0 ^; 258 !; 23 ?; 281 :)
% 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(append_decl,type,
append:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) > ( TA @ list ) ) ).
thf(distinct_decl,type,
distinct:
!>[TA: $tType] : ( ( TA @ list ) > $o ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( TA @ list ) ).
thf(list_case_decl,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ list @ fun ) @ ( TA @ fun ) ) > ( TA @ list ) > TB ) ).
thf(list_ex1_decl,type,
list_ex1:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(splice_decl,type,
splice:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) > ( TA @ list ) ) ).
thf(a_decl,type,
a: arrow_411405190le_alt ).
thf(b_decl,type,
b: arrow_411405190le_alt ).
thf(thesis_decl,type,
thesis: $o ).
thf(38,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_not__Cons__self) ).
thf(234,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(27,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( C @ ( TA @ splice ) ) @ ( B @ ( TA @ cons ) ) @ ( D @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_splice_Osimps_I3_J) ).
thf(174,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( C @ ( TA @ splice ) ) @ ( B @ ( TA @ cons ) ) @ ( D @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(4,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ append ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_append__Nil) ).
thf(61,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(30,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: arrow_411405190le_alt] : ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_third__alt) ).
thf(188,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: arrow_411405190le_alt] : ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(17,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
= ( B @ ( A @ ( TA @ append ) ) ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_self__append__conv2) ).
thf(129,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( B
= ( B @ ( A @ ( TA @ append ) ) ) ) )
& ( ( B
= ( B @ ( A @ ( TA @ append ) ) ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( TA @ nil )
= ( A @ ( B @ ( TA @ append ) ) ) )
<=> ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_Nil__is__append__conv) ).
thf(113,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) )
=> ( ( TA @ nil )
= ( A @ ( B @ ( TA @ append ) ) ) ) )
& ( ( ( TA @ nil )
= ( A @ ( B @ ( TA @ append ) ) ) )
=> ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(28,axiom,
! [TA: $tType] : ( TA @ nil @ ( TA @ distinct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_distinct_Osimps_I1_J) ).
thf(177,plain,
! [TA: $tType] : ( TA @ nil @ ( TA @ distinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(37,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA @ list] :
( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
<=> ( ? [E: TA @ list] :
( ( ( C @ ( E @ ( TA @ append ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ cons ) ) ) ) )
| ( ( C
= ( A @ ( B @ ( TA @ cons ) ) ) )
& ( D
= ( TA @ nil ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_append__eq__Cons__conv) ).
thf(218,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA @ list] :
( ( ( ? [E: TA @ list] :
( ( ( C @ ( E @ ( TA @ append ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ cons ) ) ) ) )
| ( ( C
= ( A @ ( B @ ( TA @ cons ) ) ) )
& ( D
= ( TA @ nil ) ) ) )
=> ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
=> ( ? [E: TA @ list] :
( ( ( C @ ( E @ ( TA @ append ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ cons ) ) ) ) )
| ( ( C
= ( A @ ( B @ ( TA @ cons ) ) ) )
& ( D
= ( TA @ nil ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(26,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_splice__Nil2) ).
thf(171,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_list_Osimps_I4_J) ).
thf(168,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(23,axiom,
! [TA: $tType,A: TA] : ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ distinct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_distinct__singleton) ).
thf(163,plain,
! [TA: $tType,A: TA] : ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ distinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(14,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ append ) ) @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( TA @ append ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_append__assoc) ).
thf(110,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ append ) ) @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( TA @ append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(21,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_splice_Osimps_I1_J) ).
thf(157,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(10,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons ) ) @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_append__Cons) ).
thf(93,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons ) ) @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B = A )
=> ( B
= ( A @ ( TA @ nil @ ( TA @ append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_eq__Nil__appendI) ).
thf(78,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B = A )
=> ( B
= ( A @ ( TA @ nil @ ( TA @ append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(29,axiom,
! [TA: $tType,A: TA,B: TA @ list,C: TA,D: TA @ list] :
( ( ( TA @ nil @ ( C @ ( TA @ cons ) ) @ ( D @ ( TA @ append ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( B @ ( TA @ append ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_append1__eq__conv) ).
thf(179,plain,
! [TA: $tType,A: TA,B: TA @ list,C: TA,D: TA @ list] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( TA @ nil @ ( C @ ( TA @ cons ) ) @ ( D @ ( TA @ append ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( B @ ( TA @ append ) ) ) ) )
& ( ( ( TA @ nil @ ( C @ ( TA @ cons ) ) @ ( D @ ( TA @ append ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( B @ ( TA @ append ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(13,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list,E: TA @ list] :
( ( ( D @ ( E @ ( TA @ append ) ) )
= C )
=> ( ( B
= ( A @ ( D @ ( TA @ append ) ) ) )
=> ( ( B @ ( E @ ( TA @ append ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_append__eq__appendI) ).
thf(106,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list,E: TA @ list] :
( ( ( D @ ( E @ ( TA @ append ) ) )
= C )
=> ( ( B
= ( A @ ( D @ ( TA @ append ) ) ) )
=> ( ( B @ ( E @ ( TA @ append ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(43,axiom,
! [A: arrow_411405190le_alt] :
( ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) )
=> thesis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(260,plain,
! [A: arrow_411405190le_alt] :
( ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) )
=> thesis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(22,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_list_Osimps_I3_J) ).
thf(160,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(24,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_list_Oexhaust) ).
thf(165,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(35,axiom,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_insert__Nil) ).
thf(212,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(11,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( ( B @ ( C @ ( TA @ append ) ) )
= ( B @ ( A @ ( TA @ append ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_append__same__eq) ).
thf(96,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ append ) ) )
= ( B @ ( A @ ( TA @ append ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ append ) ) )
= ( B @ ( A @ ( TA @ append ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(39,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( ( B @ ( TA @ distinct ) )
=> ( B @ ( A @ ( TA @ insert ) ) @ ( TA @ distinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_distinct__insert) ).
thf(237,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( ( B @ ( TA @ distinct ) )
=> ( B @ ( A @ ( TA @ insert ) ) @ ( TA @ distinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(42,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA] :
( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) )
<=> ( ? [E: TA @ list] :
( ( C
= ( A @ ( E @ ( TA @ append ) ) ) )
& ( ( E @ ( D @ ( TA @ cons ) ) )
= B ) )
| ( ( ( C @ ( D @ ( TA @ cons ) ) )
= A )
& ( B
= ( TA @ nil ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_Cons__eq__append__conv) ).
thf(244,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA] :
( ( ( ? [E: TA @ list] :
( ( C
= ( A @ ( E @ ( TA @ append ) ) ) )
& ( ( E @ ( D @ ( TA @ cons ) ) )
= B ) )
| ( ( ( C @ ( D @ ( TA @ cons ) ) )
= A )
& ( B
= ( TA @ nil ) ) ) )
=> ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) )
=> ( ? [E: TA @ list] :
( ( C
= ( A @ ( E @ ( TA @ append ) ) ) )
& ( ( E @ ( D @ ( TA @ cons ) ) )
= B ) )
| ( ( ( C @ ( D @ ( TA @ cons ) ) )
= A )
& ( B
= ( TA @ nil ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(20,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ cons ) ) @ ( TA @ distinct ) )
<=> ( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ distinct ) )
& ( A @ ( C @ ( TA @ cons ) ) @ ( TA @ distinct ) )
& ( C != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_distinct__length__2__or__more) ).
thf(148,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA] :
( ( ( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ distinct ) )
& ( A @ ( C @ ( TA @ cons ) ) @ ( TA @ distinct ) )
& ( C != B ) )
=> ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ cons ) ) @ ( TA @ distinct ) ) )
& ( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ cons ) ) @ ( TA @ distinct ) )
=> ( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ distinct ) )
& ( A @ ( C @ ( TA @ cons ) ) @ ( TA @ distinct ) )
& ( C != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(3,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list] :
( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) )
<=> ? [E: TA @ list] :
( ( ( C
= ( A @ ( E @ ( TA @ append ) ) ) )
& ( ( E @ ( D @ ( TA @ append ) ) )
= B ) )
| ( ( ( C @ ( E @ ( TA @ append ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ append ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_append__eq__append__conv2) ).
thf(45,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list] :
( ( ? [E: TA @ list] :
( ( ( C
= ( A @ ( E @ ( TA @ append ) ) ) )
& ( ( E @ ( D @ ( TA @ append ) ) )
= B ) )
| ( ( ( C @ ( E @ ( TA @ append ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ append ) ) ) ) ) )
=> ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) )
=> ? [E: TA @ list] :
( ( ( C
= ( A @ ( E @ ( TA @ append ) ) ) )
& ( ( E @ ( D @ ( TA @ append ) ) )
= B ) )
| ( ( ( C @ ( E @ ( TA @ append ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ append ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A @ ( B @ ( TA @ append ) ) )
= B )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_append__self__conv) ).
thf(64,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TA @ append ) ) )
= B ) )
& ( ( ( A @ ( B @ ( TA @ append ) ) )
= B )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
<=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_neq__Nil__conv) ).
thf(191,plain,
! [TA: $tType,A: TA @ list] :
( ( ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) )
=> ( A
!= ( TA @ nil ) ) )
& ( ( A
!= ( TA @ nil ) )
=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
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(44,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
= ( A @ ( B @ ( TA @ append ) ) ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_self__append__conv) ).
thf(71,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( B
= ( A @ ( B @ ( TA @ append ) ) ) ) )
& ( ( B
= ( A @ ( B @ ( TA @ append ) ) ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A @ ( B @ ( TA @ append ) ) )
= A )
<=> ( B
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_append__self__conv2) ).
thf(86,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B
= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TA @ append ) ) )
= A ) )
& ( ( ( A @ ( B @ ( TA @ append ) ) )
= A )
=> ( B
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(12,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ append ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_append__Nil2) ).
thf(103,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(32,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_list_Oinject) ).
thf(198,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(34,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_not__Cons__self2) ).
thf(209,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(19,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil @ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_splice_Osimps_I2_J) ).
thf(145,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil @ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(33,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_list__ex1__simps_I1_J) ).
thf(207,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(8,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list,E: TA] :
( ( ( D @ ( E @ ( TA @ cons ) ) )
= C )
=> ( ( B
= ( A @ ( D @ ( TA @ append ) ) ) )
=> ( ( B @ ( E @ ( TA @ cons ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_Cons__eq__appendI) ).
thf(82,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list,E: TA] :
( ( ( D @ ( E @ ( TA @ cons ) ) )
= C )
=> ( ( B
= ( A @ ( D @ ( TA @ append ) ) ) )
=> ( ( B @ ( E @ ( TA @ cons ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(18,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A @ ( B @ ( TA @ append ) ) )
= ( TA @ nil ) )
<=> ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_append__is__Nil__conv) ).
thf(136,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) )
=> ( ( A @ ( B @ ( TA @ append ) ) )
= ( TA @ nil ) ) )
& ( ( ( A @ ( B @ ( TA @ append ) ) )
= ( TA @ nil ) )
=> ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(40,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096a_A_126_061_Ab_096) ).
thf(239,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(41,axiom,
? [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: arrow_411405190le_alt] : ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_alt3) ).
thf(242,plain,
? [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: arrow_411405190le_alt] : ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(16,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( ( B @ ( C @ ( TA @ append ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_same__append__eq) ).
thf(122,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ append ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ append ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(36,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_list_Osimps_I2_J) ).
thf(215,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(263,plain,
$false,
inference(e,[status(thm)],[234,174,61,188,129,113,177,218,171,168,163,110,157,93,78,179,106,260,160,165,212,96,237,244,148,45,64,191,44,71,86,103,198,209,145,207,82,136,239,242,122,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT214_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.41 % Computer : n010.cluster.edu
% 0.11/0.41 % Model : x86_64 x86_64
% 0.11/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.41 % Memory : 8046.5625MB
% 0.11/0.41 % OS : Linux 6.8.0-71-generic
% 0.11/0.41 % CPULimit : 300
% 0.11/0.41 % WCLimit : 300
% 0.11/0.41 % DateTime : Sat Sep 26 06:42:01 UTC 2026
% 0.11/0.42 % CPUTime :
% 0.11/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.66/0.73 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.30/0.94 % [INFO] Parsing done (212ms).
% 1.30/0.95 % [INFO] Running in sequential loop mode.
% 2.60/1.20 % [INFO] eprover registered as external prover.
% 2.60/1.21 % [INFO] Scanning for conjecture ...
% 2.92/1.38 % [INFO] Found a conjecture (or negated_conjecture) and 103 axioms. Running axiom selection ...
% 3.24/1.47 % [INFO] Axiom selection finished. Selected 41 axioms (removed 62 axioms).
% 4.09/1.60 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.09/1.62 % [INFO] Type checking passed.
% 4.09/1.63 % [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 ...
% 7.90/2.65 % External prover 'e' found a proof!
% 7.90/2.65 % [INFO] Killing All external provers ...
% 7.90/2.65 % Time passed: 2140ms (effective reasoning time: 1702ms)
% 7.90/2.65 % 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)>
% 7.90/2.66 % Axioms used in derivation (41): fact_96_append__eq__appendI, fact_5_third__alt, fact_79_same__append__eq, fact_82_append__self__conv2, fact_93_append__Nil2, fact_30_splice_Osimps_I1_J, fact_88_append1__eq__conv, fact_7_distinct__singleton, fact_31_splice__Nil2, fact_85_self__append__conv2, fact_0__096a_A_126_061_Ab_096, fact_9_list_Oinject, fact_92_eq__Nil__appendI, fact_86_self__append__conv, fact_87_Nil__is__append__conv, fact_48_list__ex1__simps_I1_J, fact_16_not__Cons__self, fact_6_distinct_Osimps_I1_J, fact_14_neq__Nil__conv, fact_78_append__assoc, fact_90_append__eq__Cons__conv, fact_94_append__Nil, fact_13_list_Osimps_I3_J, fact_91_Cons__eq__appendI, fact_89_Cons__eq__append__conv, fact_11_alt3, fact_26_splice_Osimps_I2_J, fact_95_append__eq__append__conv2, fact_27_list_Osimps_I4_J, fact_81_append__Cons, fact_17_not__Cons__self2, fact_29_distinct__insert, fact_12_list_Osimps_I2_J, fact_80_append__same__eq, fact_24_insert__Nil, fact_15_list_Oexhaust, fact_84_append__is__Nil__conv, fact_83_append__self__conv, conj_0, fact_28_splice_Osimps_I3_J, fact_10_distinct__length__2__or__more
% 7.90/2.66 % No. of inferences in proof: 86
% 7.90/2.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2140 ms resp. 1702 ms w/o parsing
% 8.42/2.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.42/2.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------