%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET716^4 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 10:40:55 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 34 unt; 0 typ; 8 def)
% Number of atoms : 159 ( 109 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 183 ( 16 ~; 14 |; 8 &; 121 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 90 ( 16 ^; 71 !; 3 ?; 90 :)
% 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_sK1_SY0,type,
sK1_SY0: $i > $i ).
thf(tp_sK2_SY19,type,
sK2_SY19: $i > $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY34,type,
sK4_SY34: $i ).
thf(fun_bijective,definition,
( fun_bijective
= ( ^ [F: $i > $i] :
( ( fun_injective @ F )
& ( fun_surjective @ F ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fun_surjective) ).
thf(1,conjecture,
! [F: $i > $i,G: $i > $i] :
( ( ( fun_injective @ F )
& ( fun_injective @ G ) )
=> ( fun_injective @ ( fun_composition @ F @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
( ( ! [F: $i > $i,G: $i > $i] :
( ( ( fun_injective @ F )
& ( fun_injective @ G ) )
=> ( fun_injective @ ( fun_composition @ F @ G ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i > $i,SY1: $i > $i] :
( ( ! [SY2: $i,SY3: $i] :
( ( ( SY0 @ SY2 )
= ( SY0 @ SY3 ) )
=> ( SY2 = SY3 ) )
& ! [SY4: $i,SY5: $i] :
( ( ( SY1 @ SY4 )
= ( SY1 @ SY5 ) )
=> ( SY4 = SY5 ) ) )
=> ! [SY9: $i,SY10: $i] :
( ( ( SY1 @ ( SY0 @ SY9 ) )
= ( SY1 @ ( SY0 @ SY10 ) ) )
=> ( SY9 = SY10 ) ) ) )
= $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,
( ( ! [SY19: $i > $i] :
( ( ! [SY20: $i,SY21: $i] :
( ( ( sK1_SY0 @ SY20 )
= ( sK1_SY0 @ SY21 ) )
=> ( SY20 = SY21 ) )
& ! [SY4: $i,SY5: $i] :
( ( ( SY19 @ SY4 )
= ( SY19 @ SY5 ) )
=> ( SY4 = SY5 ) ) )
=> ! [SY24: $i,SY25: $i] :
( ( ( SY19 @ ( sK1_SY0 @ SY24 ) )
= ( SY19 @ ( sK1_SY0 @ SY25 ) ) )
=> ( SY24 = SY25 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ( ! [SY20: $i,SY21: $i] :
( ( ( sK1_SY0 @ SY20 )
= ( sK1_SY0 @ SY21 ) )
=> ( SY20 = SY21 ) )
& ! [SY28: $i,SY29: $i] :
( ( ( sK2_SY19 @ SY28 )
= ( sK2_SY19 @ SY29 ) )
=> ( SY28 = SY29 ) ) )
=> ! [SY30: $i,SY31: $i] :
( ( ( sK2_SY19 @ ( sK1_SY0 @ SY30 ) )
= ( sK2_SY19 @ ( sK1_SY0 @ SY31 ) ) )
=> ( SY30 = SY31 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY20: $i,SY21: $i] :
( ( ( sK1_SY0 @ SY20 )
= ( sK1_SY0 @ SY21 ) )
=> ( SY20 = SY21 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY28: $i,SY29: $i] :
( ( ( sK2_SY19 @ SY28 )
= ( sK2_SY19 @ SY29 ) )
=> ( SY28 = SY29 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ! [SY30: $i,SY31: $i] :
( ( ( sK2_SY19 @ ( sK1_SY0 @ SY30 ) )
= ( sK2_SY19 @ ( sK1_SY0 @ SY31 ) ) )
=> ( SY30 = SY31 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(9,plain,
( ( ~ ! [SY30: $i,SY31: $i] :
( ( ( sK2_SY19 @ ( sK1_SY0 @ SY30 ) )
= ( sK2_SY19 @ ( sK1_SY0 @ SY31 ) ) )
=> ( SY30 = SY31 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SY28: $i,SY29: $i] :
( ( ( sK2_SY19 @ SY28 )
= ( sK2_SY19 @ SY29 ) )
=> ( SY28 = SY29 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SY20: $i,SY21: $i] :
( ( ( sK1_SY0 @ SY20 )
= ( sK1_SY0 @ SY21 ) )
=> ( SY20 = SY21 ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(12,plain,
( ( ~ ! [SY30: $i,SY31: $i] :
( ( ( sK2_SY19 @ ( sK1_SY0 @ SY30 ) )
= ( sK2_SY19 @ ( sK1_SY0 @ SY31 ) ) )
=> ( SY30 = SY31 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( sK2_SY19 @ ( sK1_SY0 @ SX0 ) )
!= ( sK2_SY19 @ ( sK1_SY0 @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,fun_bijective,fun_composition,fun_decreasing,fun_image,fun_increasing,fun_injective,fun_inv_image,fun_surjective]) ).
thf(14,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( sK1_SY0 @ SX0 )
!= ( sK1_SY0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,fun_bijective,fun_composition,fun_decreasing,fun_image,fun_increasing,fun_injective,fun_inv_image,fun_surjective]) ).
thf(15,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( sK2_SY19 @ SX0 )
!= ( sK2_SY19 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,fun_bijective,fun_composition,fun_decreasing,fun_image,fun_increasing,fun_injective,fun_inv_image,fun_surjective]) ).
thf(16,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( sK2_SY19 @ ( sK1_SY0 @ SX0 ) )
!= ( sK2_SY19 @ ( sK1_SY0 @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV1: $i] :
( ( ! [SY32: $i] :
( ( ( sK1_SY0 @ SV1 )
!= ( sK1_SY0 @ SY32 ) )
| ( SV1 = SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV2: $i] :
( ( ! [SY33: $i] :
( ( ( sK2_SY19 @ SV2 )
!= ( sK2_SY19 @ SY33 ) )
| ( SV2 = SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [SY34: $i] :
( ( ( sK2_SY19 @ ( sK1_SY0 @ sK3_SX0 ) )
!= ( sK2_SY19 @ ( sK1_SY0 @ SY34 ) ) )
| ( sK3_SX0 = SY34 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(20,plain,
! [SV3: $i,SV1: $i] :
( ( ( ( sK1_SY0 @ SV1 )
!= ( sK1_SY0 @ SV3 ) )
| ( SV1 = SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
! [SV4: $i,SV2: $i] :
( ( ( ( sK2_SY19 @ SV2 )
!= ( sK2_SY19 @ SV4 ) )
| ( SV2 = SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ( ( sK2_SY19 @ ( sK1_SY0 @ sK3_SX0 ) )
!= ( sK2_SY19 @ ( sK1_SY0 @ sK4_SY34 ) ) )
| ( sK3_SX0 = sK4_SY34 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(23,plain,
! [SV3: $i,SV1: $i] :
( ( ( ( sK1_SY0 @ SV1 )
!= ( sK1_SY0 @ SV3 ) )
= $true )
| ( ( SV1 = SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV4: $i,SV2: $i] :
( ( ( ( sK2_SY19 @ SV2 )
!= ( sK2_SY19 @ SV4 ) )
= $true )
| ( ( SV2 = SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( ( sK2_SY19 @ ( sK1_SY0 @ sK3_SX0 ) )
!= ( sK2_SY19 @ ( sK1_SY0 @ sK4_SY34 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(26,plain,
( ( sK3_SX0 = sK4_SY34 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(27,plain,
! [SV3: $i,SV1: $i] :
( ( ( ( sK1_SY0 @ SV1 )
= ( sK1_SY0 @ SV3 ) )
= $false )
| ( ( SV1 = SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV4: $i,SV2: $i] :
( ( ( ( sK2_SY19 @ SV2 )
= ( sK2_SY19 @ SV4 ) )
= $false )
| ( ( SV2 = SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(29,plain,
( ( ( sK2_SY19 @ ( sK1_SY0 @ sK3_SX0 ) )
= ( sK2_SY19 @ ( sK1_SY0 @ sK4_SY34 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(30,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26,29,28,27]) ).
thf(31,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET716^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.20 % Computer : n026.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Oct 6 14:52:17 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.25
% 0.07/0.25 No.of.Axioms: 0
% 0.07/0.25
% 0.07/0.25 Length.of.Defs: 1520
% 0.07/0.25
% 0.07/0.25 Contains.Choice.Funs: false
% 0.07/0.25 .
% 0.07/0.25
% 0.07/0.25 ********************************
% 0.07/0.25 * All subproblems solved! *
% 0.07/0.25 ********************************
% 0.07/0.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,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:30,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.25
% 0.07/0.25 %**** Beginning of derivation protocol ****
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25
% 0.07/0.25 %**** End of derivation protocol ****
% 0.07/0.25 %**** no. of clauses in derivation: 31 ****
% 0.07/0.25 %**** clause counter: 30 ****
% 0.07/0.25
% 0.07/0.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,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:30,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------