%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT255_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n012.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 08:27:38 AM UTC 2026
% Result : Theorem 3.39s 1.64s
% Output : Refutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 23
% Syntax : Number of formulae : 48 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 46 equ; 0 cnn)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 438 ( 28 ~; 0 |; 12 &; 381 @)
% ( 3 <=>; 14 =>; 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 : 14 ( 12 usr; 6 con; 0-5 aty)
% Number of variables : 126 ( 0 ^; 112 !; 14 ?; 126 :)
% 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_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(c_decl,type,
c: arrow_411405190le_alt ).
thf(d_decl,type,
d: arrow_411405190le_alt ).
thf(thesis_decl,type,
thesis: $o ).
thf(19,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_list_Osimps_I2_J) ).
thf(88,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1,conjecture,
thesis,
file('/export/starexec/sandbox2/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(10,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_list_Osimps_I3_J) ).
thf(52,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_splice_Osimps_I1_J) ).
thf(85,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(6,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_list_Oexhaust) ).
thf(41,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)],[6]) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',fact_6_distinct__length__2__or__more) ).
thf(32,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)],[5]) ).
thf(7,axiom,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_insert__Nil) ).
thf(44,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,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/sandbox2/benchmark/theBenchmark.p',fact_5_list_Oinject) ).
thf(71,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)],[15]) ).
thf(20,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_list__ex1__simps_I1_J) ).
thf(91,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(16,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_not__Cons__self2) ).
thf(80,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(22,axiom,
! [TA: $tType,A: TA] : ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ distinct ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_distinct__singleton) ).
thf(95,plain,
! [TA: $tType,A: TA] : ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ distinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(9,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/sandbox2/benchmark/theBenchmark.p',fact_7_alt3) ).
thf(50,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)],[9]) ).
thf(21,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( ( B @ ( TA @ distinct ) )
=> ( B @ ( A @ ( TA @ insert ) ) @ ( TA @ distinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_distinct__insert) ).
thf(93,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)],[21]) ).
thf(4,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil @ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_splice_Osimps_I2_J) ).
thf(29,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)],[4]) ).
thf(13,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_splice__Nil2) ).
thf(65,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(23,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_not__Cons__self) ).
thf(97,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(3,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/sandbox2/benchmark/theBenchmark.p',fact_25_list_Osimps_I4_J) ).
thf(26,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)],[3]) ).
thf(11,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
<=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_neq__Nil__conv) ).
thf(55,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)],[11]) ).
thf(8,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/sandbox2/benchmark/theBenchmark.p',fact_1_third__alt) ).
thf(47,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)],[8]) ).
thf(14,axiom,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096c_A_126_061_Ad_096) ).
thf(68,plain,
c != d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',fact_26_splice_Osimps_I3_J) ).
thf(62,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)],[12]) ).
thf(17,axiom,
! [TA: $tType] : ( TA @ nil @ ( TA @ distinct ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_distinct_Osimps_I1_J) ).
thf(83,plain,
! [TA: $tType] : ( TA @ nil @ ( TA @ distinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(24,axiom,
! [A: arrow_411405190le_alt] :
( ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( d @ ( arrow_411405190le_alt @ cons ) ) @ ( c @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) )
=> thesis ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(100,plain,
! [A: arrow_411405190le_alt] :
( ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( d @ ( arrow_411405190le_alt @ cons ) ) @ ( c @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) )
=> thesis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(103,plain,
$false,
inference(e,[status(thm)],[88,25,52,85,41,32,44,71,91,80,95,50,93,29,65,97,26,55,47,68,62,83,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SCT255_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.07/0.32 % Computer : n012.cluster.edu
% 0.07/0.32 % Model : x86_64 x86_64
% 0.07/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.32 % Memory : 8046.5625MB
% 0.07/0.32 % OS : Linux 6.8.0-71-generic
% 0.07/0.32 % CPULimit : 300
% 0.07/0.32 % WCLimit : 300
% 0.07/0.32 % DateTime : Sat Sep 26 06:46:06 UTC 2026
% 0.07/0.33 % CPUTime :
% 0.07/0.33 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.52/0.62 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.79 % [INFO] Parsing done (164ms).
% 1.09/0.80 % [INFO] Running in sequential loop mode.
% 1.37/1.00 % [INFO] eprover registered as external prover.
% 1.37/1.01 % [INFO] Scanning for conjecture ...
% 1.70/1.10 % [INFO] Found a conjecture (or negated_conjecture) and 119 axioms. Running axiom selection ...
% 1.99/1.14 % [INFO] Axiom selection finished. Selected 22 axioms (removed 97 axioms).
% 1.99/1.18 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.99/1.19 % [INFO] Type checking passed.
% 1.99/1.19 % [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 ...
% 3.39/1.63 % External prover 'e' found a proof!
% 3.39/1.64 % [INFO] Killing All external provers ...
% 3.39/1.64 % Time passed: 1232ms (effective reasoning time: 833ms)
% 3.39/1.64 % 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)>
% 3.39/1.64 % 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
% 3.39/1.64 % No. of inferences in proof: 48
% 3.39/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1232 ms resp. 833 ms w/o parsing
% 3.39/1.68 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.39/1.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------