TSTP Solution File: DAT231^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT231^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 7 07:39:48 EDT 2024
% Result : Theorem 6.61s 2.40s
% Output : Refutation 6.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 49
% Syntax : Number of formulae : 82 ( 58 unt; 18 typ; 0 def)
% Number of atoms : 146 ( 64 equ; 6 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 1259 ( 14 ~; 2 |; 44 &;1175 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 11 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 183 ( 183 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 5 con; 0-8 aty)
% Number of variables : 452 ( 0 ^ 424 !; 0 ?; 452 :)
% ( 28 !>; 0 ?*; 0 @-; 0 @+)
% 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_type,type,
rBT_Impl_Mirabelle_B: rBT_Im1923302023_color ).
thf(rBT_Im1805589839lor_of_type,type,
rBT_Im1805589839lor_of:
!>[TA: $tType,TB: $tType] : ( ( rBT_Im246033960le_rbt @ TB @ TA ) > rBT_Im1923302023_color ) ).
thf(rBT_Im1040612427e_inv1_type,type,
rBT_Im1040612427e_inv1:
!>[TA: $tType,TB: $tType] : ( ( rBT_Im246033960le_rbt @ TB @ TA ) > $o ) ).
thf(rBT_Im1071879905_inv1l_type,type,
rBT_Im1071879905_inv1l:
!>[TA: $tType,TB: $tType] : ( ( rBT_Im246033960le_rbt @ TB @ TA ) > $o ) ).
thf(rBT_Im1259024060reater_type,type,
rBT_Im1259024060reater:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > TB > ( rBT_Im246033960le_rbt @ TB @ TA ) > $o ) ).
thf(rBT_Im2075124343t_less_type,type,
rBT_Im2075124343t_less:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > TB > ( rBT_Im246033960le_rbt @ TB @ TA ) > $o ) ).
thf(rBT_Im759614907sorted_type,type,
rBT_Im759614907sorted:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > ( rBT_Im246033960le_rbt @ TB @ TA ) > $o ) ).
thf(rBT_Im480247531Branch_type,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_type,type,
rBT_Im418718756_Empty:
!>[TA: $tType,TB: $tType] : ( rBT_Im246033960le_rbt @ TB @ TA ) ).
thf(rBT_Im858806507se_rbt_type,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_Im1931894874ed_rbt_type,type,
rBT_Im1931894874ed_rbt:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TA > $o ) > ( rBT_Im246033960le_rbt @ TB @ TA ) > $o ) ).
thf(rBT_Im1947144893ec_rbt_type,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_type,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_type,type,
t: rBT_Im246033960le_rbt @ a @ b ).
thf(30,axiom,
rBT_Im1040612427e_inv1 @ a @ b @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(120,plain,
rBT_Im1040612427e_inv1 @ a @ b @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: rBT_Im1923302023_color,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im759614907sorted @ TA @ TB @ A @ ( rBT_Im480247531Branch @ TA @ TB @ B @ C @ D @ E @ F ) )
= ( ( rBT_Im2075124343t_less @ TA @ TB @ A @ D @ C )
& ( rBT_Im1259024060reater @ TA @ TB @ A @ D @ F )
& ( rBT_Im759614907sorted @ TA @ TB @ A @ C )
& ( rBT_Im759614907sorted @ TA @ TB @ A @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_ord_Orbt__sorted_Osimps_I2_J) ).
thf(52,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: rBT_Im1923302023_color,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im759614907sorted @ TA @ TB @ A @ ( rBT_Im480247531Branch @ TA @ TB @ B @ C @ D @ E @ F ) )
= ( ( rBT_Im2075124343t_less @ TA @ TB @ A @ D @ C )
& ( rBT_Im1259024060reater @ TA @ TB @ A @ D @ F )
& ( rBT_Im759614907sorted @ TA @ TB @ A @ C )
& ( rBT_Im759614907sorted @ TA @ TB @ A @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,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_102_rbt_Orel__eq) ).
thf(46,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)],[7]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) )
= ( ( A @ B @ E )
& ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ D )
& ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_ord_Orbt__greater__simps_I2_J) ).
thf(74,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) )
= ( ( A @ B @ E )
& ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ D )
& ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,conjecture,
rBT_Im1071879905_inv1l @ a @ b @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ( rBT_Im1071879905_inv1l @ a @ b @ t ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(33,plain,
~ ( rBT_Im1071879905_inv1l @ a @ b @ t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType] :
( ( rBT_Im1805589839lor_of @ TB @ TA @ ( rBT_Im418718756_Empty @ TB @ TA ) )
= rBT_Impl_Mirabelle_B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_color__of_Osimps_I1_J) ).
thf(34,plain,
! [TA: $tType,TB: $tType] :
( ( rBT_Im1805589839lor_of @ TB @ TA @ ( rBT_Im418718756_Empty @ TB @ TA ) )
= rBT_Impl_Mirabelle_B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,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_104_rbt_Orel__inject_I2_J) ).
thf(39,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)],[5]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o] : ( rBT_Im759614907sorted @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_ord_Orbt__sorted_Osimps_I1_J) ).
thf(80,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o] : ( rBT_Im759614907sorted @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType] : ( rBT_Im1040612427e_inv1 @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_inv1_Osimps_I1_J) ).
thf(82,plain,
! [TA: $tType,TB: $tType] : ( rBT_Im1040612427e_inv1 @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(25,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_94_rbt_Orel__distinct_I2_J) ).
thf(107,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)],[25]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TB @ TA,C: TB,D: TA,E: rBT_Im246033960le_rbt @ TB @ TA] :
( ( rBT_Im1040612427e_inv1 @ TB @ TA @ ( rBT_Im480247531Branch @ TB @ TA @ A @ B @ C @ D @ E ) )
= ( ( rBT_Im1040612427e_inv1 @ TB @ TA @ B )
& ( rBT_Im1040612427e_inv1 @ TB @ TA @ E )
& ( ( A = rBT_Impl_Mirabelle_B )
| ( ( ( rBT_Im1805589839lor_of @ TB @ TA @ B )
= rBT_Impl_Mirabelle_B )
& ( ( rBT_Im1805589839lor_of @ TB @ TA @ E )
= rBT_Impl_Mirabelle_B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_inv1_Osimps_I2_J) ).
thf(111,plain,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TB @ TA,C: TB,D: TA,E: rBT_Im246033960le_rbt @ TB @ TA] :
( ( rBT_Im1040612427e_inv1 @ TB @ TA @ ( rBT_Im480247531Branch @ TB @ TA @ A @ B @ C @ D @ E ) )
= ( ( rBT_Im1040612427e_inv1 @ TB @ TA @ B )
& ( rBT_Im1040612427e_inv1 @ TB @ TA @ E )
& ( ( A = rBT_Impl_Mirabelle_B )
| ( ( ( rBT_Im1805589839lor_of @ TB @ TA @ B )
= rBT_Impl_Mirabelle_B )
& ( ( rBT_Im1805589839lor_of @ TB @ TA @ E )
= rBT_Impl_Mirabelle_B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(6,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_103_rbt_Orel__intros_I2_J) ).
thf(42,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)],[6]) ).
thf(4,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_105_rbt_Octr__transfer_I1_J) ).
thf(37,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)],[4]) ).
thf(31,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_Im1071879905_inv1l @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E ) )
= ( ( rBT_Im1040612427e_inv1 @ TA @ TB @ B )
& ( rBT_Im1040612427e_inv1 @ TA @ TB @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_inv1l_Osimps_I2_J) ).
thf(121,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_Im1071879905_inv1l @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E ) )
= ( ( rBT_Im1040612427e_inv1 @ TA @ TB @ B )
& ( rBT_Im1040612427e_inv1 @ TA @ TB @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(20,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_10_rbt_Oinduct) ).
thf(84,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)],[20]) ).
thf(23,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_95_rbt_Orel__distinct_I1_J) ).
thf(102,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)],[23]) ).
thf(11,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_106_rbt_Opred__inject_I1_J) ).
thf(60,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)],[11]) ).
thf(29,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_7_rbt_Odistinct_I1_J) ).
thf(117,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)],[29]) ).
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_21_rbt_Osimps_I4_J) ).
thf(65,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(21,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA] : ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_ord_Orbt__less__simps_I1_J) ).
thf(97,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA] : ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA] : ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_ord_Orbt__greater__simps_I1_J) ).
thf(109,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA] : ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType] : ( rBT_Im1071879905_inv1l @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_inv1l_Osimps_I1_J) ).
thf(124,plain,
! [TA: $tType,TB: $tType] : ( rBT_Im1071879905_inv1l @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(17,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_33_rbt_Osimps_I7_J) ).
thf(77,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)],[17]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) )
= ( ( A @ E @ B )
& ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ D )
& ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_ord_Orbt__less__simps_I2_J) ).
thf(71,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) )
= ( ( A @ E @ B )
& ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ D )
& ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(8,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_93_rbt_Opred__inject_I2_J) ).
thf(49,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)],[8]) ).
thf(22,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_11_rbt_Oexhaust) ).
thf(99,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)],[22]) ).
thf(24,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_22_rbt_Osimps_I5_J) ).
thf(104,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)],[24]) ).
thf(10,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_101_rbt_Orel__refl) ).
thf(55,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)],[10]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TB @ TA,C: TB,D: TA,E: rBT_Im246033960le_rbt @ TB @ TA] :
( ( rBT_Im1805589839lor_of @ TB @ TA @ ( rBT_Im480247531Branch @ TB @ TA @ A @ B @ C @ D @ E ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_color__of_Osimps_I2_J) ).
thf(114,plain,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TB @ TA,C: TB,D: TA,E: rBT_Im246033960le_rbt @ TB @ TA] :
( ( rBT_Im1805589839lor_of @ TB @ TA @ ( rBT_Im480247531Branch @ TB @ TA @ A @ B @ C @ D @ E ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(14,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_5_rbt_Oinject) ).
thf(68,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)],[14]) ).
thf(12,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_32_rbt_Osimps_I6_J) ).
thf(62,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)],[12]) ).
thf(126,plain,
$false,
inference(e,[status(thm)],[120,52,46,74,33,34,39,80,82,107,111,42,37,121,84,102,60,117,65,97,109,124,77,71,49,99,104,55,114,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : DAT231^1 : TPTP v8.1.2. Released v7.0.0.
% 0.03/0.13 % Command : run_Leo-III %s %d
% 0.13/0.32 % Computer : n032.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 6 11:35:38 EDT 2024
% 0.13/0.32 % CPUTime :
% 0.67/0.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.47/0.96 % [INFO] Parsing done (234ms).
% 1.62/0.97 % [INFO] Running in sequential loop mode.
% 2.28/1.18 % [INFO] eprover registered as external prover.
% 2.35/1.18 % [INFO] cvc4 registered as external prover.
% 2.35/1.19 % [INFO] Scanning for conjecture ...
% 2.52/1.29 % [INFO] Found a conjecture and 288 axioms. Running axiom selection ...
% 2.70/1.34 % [INFO] Axiom selection finished. Selected 30 axioms (removed 258 axioms).
% 2.89/1.43 % [INFO] Problem is higher-order (TPTP THF).
% 2.89/1.44 % [INFO] Type checking passed.
% 2.89/1.45 % [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 ...
% 6.61/2.40 % External prover 'e' found a proof!
% 6.61/2.40 % [INFO] Killing All external provers ...
% 6.61/2.40 % Time passed: 1966ms (effective reasoning time: 1431ms)
% 6.61/2.40 % 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)>
% 6.61/2.40 % Axioms used in derivation (30): fact_27_ord_Orbt__sorted_Osimps_I2_J, fact_93_rbt_Opred__inject_I2_J, fact_5_rbt_Oinject, fact_3_inv1_Osimps_I2_J, fact_104_rbt_Orel__inject_I2_J, fact_0_inv1l_Osimps_I2_J, fact_106_rbt_Opred__inject_I1_J, fact_9_color__of_Osimps_I1_J, conj_0, fact_102_rbt_Orel__eq, fact_10_rbt_Oinduct, fact_8_color__of_Osimps_I2_J, fact_2_inv1_Osimps_I1_J, fact_33_rbt_Osimps_I7_J, fact_105_rbt_Octr__transfer_I1_J, fact_29_ord_Orbt__less__simps_I1_J, fact_14_ord_Orbt__sorted_Osimps_I1_J, fact_31_ord_Orbt__less__simps_I2_J, fact_22_rbt_Osimps_I5_J, fact_94_rbt_Orel__distinct_I2_J, fact_21_rbt_Osimps_I4_J, fact_103_rbt_Orel__intros_I2_J, fact_1_inv1l_Osimps_I1_J, fact_11_rbt_Oexhaust, fact_101_rbt_Orel__refl, fact_95_rbt_Orel__distinct_I1_J, fact_28_ord_Orbt__greater__simps_I1_J, fact_30_ord_Orbt__greater__simps_I2_J, fact_7_rbt_Odistinct_I1_J, fact_32_rbt_Osimps_I6_J
% 6.61/2.40 % No. of inferences in proof: 64
% 6.61/2.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1966 ms resp. 1431 ms w/o parsing
% 6.84/2.45 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.84/2.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------