%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET741^4 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Wed Oct 7 10:40:57 AM UTC 2026
% Result : Theorem 0.07s 0.16s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 76 ( 71 unt; 0 typ; 8 def)
% Number of atoms : 282 ( 192 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 418 ( 51 ~; 14 |; 20 &; 309 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 177 ( 16 ^; 136 !; 25 ?; 177 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_fun_bijective,type,
fun_bijective: ( $i > $i ) > $o ).
thf(tp_fun_composition,type,
fun_composition: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(tp_fun_decreasing,type,
fun_decreasing: ( $i > $i ) > ( $i > $i > $o ) > $o ).
thf(tp_fun_image,type,
fun_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).
thf(tp_fun_increasing,type,
fun_increasing: ( $i > $i ) > ( $i > $i > $o ) > $o ).
thf(tp_fun_injective,type,
fun_injective: ( $i > $i ) > $o ).
thf(tp_fun_inv_image,type,
fun_inv_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).
thf(tp_fun_surjective,type,
fun_surjective: ( $i > $i ) > $o ).
thf(tp_sK10_SY82,type,
sK10_SY82: $i > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i > $i ).
thf(tp_sK2_SY44,type,
sK2_SY44: $i > $i ).
thf(tp_sK3_SY56,type,
sK3_SY56: $i > $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SY77,type,
sK5_SY77: $i > $i ).
thf(tp_sK6_SY78,type,
sK6_SY78: $i > $i ).
thf(tp_sK7_SY80,type,
sK7_SY80: $i ).
thf(tp_sK8_SX0,type,
sK8_SX0: $i ).
thf(tp_sK9_SY81,type,
sK9_SY81: $i > $i ).
thf(fun_bijective,definition,
( fun_bijective
= ( ^ [F: $i > $i] :
( ( fun_injective @ F )
& ( fun_surjective @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_bijective) ).
thf(fun_composition,definition,
( fun_composition
= ( ^ [F: $i > $i,G: $i > $i,X: $i] : ( G @ ( F @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_composition) ).
thf(fun_decreasing,definition,
( fun_decreasing
= ( ^ [F: $i > $i,SMALLER: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( SMALLER @ X @ Y )
=> ( SMALLER @ ( F @ Y ) @ ( F @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_decreasing) ).
thf(fun_image,definition,
( fun_image
= ( ^ [F: $i > $i,A: $i > $o,Y: $i] :
? [X: $i] :
( ( A @ X )
& ( Y
= ( F @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_image) ).
thf(fun_increasing,definition,
( fun_increasing
= ( ^ [F: $i > $i,SMALLER: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( SMALLER @ X @ Y )
=> ( SMALLER @ ( F @ X ) @ ( F @ Y ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_increasing) ).
thf(fun_injective,definition,
( fun_injective
= ( ^ [F: $i > $i] :
! [X: $i,Y: $i] :
( ( ( F @ X )
= ( F @ Y ) )
=> ( X = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_injective) ).
thf(fun_inv_image,definition,
( fun_inv_image
= ( ^ [F: $i > $i,B: $i > $o,X: $i] :
? [Y: $i] :
( ( B @ Y )
& ( Y
= ( F @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_inv_image) ).
thf(fun_surjective,definition,
( fun_surjective
= ( ^ [F: $i > $i] :
! [Y: $i] :
? [X: $i] :
( Y
= ( F @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fun_surjective) ).
thf(1,conjecture,
! [F: $i > $i,G: $i > $i,H: $i > $i] :
( ( ( fun_injective @ ( fun_composition @ ( fun_composition @ F @ G ) @ H ) )
& ( fun_surjective @ ( fun_composition @ ( fun_composition @ G @ H ) @ F ) )
& ( fun_surjective @ ( fun_composition @ ( fun_composition @ H @ F ) @ G ) ) )
=> ( fun_bijective @ H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
( ( ! [F: $i > $i,G: $i > $i,H: $i > $i] :
( ( ( fun_injective @ ( fun_composition @ ( fun_composition @ F @ G ) @ H ) )
& ( fun_surjective @ ( fun_composition @ ( fun_composition @ G @ H ) @ F ) )
& ( fun_surjective @ ( fun_composition @ ( fun_composition @ H @ F ) @ G ) ) )
=> ( fun_bijective @ H ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i > $i,SY1: $i > $i,SY2: $i > $i] :
( ( ! [SY9: $i,SY10: $i] :
( ( ( SY2 @ ( SY1 @ ( SY0 @ SY9 ) ) )
= ( SY2 @ ( SY1 @ ( SY0 @ SY10 ) ) ) )
=> ( SY9 = SY10 ) )
& ! [SY17: $i] :
? [SY18: $i] :
( SY17
= ( SY0 @ ( SY2 @ ( SY1 @ SY18 ) ) ) )
& ! [SY25: $i] :
? [SY26: $i] :
( SY25
= ( SY1 @ ( SY0 @ ( SY2 @ SY26 ) ) ) ) )
=> ( ! [SY27: $i,SY28: $i] :
( ( ( SY2 @ SY27 )
= ( SY2 @ SY28 ) )
=> ( SY27 = SY28 ) )
& ! [SY29: $i] :
? [SY30: $i] :
( SY29
= ( SY2 @ SY30 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,fun_bijective,fun_composition,fun_decreasing,fun_image,fun_increasing,fun_injective,fun_inv_image,fun_surjective]) ).
thf(4,plain,
( ( ! [SY44: $i > $i,SY45: $i > $i] :
( ( ! [SY46: $i,SY47: $i] :
( ( ( SY45 @ ( SY44 @ ( sK1_SY0 @ SY46 ) ) )
= ( SY45 @ ( SY44 @ ( sK1_SY0 @ SY47 ) ) ) )
=> ( SY46 = SY47 ) )
& ! [SY48: $i] :
? [SY49: $i] :
( SY48
= ( sK1_SY0 @ ( SY45 @ ( SY44 @ SY49 ) ) ) )
& ! [SY50: $i] :
? [SY51: $i] :
( SY50
= ( SY44 @ ( sK1_SY0 @ ( SY45 @ SY51 ) ) ) ) )
=> ( ! [SY27: $i,SY28: $i] :
( ( ( SY45 @ SY27 )
= ( SY45 @ SY28 ) )
=> ( SY27 = SY28 ) )
& ! [SY29: $i] :
? [SY30: $i] :
( SY29
= ( SY45 @ SY30 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY56: $i > $i] :
( ( ! [SY57: $i,SY58: $i] :
( ( ( SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SY57 ) ) )
= ( SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SY58 ) ) ) )
=> ( SY57 = SY58 ) )
& ! [SY59: $i] :
? [SY60: $i] :
( SY59
= ( sK1_SY0 @ ( SY56 @ ( sK2_SY44 @ SY60 ) ) ) )
& ! [SY61: $i] :
? [SY62: $i] :
( SY61
= ( sK2_SY44 @ ( sK1_SY0 @ ( SY56 @ SY62 ) ) ) ) )
=> ( ! [SY27: $i,SY28: $i] :
( ( ( SY56 @ SY27 )
= ( SY56 @ SY28 ) )
=> ( SY27 = SY28 ) )
& ! [SY29: $i] :
? [SY30: $i] :
( SY29
= ( SY56 @ SY30 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ( ! [SY67: $i,SY68: $i] :
( ( ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SY67 ) ) )
= ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SY68 ) ) ) )
=> ( SY67 = SY68 ) )
& ! [SY69: $i] :
? [SY70: $i] :
( SY69
= ( sK1_SY0 @ ( sK3_SY56 @ ( sK2_SY44 @ SY70 ) ) ) )
& ! [SY71: $i] :
? [SY72: $i] :
( SY71
= ( sK2_SY44 @ ( sK1_SY0 @ ( sK3_SY56 @ SY72 ) ) ) ) )
=> ( ! [SY73: $i,SY74: $i] :
( ( ( sK3_SY56 @ SY73 )
= ( sK3_SY56 @ SY74 ) )
=> ( SY73 = SY74 ) )
& ! [SY75: $i] :
? [SY76: $i] :
( SY75
= ( sK3_SY56 @ SY76 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ! [SY67: $i,SY68: $i] :
( ( ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SY67 ) ) )
= ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SY68 ) ) ) )
=> ( SY67 = SY68 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY69: $i] :
? [SY70: $i] :
( SY69
= ( sK1_SY0 @ ( sK3_SY56 @ ( sK2_SY44 @ SY70 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(9,plain,
( ( ! [SY71: $i] :
? [SY72: $i] :
( SY71
= ( sK2_SY44 @ ( sK1_SY0 @ ( sK3_SY56 @ SY72 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(10,plain,
( ( ! [SY73: $i,SY74: $i] :
( ( ( sK3_SY56 @ SY73 )
= ( sK3_SY56 @ SY74 ) )
=> ( SY73 = SY74 ) )
& ! [SY75: $i] :
? [SY76: $i] :
( SY75
= ( sK3_SY56 @ SY76 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(11,plain,
( ( ! [SY73: $i,SY74: $i] :
( ( ( sK3_SY56 @ SY73 )
= ( sK3_SY56 @ SY74 ) )
=> ( SY73 = SY74 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[10]) ).
thf(12,plain,
( ( ! [SY75: $i] :
? [SY76: $i] :
( SY75
= ( sK3_SY56 @ SY76 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[10]) ).
thf(13,plain,
( ( ~ ! [SY73: $i,SY74: $i] :
( ( ( sK3_SY56 @ SY73 )
= ( sK3_SY56 @ SY74 ) )
=> ( SY73 = SY74 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ! [SY75: $i] :
? [SY76: $i] :
( SY75
= ( sK3_SY56 @ SY76 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(15,plain,
( ( ! [SY71: $i] :
? [SY72: $i] :
( SY71
= ( sK2_SY44 @ ( sK1_SY0 @ ( sK3_SY56 @ SY72 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(16,plain,
( ( ! [SY69: $i] :
? [SY70: $i] :
( SY69
= ( sK1_SY0 @ ( sK3_SY56 @ ( sK2_SY44 @ SY70 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(17,plain,
( ( ! [SY67: $i,SY68: $i] :
( ( ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SY67 ) ) )
= ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SY68 ) ) ) )
=> ( SY67 = SY68 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(18,plain,
( ( ~ ! [SY73: $i,SY74: $i] :
( ( ( sK3_SY56 @ SY73 )
= ( sK3_SY56 @ SY74 ) )
=> ( SY73 = SY74 ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(19,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
( SX0
!= ( sK2_SY44 @ ( sK1_SY0 @ ( sK3_SY56 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,fun_bijective,fun_composition,fun_decreasing,fun_image,fun_increasing,fun_injective,fun_inv_image,fun_surjective]) ).
thf(20,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
( SX0
!= ( sK1_SY0 @ ( sK3_SY56 @ ( sK2_SY44 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,fun_bijective,fun_composition,fun_decreasing,fun_image,fun_increasing,fun_injective,fun_inv_image,fun_surjective]) ).
thf(21,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SX0 ) ) )
!= ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SX1 ) ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17,fun_bijective,fun_composition,fun_decreasing,fun_image,fun_increasing,fun_injective,fun_inv_image,fun_surjective]) ).
thf(22,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( sK3_SY56 @ SX0 )
!= ( sK3_SY56 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18,fun_bijective,fun_composition,fun_decreasing,fun_image,fun_increasing,fun_injective,fun_inv_image,fun_surjective]) ).
thf(23,plain,
! [SV1: $i] :
( ( ~ ! [SY77: $i] :
( SV1
!= ( sK2_SY44 @ ( sK1_SY0 @ ( sK3_SY56 @ SY77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV2: $i] :
( ( ~ ! [SY78: $i] :
( SV2
!= ( sK1_SY0 @ ( sK3_SY56 @ ( sK2_SY44 @ SY78 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV3: $i] :
( ( ! [SY79: $i] :
( ( ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SV3 ) ) )
!= ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SY79 ) ) ) )
| ( SV3 = SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( sK3_SY56 @ SX0 )
!= ( sK3_SY56 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV1: $i] :
( ( ! [SY77: $i] :
( SV1
!= ( sK2_SY44 @ ( sK1_SY0 @ ( sK3_SY56 @ SY77 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV2: $i] :
( ( ! [SY78: $i] :
( SV2
!= ( sK1_SY0 @ ( sK3_SY56 @ ( sK2_SY44 @ SY78 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV4: $i,SV3: $i] :
( ( ( ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SV3 ) ) )
!= ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SV4 ) ) ) )
| ( SV3 = SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(30,plain,
( ( ! [SY80: $i] :
( ( ( sK3_SY56 @ sK4_SX0 )
!= ( sK3_SY56 @ SY80 ) )
| ( sK4_SX0 = SY80 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[26]) ).
thf(31,plain,
! [SV1: $i] :
( ( SV1
!= ( sK2_SY44 @ ( sK1_SY0 @ ( sK3_SY56 @ ( sK5_SY77 @ SV1 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(32,plain,
! [SV2: $i] :
( ( SV2
!= ( sK1_SY0 @ ( sK3_SY56 @ ( sK2_SY44 @ ( sK6_SY78 @ SV2 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[28]) ).
thf(33,plain,
! [SV4: $i,SV3: $i] :
( ( ( ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SV3 ) ) )
!= ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SV4 ) ) ) )
= $true )
| ( ( SV3 = SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(34,plain,
( ( ( ( sK3_SY56 @ sK4_SX0 )
!= ( sK3_SY56 @ sK7_SY80 ) )
| ( sK4_SX0 = sK7_SY80 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(35,plain,
! [SV1: $i] :
( ( SV1
= ( sK2_SY44 @ ( sK1_SY0 @ ( sK3_SY56 @ ( sK5_SY77 @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(36,plain,
! [SV2: $i] :
( ( SV2
= ( sK1_SY0 @ ( sK3_SY56 @ ( sK2_SY44 @ ( sK6_SY78 @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(37,plain,
! [SV4: $i,SV3: $i] :
( ( ( ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SV3 ) ) )
= ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SV4 ) ) ) )
= $false )
| ( ( SV3 = SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(38,plain,
( ( ( sK3_SY56 @ sK4_SX0 )
!= ( sK3_SY56 @ sK7_SY80 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(39,plain,
( ( sK4_SX0 = sK7_SY80 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(40,plain,
( ( ( sK3_SY56 @ sK4_SX0 )
= ( sK3_SY56 @ sK7_SY80 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(41,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,40,39,37,36]) ).
thf(42,plain,
( ( ! [SY71: $i] :
? [SY72: $i] :
( SY71
= ( sK2_SY44 @ ( sK1_SY0 @ ( sK3_SY56 @ SY72 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(43,plain,
( ( ! [SY69: $i] :
? [SY70: $i] :
( SY69
= ( sK1_SY0 @ ( sK3_SY56 @ ( sK2_SY44 @ SY70 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(44,plain,
( ( ! [SY67: $i,SY68: $i] :
( ( ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SY67 ) ) )
= ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SY68 ) ) ) )
=> ( SY67 = SY68 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(45,plain,
( ( ~ ! [SY75: $i] :
? [SY76: $i] :
( SY75
= ( sK3_SY56 @ SY76 ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(46,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
( SX0
!= ( sK1_SY0 @ ( sK3_SY56 @ ( sK2_SY44 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43,fun_bijective,fun_composition,fun_decreasing,fun_image,fun_increasing,fun_injective,fun_inv_image,fun_surjective]) ).
thf(47,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
( SX0
!= ( sK2_SY44 @ ( sK1_SY0 @ ( sK3_SY56 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42,fun_bijective,fun_composition,fun_decreasing,fun_image,fun_increasing,fun_injective,fun_inv_image,fun_surjective]) ).
thf(48,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SX0 ) ) )
!= ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SX1 ) ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44,fun_bijective,fun_composition,fun_decreasing,fun_image,fun_increasing,fun_injective,fun_inv_image,fun_surjective]) ).
thf(49,plain,
( ( ~ ! [SX0: $i] :
~ ! [SX1: $i] :
( SX0
!= ( sK3_SY56 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45,fun_bijective,fun_composition,fun_decreasing,fun_image,fun_increasing,fun_injective,fun_inv_image,fun_surjective]) ).
thf(50,plain,
! [SV5: $i] :
( ( ~ ! [SY81: $i] :
( SV5
!= ( sK1_SY0 @ ( sK3_SY56 @ ( sK2_SY44 @ SY81 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV6: $i] :
( ( ~ ! [SY82: $i] :
( SV6
!= ( sK2_SY44 @ ( sK1_SY0 @ ( sK3_SY56 @ SY82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV7: $i] :
( ( ! [SY83: $i] :
( ( ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SV7 ) ) )
!= ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SY83 ) ) ) )
| ( SV7 = SY83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(53,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
( SX0
!= ( sK3_SY56 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV5: $i] :
( ( ! [SY81: $i] :
( SV5
!= ( sK1_SY0 @ ( sK3_SY56 @ ( sK2_SY44 @ SY81 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV6: $i] :
( ( ! [SY82: $i] :
( SV6
!= ( sK2_SY44 @ ( sK1_SY0 @ ( sK3_SY56 @ SY82 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV8: $i,SV7: $i] :
( ( ( ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SV7 ) ) )
!= ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SV8 ) ) ) )
| ( SV7 = SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(57,plain,
( ( ~ ! [SY84: $i] :
( sK8_SX0
!= ( sK3_SY56 @ SY84 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[53]) ).
thf(58,plain,
! [SV5: $i] :
( ( SV5
!= ( sK1_SY0 @ ( sK3_SY56 @ ( sK2_SY44 @ ( sK9_SY81 @ SV5 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[54]) ).
thf(59,plain,
! [SV6: $i] :
( ( SV6
!= ( sK2_SY44 @ ( sK1_SY0 @ ( sK3_SY56 @ ( sK10_SY82 @ SV6 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[55]) ).
thf(60,plain,
! [SV8: $i,SV7: $i] :
( ( ( ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SV7 ) ) )
!= ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SV8 ) ) ) )
= $true )
| ( ( SV7 = SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(61,plain,
( ( ! [SY84: $i] :
( sK8_SX0
!= ( sK3_SY56 @ SY84 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(62,plain,
! [SV5: $i] :
( ( SV5
= ( sK1_SY0 @ ( sK3_SY56 @ ( sK2_SY44 @ ( sK9_SY81 @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(63,plain,
! [SV6: $i] :
( ( SV6
= ( sK2_SY44 @ ( sK1_SY0 @ ( sK3_SY56 @ ( sK10_SY82 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(64,plain,
! [SV8: $i,SV7: $i] :
( ( ( ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SV7 ) ) )
= ( sK3_SY56 @ ( sK2_SY44 @ ( sK1_SY0 @ SV8 ) ) ) )
= $false )
| ( ( SV7 = SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV9: $i] :
( ( sK8_SX0
!= ( sK3_SY56 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV9: $i] :
( ( sK8_SX0
= ( sK3_SY56 @ SV9 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(67,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[62,66,64,63]) ).
thf(68,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[67,41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET741^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.12 % Computer : n012.cluster.edu
% 0.07/0.12 % Model : x86_64 x86_64
% 0.07/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.12 % Memory : 8046.5625MB
% 0.07/0.12 % OS : Linux 6.8.0-71-generic
% 0.07/0.12 % CPULimit : 300
% 0.07/0.12 % WCLimit : 300
% 0.07/0.12 % DateTime : Tue Oct 6 14:49:46 UTC 2026
% 0.07/0.12 % CPUTime :
% 0.07/0.12 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.16
% 0.07/0.16 No.of.Axioms: 0
% 0.07/0.16
% 0.07/0.16 Length.of.Defs: 1512
% 0.07/0.16
% 0.07/0.16 Contains.Choice.Funs: false
% 0.07/0.16 ..
% 0.07/0.16
% 0.07/0.16 ********************************
% 0.07/0.16 * All subproblems solved! *
% 0.07/0.16 ********************************
% 0.07/0.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:67,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.16
% 0.07/0.16 %**** Beginning of derivation protocol ****
% 0.07/0.16 % SZS output start CNFRefutation
% See solution above
% 0.07/0.16
% 0.07/0.16 %**** End of derivation protocol ****
% 0.07/0.16 %**** no. of clauses in derivation: 68 ****
% 0.07/0.16 %**** clause counter: 67 ****
% 0.07/0.16
% 0.07/0.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:67,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------