%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET764^4 : 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 : n003.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 10:41:01 AM UTC 2026
% Result : Theorem 0.08s 0.24s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 23
% Syntax : Number of formulae : 52 ( 42 unt; 0 typ; 22 def)
% Number of atoms : 211 ( 85 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 146 ( 59 ~; 20 |; 12 &; 51 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 4 con; 0-3 aty)
% Number of variables : 103 ( 64 ^; 29 !; 10 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_complement,type,
complement: ( $i > $o ) > $i > $o ).
thf(tp_disjoint,type,
disjoint: ( $i > $o ) > ( $i > $o ) > $o ).
thf(tp_emptyset,type,
emptyset: $i > $o ).
thf(tp_excl_union,type,
excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
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_in,type,
in: $i > ( $i > $o ) > $o ).
thf(tp_intersection,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_is_a,type,
is_a: $i > ( $i > $o ) > $o ).
thf(tp_meets,type,
meets: ( $i > $o ) > ( $i > $o ) > $o ).
thf(tp_misses,type,
misses: ( $i > $o ) > ( $i > $o ) > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i > $i ).
thf(tp_sK2_SV1,type,
sK2_SV1: $i ).
thf(tp_sK3_SX1,type,
sK3_SX1: $i ).
thf(tp_setminus,type,
setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_singleton,type,
singleton: $i > $i > $o ).
thf(tp_subset,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(tp_union,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_unord_pair,type,
unord_pair: $i > $i > $i > $o ).
thf(complement,definition,
( complement
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement) ).
thf(disjoint,definition,
( disjoint
= ( ^ [X: $i > $o,Y: $i > $o] :
( ( intersection @ X @ Y )
= emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint) ).
thf(emptyset,definition,
( emptyset
= ( ^ [X: $i] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset) ).
thf(excl_union,definition,
( excl_union
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( ( X @ U )
& ~ ( Y @ U ) )
| ( ~ ( X @ U )
& ( Y @ U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',excl_union) ).
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(in,definition,
( in
= ( ^ [X: $i,M: $i > $o] : ( M @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in) ).
thf(intersection,definition,
( intersection
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
thf(is_a,definition,
( is_a
= ( ^ [X: $i,M: $i > $o] : ( M @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',is_a) ).
thf(meets,definition,
( meets
= ( ^ [X: $i > $o,Y: $i > $o] :
? [U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meets) ).
thf(misses,definition,
( misses
= ( ^ [X: $i > $o,Y: $i > $o] :
~ ? [U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',misses) ).
thf(setminus,definition,
( setminus
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ~ ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminus) ).
thf(singleton,definition,
( singleton
= ( ^ [X: $i,U: $i] : ( U = X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(subset,definition,
( subset
= ( ^ [X: $i > $o,Y: $i > $o] :
! [U: $i] :
( ( X @ U )
=> ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
thf(union,definition,
( union
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
thf(unord_pair,definition,
( unord_pair
= ( ^ [X: $i,Y: $i,U: $i] :
( ( U = X )
| ( U = Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unord_pair) ).
thf(1,conjecture,
! [F: $i > $i] :
( ( fun_inv_image @ F @ emptyset )
= emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
( ( ! [F: $i > $i] :
( ( fun_inv_image @ F @ emptyset )
= emptyset ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i > $i] :
( ( ^ [SY4: $i] :
? [SY5: $i] :
( $false
& ( SY5
= ( SY0 @ SY4 ) ) ) )
= ( ^ [X: $i] : $false ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,complement,disjoint,emptyset,excl_union,fun_bijective,fun_composition,fun_decreasing,fun_image,fun_increasing,fun_injective,fun_inv_image,fun_surjective,in,intersection,is_a,meets,misses,setminus,singleton,subset,union,unord_pair]) ).
thf(4,plain,
( ( ( ^ [SY10: $i] :
? [SY11: $i] :
( $false
& ( SY11
= ( sK1_SY0 @ SY10 ) ) ) )
= ( ^ [X: $i] : $false ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ( ^ [SY10: $i] :
? [SY11: $i] :
( $false
& ( SY11
= ( sK1_SY0 @ SY10 ) ) ) )
!= ( ^ [X: $i] : $false ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(6,plain,
( ( ( ^ [SY10: $i] :
? [SY11: $i] : $false )
!= ( ^ [X: $i] : $false ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(7,plain,
( ( ( ^ [SY10: $i] :
? [SY11: $i] : $false )
!= ( ^ [X: $i] : $false ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(8,plain,
( ( ( ^ [SX0: $i] :
~ ! [SX1: $i] : ~ $false )
!= ( ^ [SX0: $i] : $false ) )
= $true ),
inference(unfold_def,[status(thm)],[7,complement,disjoint,emptyset,excl_union,fun_bijective,fun_composition,fun_decreasing,fun_image,fun_increasing,fun_injective,fun_inv_image,fun_surjective,in,intersection,is_a,meets,misses,setminus,singleton,subset,union,unord_pair]) ).
thf(9,plain,
( ( ( ^ [SX0: $i] :
~ ! [SX1: $i] : ~ $false )
= ( ^ [SX0: $i] : $false ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SV1: $i] :
( ( ~ ! [SX1: $i] : ~ $false )
= $false ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[9]) ).
thf(11,plain,
( ( ( ^ [SX0: $i] :
~ ! [SX1: $i] : ~ $false )
= ( ^ [SX0: $i] : $false ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[9]) ).
thf(12,plain,
( ( ( ~ ! [SX1: $i] : ~ $false )
= $false )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(13,plain,
( ( ~ ( ~ ! [SX1: $i] : ~ $false
| $false )
| ~ ( ~ ~ ! [SX1: $i] : ~ $false
| ~ $false ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[12]) ).
thf(14,plain,
( ( ( ~ ! [SX1: $i] : ~ $false )
= $false )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( ~ ! [SX1: $i] : ~ $false
| $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( ~ ~ ! [SX1: $i] : ~ $false
| ~ $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
( ( ~ ! [SX1: $i] : ~ $false
| $false )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ~ ! [SX1: $i] : ~ $false
| ~ $false )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( ( ~ ! [SX1: $i] : ~ $false )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ( ~ ~ ! [SX1: $i] : ~ $false )
= $true )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(21,plain,
( ( ( ! [SX1: $i] : ~ $false )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(22,plain,
( ( ( ~ ! [SX1: $i] : ~ $false )
= $false )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(23,plain,
( ( ( ~ $false ) = $false )
| ( $false = $true ) ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(24,plain,
( ( ( ! [SX1: $i] : ~ $false )
= $true )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(25,plain,
( ( $false = $true )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(26,plain,
( ( ( ~ $false ) = $true )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(27,plain,
( ( $false = $false )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(28,plain,
( ( $false = $false )
| ( $false = $false ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(29,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[11,28,25,14]) ).
thf(30,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET764^4 : 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
% 0.08/0.20 % Computer : n003.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Oct 6 14:53:09 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.24
% 0.08/0.24 No.of.Axioms: 0
% 0.08/0.24
% 0.08/0.24 Length.of.Defs: 3617
% 0.08/0.24
% 0.08/0.24 Contains.Choice.Funs: false
% 0.08/0.24
% 0.08/0.24 ********************************
% 0.08/0.24 * All subproblems solved! *
% 0.08/0.24 ********************************
% 0.08/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:29,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.08/0.24
% 0.08/0.24 %**** Beginning of derivation protocol ****
% 0.08/0.24 % SZS output start CNFRefutation
% See solution above
% 0.08/0.24
% 0.08/0.24 %**** End of derivation protocol ****
% 0.08/0.24 %**** no. of clauses in derivation: 30 ****
% 0.08/0.24 %**** clause counter: 29 ****
% 0.08/0.24
% 0.08/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:29,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------