%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : DAT229^1 : TPTP v9.3.1. Released v7.0.0.
% 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 : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:48:09 AM UTC 2026
% Result : Theorem 8.25s 3.29s
% Output : Refutation 8.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 33
% Syntax : Number of formulae : 68 ( 48 unt; 0 typ; 0 def)
% Number of atoms : 120 ( 74 equ; 6 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1088 ( 18 ~; 0 |; 22 &;1008 @)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 9 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 118 ( 118 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 7 con; 0-8 aty)
% Number of variables : 404 ( 0 ^; 404 !; 0 ?; 404 :)
% Comments :
%------------------------------------------------------------------------------
thf(rBT_Im1923302023_color_type,type,
rBT_Im1923302023_color: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(rBT_Impl_Mirabelle_B_decl,type,
rBT_Impl_Mirabelle_B: rBT_Im1923302023_color ).
thf(rBT_Impl_Mirabelle_R_decl,type,
rBT_Impl_Mirabelle_R: rBT_Im1923302023_color ).
thf(rBT_Im1975547051_color_decl,type,
rBT_Im1975547051_color:
!>[TA: $tType] : ( TA > TA > rBT_Im1923302023_color > TA ) ).
thf(rBT_Im1059957627_color_decl,type,
rBT_Im1059957627_color:
!>[TA: $tType] : ( TA > TA > rBT_Im1923302023_color > TA ) ).
thf(rBT_Im480247531Branch_decl,type,
rBT_Im480247531Branch:
!>[TA: $tType,TB: $tType] : ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ TB @ TA ) > TB > TA > ( rBT_Im246033960le_rbt @ TB @ TA ) > ( rBT_Im246033960le_rbt @ TB @ TA ) ) ).
thf(rBT_Im418718756_Empty_decl,type,
rBT_Im418718756_Empty:
!>[TA: $tType,TB: $tType] : ( rBT_Im246033960le_rbt @ TB @ TA ) ).
thf(rBT_Im858806507se_rbt_decl,type,
rBT_Im858806507se_rbt:
!>[TA: $tType,TB: $tType,TC: $tType] : ( TC > ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ TB @ TA ) > TB > TA > ( rBT_Im246033960le_rbt @ TB @ TA ) > TC ) > ( rBT_Im246033960le_rbt @ TB @ TA ) > TC ) ).
thf(rBT_Im206295089ap_rbt_decl,type,
rBT_Im206295089ap_rbt:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > TC ) > ( TB > TA ) > ( rBT_Im246033960le_rbt @ TD @ TB ) > ( rBT_Im246033960le_rbt @ TC @ TA ) ) ).
thf(rBT_Im1931894874ed_rbt_decl,type,
rBT_Im1931894874ed_rbt:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TA > $o ) > ( rBT_Im246033960le_rbt @ TB @ TA ) > $o ) ).
thf(rBT_Im1947144893ec_rbt_decl,type,
rBT_Im1947144893ec_rbt:
!>[TA: $tType,TB: $tType,TC: $tType] : ( TC > ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ TB @ TA ) > TB > TA > ( rBT_Im246033960le_rbt @ TB @ TA ) > TC > TC > TC ) > ( rBT_Im246033960le_rbt @ TB @ TA ) > TC ) ).
thf(rBT_Im1000242676el_rbt_decl,type,
rBT_Im1000242676el_rbt:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > TC > $o ) > ( TB > TA > $o ) > ( rBT_Im246033960le_rbt @ TD @ TB ) > ( rBT_Im246033960le_rbt @ TC @ TA ) > $o ) ).
thf(t_decl,type,
t: rBT_Im246033960le_rbt @ a @ b ).
thf(thesis_decl,type,
thesis: $o ).
thf(23,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( rBT_Im1059957627_color @ TA @ A @ B @ rBT_Impl_Mirabelle_R )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_color_Osimps_I5_J) ).
thf(110,plain,
! [TA: $tType,A: TA,B: TA] :
( ( rBT_Im1059957627_color @ TA @ A @ B @ rBT_Impl_Mirabelle_R )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(27,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( rBT_Im1975547051_color @ TA @ A @ B @ rBT_Impl_Mirabelle_R )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_color_Osimps_I3_J) ).
thf(121,plain,
! [TA: $tType,A: TA,B: TA] :
( ( rBT_Im1975547051_color @ TA @ A @ B @ rBT_Impl_Mirabelle_R )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ TA @ TB ) > TA > TB > ( rBT_Im246033960le_rbt @ TA @ TB ) > TC > TC > TC,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1947144893ec_rbt @ TC @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) )
= ( B @ C @ D @ E @ F @ G @ ( rBT_Im1947144893ec_rbt @ TC @ TA @ TB @ A @ B @ D ) @ ( rBT_Im1947144893ec_rbt @ TC @ TA @ TB @ A @ B @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_rbt_Osimps_I7_J) ).
thf(116,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ TA @ TB ) > TA > TB > ( rBT_Im246033960le_rbt @ TA @ TB ) > TC > TC > TC,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1947144893ec_rbt @ TC @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) )
= ( B @ C @ D @ E @ F @ G @ ( rBT_Im1947144893ec_rbt @ TC @ TA @ TB @ A @ B @ D ) @ ( rBT_Im1947144893ec_rbt @ TC @ TA @ TB @ A @ B @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(15,axiom,
! [A: rBT_Im1923302023_color > $o,B: rBT_Im1923302023_color] :
( ( A @ rBT_Impl_Mirabelle_R )
=> ( ( A @ rBT_Impl_Mirabelle_B )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_color_Oinduct) ).
thf(85,plain,
! [A: rBT_Im1923302023_color > $o,B: rBT_Im1923302023_color] :
( ( A @ rBT_Impl_Mirabelle_R )
=> ( ( A @ rBT_Impl_Mirabelle_B )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(32,axiom,
! [A: rBT_Im246033960le_rbt @ a @ b,B: a,C: b,D: rBT_Im246033960le_rbt @ a @ b] :
( ( t
= ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) )
=> thesis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Black) ).
thf(137,plain,
! [A: rBT_Im246033960le_rbt @ a @ b,B: a,C: b,D: rBT_Im246033960le_rbt @ a @ b] :
( ( t
= ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) )
=> thesis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im418718756_Empty @ TA @ TB )
!= ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_rbt_Odistinct_I1_J) ).
thf(97,plain,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im418718756_Empty @ TA @ TB )
!= ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(33,axiom,
! [A: rBT_Im246033960le_rbt @ a @ b,B: a,C: b,D: rBT_Im246033960le_rbt @ a @ b] :
( ( t
= ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) )
=> thesis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(141,plain,
! [A: rBT_Im246033960le_rbt @ a @ b,B: a,C: b,D: rBT_Im246033960le_rbt @ a @ b] :
( ( t
= ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) )
=> thesis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A
!= ( rBT_Im418718756_Empty @ TA @ TB ) )
=> ~ ! [B: rBT_Im1923302023_color,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( rBT_Im480247531Branch @ TA @ TB @ B @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_rbt_Oexhaust) ).
thf(124,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A
!= ( rBT_Im418718756_Empty @ TA @ TB ) )
=> ~ ! [B: rBT_Im1923302023_color,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( rBT_Im480247531Branch @ TA @ TB @ B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TD @ TC,E: TD,F: TC,G: rBT_Im246033960le_rbt @ TD @ TC,H: rBT_Im1923302023_color,I: rBT_Im246033960le_rbt @ TA @ TB,J: TA,K: TB,L: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1000242676el_rbt @ TD @ TA @ TC @ TB @ A @ B @ ( rBT_Im480247531Branch @ TD @ TC @ C @ D @ E @ F @ G ) @ ( rBT_Im480247531Branch @ TA @ TB @ H @ I @ J @ K @ L ) )
= ( ( C = H )
& ( rBT_Im1000242676el_rbt @ TD @ TA @ TC @ TB @ A @ B @ D @ I )
& ( A @ E @ J )
& ( B @ F @ K )
& ( rBT_Im1000242676el_rbt @ TD @ TA @ TC @ TB @ A @ B @ G @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_rbt_Orel__inject_I2_J) ).
thf(45,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TD @ TC,E: TD,F: TC,G: rBT_Im246033960le_rbt @ TD @ TC,H: rBT_Im1923302023_color,I: rBT_Im246033960le_rbt @ TA @ TB,J: TA,K: TB,L: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1000242676el_rbt @ TD @ TA @ TC @ TB @ A @ B @ ( rBT_Im480247531Branch @ TD @ TC @ C @ D @ E @ F @ G ) @ ( rBT_Im480247531Branch @ TA @ TB @ H @ I @ J @ K @ L ) )
= ( ( C = H )
& ( rBT_Im1000242676el_rbt @ TD @ TA @ TC @ TB @ A @ B @ D @ I )
& ( A @ E @ J )
& ( B @ F @ K )
& ( rBT_Im1000242676el_rbt @ TD @ TA @ TC @ TB @ A @ B @ G @ L ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType] :
( ( rBT_Im1000242676el_rbt @ TA @ TA @ TB @ TB @ ( (=) @ TA ) @ ( (=) @ TB ) )
= ( (=) @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_rbt_Orel__eq) ).
thf(59,plain,
! [TA: $tType,TB: $tType] :
( ( rBT_Im1000242676el_rbt @ TA @ TA @ TB @ TB @ ( (=) @ TA ) @ ( (=) @ TB ) )
= ( (=) @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TB > TB > $o,C: rBT_Im246033960le_rbt @ TA @ TB] :
( ! [D: TA] : ( A @ D @ D )
=> ( ! [D: TB] : ( B @ D @ D )
=> ( rBT_Im1000242676el_rbt @ TA @ TA @ TB @ TB @ A @ B @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_rbt_Orel__refl) ).
thf(54,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TB > TB > $o,C: rBT_Im246033960le_rbt @ TA @ TB] :
( ! [D: TA] : ( A @ D @ D )
=> ( ! [D: TB] : ( B @ D @ D )
=> ( rBT_Im1000242676el_rbt @ TA @ TA @ TB @ TB @ A @ B @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(34,axiom,
! [A: rBT_Im246033960le_rbt @ a @ b,B: a,C: b,D: rBT_Im246033960le_rbt @ a @ b] :
( ( t
= ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ A @ B @ C @ D ) )
=> thesis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_Red) ).
thf(145,plain,
! [A: rBT_Im246033960le_rbt @ a @ b,B: a,C: b,D: rBT_Im246033960le_rbt @ a @ b] :
( ( t
= ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ A @ B @ C @ D ) )
=> thesis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TB > $o,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1931894874ed_rbt @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) )
= ( ( rBT_Im1931894874ed_rbt @ TA @ TB @ A @ B @ D )
& ( A @ E )
& ( B @ F )
& ( rBT_Im1931894874ed_rbt @ TA @ TB @ A @ B @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_rbt_Opred__inject_I2_J) ).
thf(48,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TB > $o,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1931894874ed_rbt @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) )
= ( ( rBT_Im1931894874ed_rbt @ TA @ TB @ A @ B @ D )
& ( A @ E )
& ( B @ F )
& ( rBT_Im1931894874ed_rbt @ TA @ TB @ A @ B @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ TC @ TB ) > TC > TB > ( rBT_Im246033960le_rbt @ TC @ TB ) > TA > TA > TA] :
( ( rBT_Im1947144893ec_rbt @ TA @ TC @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TC @ TB ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_rbt_Osimps_I6_J) ).
thf(127,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ TC @ TB ) > TC > TB > ( rBT_Im246033960le_rbt @ TC @ TB ) > TA > TA > TA] :
( ( rBT_Im1947144893ec_rbt @ TA @ TC @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TC @ TB ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] : ( rBT_Im1000242676el_rbt @ TD @ TA @ TC @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TD @ TC ) @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_rbt_Octr__transfer_I1_J) ).
thf(43,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] : ( rBT_Im1000242676el_rbt @ TD @ TA @ TC @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TD @ TC ) @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TB,D: rBT_Im1923302023_color] :
( ( A @ ( rBT_Im1975547051_color @ TB @ B @ C @ D ) )
= ( rBT_Im1975547051_color @ TA @ ( A @ B ) @ ( A @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_color_Ocase__distrib) ).
thf(40,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TB,D: rBT_Im1923302023_color] :
( ( A @ ( rBT_Im1975547051_color @ TB @ B @ C @ D ) )
= ( rBT_Im1975547051_color @ TA @ ( A @ B ) @ ( A @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType,A: ( rBT_Im246033960le_rbt @ TA @ TB ) > $o,B: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A @ ( rBT_Im418718756_Empty @ TA @ TB ) )
=> ( ! [C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A @ D )
=> ( ( A @ G )
=> ( A @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_rbt_Oinduct) ).
thf(62,plain,
! [TA: $tType,TB: $tType,A: ( rBT_Im246033960le_rbt @ TA @ TB ) > $o,B: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A @ ( rBT_Im418718756_Empty @ TA @ TB ) )
=> ( ! [C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A @ D )
=> ( ( A @ G )
=> ( A @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB,F: rBT_Im1923302023_color,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB] :
( ( ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E )
= ( rBT_Im480247531Branch @ TA @ TB @ F @ G @ H @ I @ J ) )
= ( ( A = F )
& ( B = G )
& ( C = H )
& ( D = I )
& ( E = J ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_rbt_Oinject) ).
thf(100,plain,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB,F: rBT_Im1923302023_color,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB] :
( ( ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E )
= ( rBT_Im480247531Branch @ TA @ TB @ F @ G @ H @ I @ J ) )
= ( ( A = F )
& ( B = G )
& ( C = H )
& ( D = I )
& ( E = J ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(31,axiom,
( ( t
= ( rBT_Im418718756_Empty @ a @ b ) )
=> thesis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_Empty) ).
thf(134,plain,
( ( t
= ( rBT_Im418718756_Empty @ a @ b ) )
=> thesis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
~ ( rBT_Im1000242676el_rbt @ TD @ TA @ TC @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TD @ TC ) @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_rbt_Orel__distinct_I1_J) ).
thf(105,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
~ ( rBT_Im1000242676el_rbt @ TD @ TA @ TC @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TD @ TC ) @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(24,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( rBT_Im1059957627_color @ TA @ A @ B @ rBT_Impl_Mirabelle_B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_color_Osimps_I6_J) ).
thf(113,plain,
! [TA: $tType,A: TA,B: TA] :
( ( rBT_Im1059957627_color @ TA @ A @ B @ rBT_Impl_Mirabelle_B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA,B: TC > TB] :
( ( rBT_Im206295089ap_rbt @ TD @ TA @ TC @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TD @ TC ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_rbt_Osimps_I8_J) ).
thf(76,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA,B: TC > TB] :
( ( rBT_Im206295089ap_rbt @ TD @ TA @ TC @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TD @ TC ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TD @ TC,E: TD,F: TC,G: rBT_Im246033960le_rbt @ TD @ TC] :
~ ( rBT_Im1000242676el_rbt @ TD @ TA @ TC @ TB @ A @ B @ ( rBT_Im480247531Branch @ TD @ TC @ C @ D @ E @ F @ G ) @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_rbt_Orel__distinct_I2_J) ).
thf(103,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TD @ TC,E: TD,F: TC,G: rBT_Im246033960le_rbt @ TD @ TC] :
~ ( rBT_Im1000242676el_rbt @ TD @ TA @ TC @ TB @ A @ B @ ( rBT_Im480247531Branch @ TD @ TC @ C @ D @ E @ F @ G ) @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ TA @ TB ) > TA > TB > ( rBT_Im246033960le_rbt @ TA @ TB ) > TC,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im858806507se_rbt @ TC @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) )
= ( B @ C @ D @ E @ F @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_rbt_Osimps_I5_J) ).
thf(91,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ TA @ TB ) > TA > TB > ( rBT_Im246033960le_rbt @ TA @ TB ) > TC,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im858806507se_rbt @ TC @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) )
= ( B @ C @ D @ E @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(30,axiom,
! [A: rBT_Im246033960le_rbt @ a @ b,B: a,C: b,D: rBT_Im246033960le_rbt @ a @ b] :
( ( t
= ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ A @ B @ C @ D ) )
=> thesis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(130,plain,
! [A: rBT_Im246033960le_rbt @ a @ b,B: a,C: b,D: rBT_Im246033960le_rbt @ a @ b] :
( ( t
= ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ A @ B @ C @ D ) )
=> thesis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(2,negated_conjecture,
~ thesis,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(35,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TB > $o] : ( rBT_Im1931894874ed_rbt @ TA @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_rbt_Opred__inject_I1_J) ).
thf(119,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TB > $o] : ( rBT_Im1931894874ed_rbt @ TA @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(14,axiom,
! [A: rBT_Im1923302023_color] :
( ( A != rBT_Impl_Mirabelle_R )
=> ( A = rBT_Impl_Mirabelle_B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_color_Oexhaust) ).
thf(82,plain,
! [A: rBT_Im1923302023_color] :
( ( A != rBT_Impl_Mirabelle_R )
=> ( A = rBT_Impl_Mirabelle_B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: rBT_Im1923302023_color,B: rBT_Im1923302023_color,C: TD > TA > $o,D: TC > TB > $o,E: rBT_Im246033960le_rbt @ TD @ TC,F: rBT_Im246033960le_rbt @ TA @ TB,G: TD,H: TA,I: TC,J: TB,K: rBT_Im246033960le_rbt @ TD @ TC,L: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A = B )
=> ( ( rBT_Im1000242676el_rbt @ TD @ TA @ TC @ TB @ C @ D @ E @ F )
=> ( ( C @ G @ H )
=> ( ( D @ I @ J )
=> ( ( rBT_Im1000242676el_rbt @ TD @ TA @ TC @ TB @ C @ D @ K @ L )
=> ( rBT_Im1000242676el_rbt @ TD @ TA @ TC @ TB @ C @ D @ ( rBT_Im480247531Branch @ TD @ TC @ A @ E @ G @ I @ K ) @ ( rBT_Im480247531Branch @ TA @ TB @ B @ F @ H @ J @ L ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_rbt_Orel__intros_I2_J) ).
thf(36,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: rBT_Im1923302023_color,B: rBT_Im1923302023_color,C: TD > TA > $o,D: TC > TB > $o,E: rBT_Im246033960le_rbt @ TD @ TC,F: rBT_Im246033960le_rbt @ TA @ TB,G: TD,H: TA,I: TC,J: TB,K: rBT_Im246033960le_rbt @ TD @ TC,L: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A = B )
=> ( ( rBT_Im1000242676el_rbt @ TD @ TA @ TC @ TB @ C @ D @ E @ F )
=> ( ( C @ G @ H )
=> ( ( D @ I @ J )
=> ( ( rBT_Im1000242676el_rbt @ TD @ TA @ TC @ TB @ C @ D @ K @ L )
=> ( rBT_Im1000242676el_rbt @ TD @ TA @ TC @ TB @ C @ D @ ( rBT_Im480247531Branch @ TD @ TC @ A @ E @ G @ I @ K ) @ ( rBT_Im480247531Branch @ TA @ TB @ B @ F @ H @ J @ L ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TC,B: TB > TD,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im206295089ap_rbt @ TA @ TC @ TB @ TD @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) )
= ( rBT_Im480247531Branch @ TC @ TD @ C @ ( rBT_Im206295089ap_rbt @ TA @ TC @ TB @ TD @ A @ B @ D ) @ ( A @ E ) @ ( B @ F ) @ ( rBT_Im206295089ap_rbt @ TA @ TC @ TB @ TD @ A @ B @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_rbt_Osimps_I9_J) ).
thf(51,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TC,B: TB > TD,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im206295089ap_rbt @ TA @ TC @ TB @ TD @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) )
= ( rBT_Im480247531Branch @ TC @ TD @ C @ ( rBT_Im206295089ap_rbt @ TA @ TC @ TB @ TD @ A @ B @ D ) @ ( A @ E ) @ ( B @ F ) @ ( rBT_Im206295089ap_rbt @ TA @ TC @ TB @ TD @ A @ B @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(22,axiom,
rBT_Impl_Mirabelle_R != rBT_Impl_Mirabelle_B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_color_Odistinct_I1_J) ).
thf(107,plain,
rBT_Impl_Mirabelle_R != rBT_Impl_Mirabelle_B,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ TC @ TB ) > TC > TB > ( rBT_Im246033960le_rbt @ TC @ TB ) > TA] :
( ( rBT_Im858806507se_rbt @ TA @ TC @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TC @ TB ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_rbt_Osimps_I4_J) ).
thf(79,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ TC @ TB ) > TC > TB > ( rBT_Im246033960le_rbt @ TC @ TB ) > TA] :
( ( rBT_Im858806507se_rbt @ TA @ TC @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TC @ TB ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(17,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( rBT_Im1975547051_color @ TA @ A @ B @ rBT_Impl_Mirabelle_B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_color_Osimps_I4_J) ).
thf(94,plain,
! [TA: $tType,A: TA,B: TA] :
( ( rBT_Im1975547051_color @ TA @ A @ B @ rBT_Impl_Mirabelle_B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(151,plain,
$false,
inference(e,[status(thm)],[110,121,116,85,137,97,141,124,45,59,54,145,48,127,43,40,62,100,134,105,113,76,103,91,130,35,119,82,36,51,107,79,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT229^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % 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
% 0.10/0.22 % Computer : n006.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 18:12:39 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 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
% 0.98/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.90/1.19 % [INFO] Parsing done (368ms).
% 2.20/1.20 % [INFO] Running in sequential loop mode.
% 3.00/1.58 % [INFO] eprover registered as external prover.
% 3.00/1.59 % [INFO] Scanning for conjecture ...
% 3.38/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 283 axioms. Running axiom selection ...
% 3.57/1.81 % [INFO] Axiom selection finished. Selected 32 axioms (removed 251 axioms).
% 3.91/1.97 % [INFO] Problem is higher-order (TPTP THF).
% 3.91/1.98 % [INFO] Type checking passed.
% 3.91/1.99 % [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 ...
% 6.28/2.63 % [INFO] [Domain constraints] Detected constraint on rBT_Im1923302023_color
% 6.28/2.63 % [INFO] [Domain constraints] dom(rBT_Im1923302023_color) ⊆ {rBT_Impl_Mirabelle_R,rBT_Impl_Mirabelle_B}
% 8.25/3.29 % External prover 'e' found a proof!
% 8.25/3.29 % [INFO] Killing All external provers ...
% 8.25/3.29 % Time passed: 2919ms (effective reasoning time: 2086ms)
% 8.25/3.29 % 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)>
% 8.25/3.29 % Axioms used in derivation (32): fact_24_color_Ocase__distrib, fact_19_rbt_Orel__distinct_I2_J, fact_11_color_Osimps_I5_J, fact_21_rbt_Opred__inject_I1_J, fact_37_rbt_Osimps_I8_J, fact_14_rbt_Osimps_I4_J, fact_18_rbt_Opred__inject_I2_J, fact_51_rbt_Osimps_I9_J, conj_1, fact_0_Empty, fact_8_color_Oinduct, fact_23_rbt_Orel__refl, fact_25_rbt_Orel__intros_I2_J, fact_2_Black, fact_10_color_Osimps_I6_J, fact_17_rbt_Osimps_I7_J, fact_6_rbt_Oinduct, fact_26_rbt_Orel__inject_I2_J, fact_15_rbt_Osimps_I5_J, fact_1_rbt_Oinject, fact_9_color_Oexhaust, fact_27_rbt_Octr__transfer_I1_J, conj_2, fact_22_rbt_Orel__eq, fact_20_rbt_Orel__distinct_I1_J, fact_5_color_Odistinct_I1_J, fact_7_rbt_Oexhaust, fact_13_color_Osimps_I3_J, fact_3_Red, fact_12_color_Osimps_I4_J, fact_16_rbt_Osimps_I6_J, fact_4_rbt_Odistinct_I1_J
% 8.25/3.29 % No. of inferences in proof: 68
% 8.25/3.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2919 ms resp. 2086 ms w/o parsing
% 8.57/3.39 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.57/3.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------