%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV420^1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n018.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 10:50:04 AM UTC 2026
% Result : Theorem 1.09s 0.53s
% Output : CNFRefutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 21
% Syntax : Number of formulae : 50 ( 49 unt; 0 typ; 20 def)
% Number of atoms : 365 ( 135 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 904 ( 109 ~; 97 |; 93 &; 511 @)
% ( 0 <=>; 94 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 100 ( 100 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 38 usr; 10 con; 0-3 aty)
% Number of variables : 220 ( 58 ^; 130 !; 32 ?; 220 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bijection,type,
bijection: ( $i > $o ) > ( $i > $i ) > ( $i > $o ) > $o ).
thf(tp_complement,type,
complement: ( $i > $o ) > $i > $o ).
thf(tp_disjoint,type,
disjoint: ( $i > $o ) > ( $i > $o ) > $o ).
thf(tp_embedding,type,
embedding: ( $i > $o ) > ( $i > $o ) > $o ).
thf(tp_emptyset,type,
emptyset: $i > $o ).
thf(tp_equinumerous,type,
equinumerous: ( $i > $o ) > ( $i > $o ) > $o ).
thf(tp_excl_union,type,
excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_in,type,
in: $i > ( $i > $o ) > $o ).
thf(tp_injection,type,
injection: ( $i > $o ) > ( $i > $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_is_function,type,
is_function: ( $i > $o ) > ( $i > $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_sK10_SY263,type,
sK10_SY263: $i ).
thf(tp_sK11_REN,type,
sK11_REN: $o ).
thf(tp_sK12_REN,type,
sK12_REN: $o ).
thf(tp_sK13_SY249,type,
sK13_SY249: $i > $i ).
thf(tp_sK14_SY274,type,
sK14_SY274: $i > $i ).
thf(tp_sK15_SY272,type,
sK15_SY272: $i ).
thf(tp_sK16_SY269,type,
sK16_SY269: $i ).
thf(tp_sK17_REN,type,
sK17_REN: $o ).
thf(tp_sK18_REN,type,
sK18_REN: $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i > $o ).
thf(tp_sK2_SY176,type,
sK2_SY176: $i > $o ).
thf(tp_sK3_SY199,type,
sK3_SY199: $i > $o ).
thf(tp_sK4_SY221,type,
sK4_SY221: $i > $o ).
thf(tp_sK5_SY240,type,
sK5_SY240: ( $i > $i ) > $i ).
thf(tp_sK6_SY262,type,
sK6_SY262: ( $i > $i ) > $i ).
thf(tp_sK7_SY201,type,
sK7_SY201: $i > $i ).
thf(tp_sK8_SY268,type,
sK8_SY268: $i > $i ).
thf(tp_sK9_SY266,type,
sK9_SY266: $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_surjection,type,
surjection: ( $i > $o ) > ( $i > $i ) > ( $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(bijection,definition,
( bijection
= ( ^ [X: $i > $o,F: $i > $i,Y: $i > $o] :
( ( injection @ X @ F @ Y )
& ( surjection @ X @ F @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bijection) ).
thf(complement,definition,
( complement
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement) ).
thf(disjoint,definition,
( disjoint
= ( ^ [X: $i > $o,Y: $i > $o] :
( ( intersection @ X @ Y )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint) ).
thf(embedding,definition,
( embedding
= ( ^ [X: $i > $o,Y: $i > $o] :
? [F: $i > $i] : ( injection @ X @ F @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',embedding) ).
thf(emptyset,definition,
( emptyset
= ( ^ [X: $i] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset) ).
thf(equinumerous,definition,
( equinumerous
= ( ^ [X: $i > $o,Y: $i > $o] :
? [F: $i > $i] : ( bijection @ X @ F @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equinumerous) ).
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/sandbox/benchmark/theBenchmark.p',excl_union) ).
thf(in,definition,
( in
= ( ^ [X: $i,M: $i > $o] : ( M @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in) ).
thf(injection,definition,
( injection
= ( ^ [X: $i > $o,F: $i > $i,Y: $i > $o] :
( ( is_function @ X @ F @ Y )
=> ! [E1: $i,E2: $i] :
( ( ( X @ E1 )
& ( X @ E2 )
& ( ( F @ E1 )
= ( F @ E2 ) ) )
=> ( E1 = E2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injection) ).
thf(intersection,definition,
( intersection
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
thf(is_a,definition,
( is_a
= ( ^ [X: $i,M: $i > $o] : ( M @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',is_a) ).
thf(is_function,definition,
( is_function
= ( ^ [X: $i > $o,F: $i > $i,Y: $i > $o] :
! [E: $i] :
( ( X @ E )
=> ( Y @ ( F @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',is_function) ).
thf(meets,definition,
( meets
= ( ^ [X: $i > $o,Y: $i > $o] :
? [U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meets) ).
thf(misses,definition,
( misses
= ( ^ [X: $i > $o,Y: $i > $o] :
~ ? [U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',misses) ).
thf(setminus,definition,
( setminus
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ~ ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminus) ).
thf(singleton,definition,
( singleton
= ( ^ [X: $i,U: $i] : ( U = X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(subset,definition,
( subset
= ( ^ [X: $i > $o,Y: $i > $o] :
! [U: $i] :
( ( X @ U )
=> ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
thf(surjection,definition,
( surjection
= ( ^ [X: $i > $o,F: $i > $i,Y: $i > $o] :
( ( is_function @ X @ F @ Y )
=> ! [E1: $i] :
( ( Y @ E1 )
=> ? [E2: $i] :
( ( X @ E2 )
& ( ( F @ E2 )
= E1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',surjection) ).
thf(union,definition,
( union
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
thf(unord_pair,definition,
( unord_pair
= ( ^ [X: $i,Y: $i,U: $i] :
( ( U = X )
| ( U = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unord_pair) ).
thf(1,conjecture,
! [A: $i > $o,Ap: $i > $o,B: $i > $o,Bp: $i > $o] :
( ( ( equinumerous @ A @ Ap )
& ( equinumerous @ B @ Bp )
& ( ( intersection @ Ap @ Bp )
= emptyset ) )
=> ( embedding @ ( union @ A @ B ) @ ( union @ Ap @ Bp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
( ( ! [A: $i > $o,Ap: $i > $o,B: $i > $o,Bp: $i > $o] :
( ( ( equinumerous @ A @ Ap )
& ( equinumerous @ B @ Bp )
& ( ( intersection @ Ap @ Bp )
= emptyset ) )
=> ( embedding @ ( union @ A @ B ) @ ( union @ Ap @ Bp ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i > $o,SY1: $i > $o,SY2: $i > $o,SY3: $i > $o] :
( ( ? [SY55: $i > $i] :
( ( ! [SY56: $i] :
( ( SY0 @ SY56 )
=> ( SY1 @ ( SY55 @ SY56 ) ) )
=> ! [SY44: $i,SY45: $i] :
( ( ( SY0 @ SY44 )
& ( SY0 @ SY45 )
& ( ( SY55 @ SY44 )
= ( SY55 @ SY45 ) ) )
=> ( SY44 = SY45 ) ) )
& ( ! [SY59: $i] :
( ( SY0 @ SY59 )
=> ( SY1 @ ( SY55 @ SY59 ) ) )
=> ! [SY60: $i] :
( ( SY1 @ SY60 )
=> ? [SY48: $i] :
( ( SY0 @ SY48 )
& ( ( SY55 @ SY48 )
= SY60 ) ) ) ) )
& ? [SY113: $i > $i] :
( ( ! [SY114: $i] :
( ( SY2 @ SY114 )
=> ( SY3 @ ( SY113 @ SY114 ) ) )
=> ! [SY102: $i,SY103: $i] :
( ( ( SY2 @ SY102 )
& ( SY2 @ SY103 )
& ( ( SY113 @ SY102 )
= ( SY113 @ SY103 ) ) )
=> ( SY102 = SY103 ) ) )
& ( ! [SY117: $i] :
( ( SY2 @ SY117 )
=> ( SY3 @ ( SY113 @ SY117 ) ) )
=> ! [SY118: $i] :
( ( SY3 @ SY118 )
=> ? [SY106: $i] :
( ( SY2 @ SY106 )
& ( ( SY113 @ SY106 )
= SY118 ) ) ) ) )
& ( ( ^ [SY122: $i] :
( ( SY1 @ SY122 )
& ( SY3 @ SY122 ) ) )
= ( ^ [X: $i] : $false ) ) )
=> ? [SY148: $i > $i] :
( ! [SY149: $i] :
( ( ( SY0 @ SY149 )
| ( SY2 @ SY149 ) )
=> ( ( SY1 @ ( SY148 @ SY149 ) )
| ( SY3 @ ( SY148 @ SY149 ) ) ) )
=> ! [SY140: $i,SY141: $i] :
( ( ( ( SY0 @ SY140 )
| ( SY2 @ SY140 ) )
& ( ( SY0 @ SY141 )
| ( SY2 @ SY141 ) )
& ( ( SY148 @ SY140 )
= ( SY148 @ SY141 ) ) )
=> ( SY140 = SY141 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,bijection,complement,disjoint,embedding,emptyset,equinumerous,excl_union,in,injection,intersection,is_a,is_function,meets,misses,setminus,singleton,subset,surjection,union,unord_pair]) ).
thf(4,plain,
( ( ! [SY176: $i > $o,SY177: $i > $o,SY178: $i > $o] :
( ( ? [SY179: $i > $i] :
( ( ! [SY180: $i] :
( ( sK1_SY0 @ SY180 )
=> ( SY176 @ ( SY179 @ SY180 ) ) )
=> ! [SY181: $i,SY182: $i] :
( ( ( sK1_SY0 @ SY181 )
& ( sK1_SY0 @ SY182 )
& ( ( SY179 @ SY181 )
= ( SY179 @ SY182 ) ) )
=> ( SY181 = SY182 ) ) )
& ( ! [SY183: $i] :
( ( sK1_SY0 @ SY183 )
=> ( SY176 @ ( SY179 @ SY183 ) ) )
=> ! [SY184: $i] :
( ( SY176 @ SY184 )
=> ? [SY185: $i] :
( ( sK1_SY0 @ SY185 )
& ( ( SY179 @ SY185 )
= SY184 ) ) ) ) )
& ? [SY113: $i > $i] :
( ( ! [SY114: $i] :
( ( SY177 @ SY114 )
=> ( SY178 @ ( SY113 @ SY114 ) ) )
=> ! [SY102: $i,SY103: $i] :
( ( ( SY177 @ SY102 )
& ( SY177 @ SY103 )
& ( ( SY113 @ SY102 )
= ( SY113 @ SY103 ) ) )
=> ( SY102 = SY103 ) ) )
& ( ! [SY117: $i] :
( ( SY177 @ SY117 )
=> ( SY178 @ ( SY113 @ SY117 ) ) )
=> ! [SY118: $i] :
( ( SY178 @ SY118 )
=> ? [SY106: $i] :
( ( SY177 @ SY106 )
& ( ( SY113 @ SY106 )
= SY118 ) ) ) ) )
& ( ( ^ [SY122: $i] :
( ( SY176 @ SY122 )
& ( SY178 @ SY122 ) ) )
= ( ^ [X: $i] : $false ) ) )
=> ? [SY195: $i > $i] :
( ! [SY196: $i] :
( ( ( sK1_SY0 @ SY196 )
| ( SY177 @ SY196 ) )
=> ( ( SY176 @ ( SY195 @ SY196 ) )
| ( SY178 @ ( SY195 @ SY196 ) ) ) )
=> ! [SY197: $i,SY198: $i] :
( ( ( ( sK1_SY0 @ SY197 )
| ( SY177 @ SY197 ) )
& ( ( sK1_SY0 @ SY198 )
| ( SY177 @ SY198 ) )
& ( ( SY195 @ SY197 )
= ( SY195 @ SY198 ) ) )
=> ( SY197 = SY198 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY199: $i > $o,SY200: $i > $o] :
( ( ? [SY201: $i > $i] :
( ( ! [SY202: $i] :
( ( sK1_SY0 @ SY202 )
=> ( sK2_SY176 @ ( SY201 @ SY202 ) ) )
=> ! [SY181: $i,SY182: $i] :
( ( ( sK1_SY0 @ SY181 )
& ( sK1_SY0 @ SY182 )
& ( ( SY201 @ SY181 )
= ( SY201 @ SY182 ) ) )
=> ( SY181 = SY182 ) ) )
& ( ! [SY205: $i] :
( ( sK1_SY0 @ SY205 )
=> ( sK2_SY176 @ ( SY201 @ SY205 ) ) )
=> ! [SY206: $i] :
( ( sK2_SY176 @ SY206 )
=> ? [SY185: $i] :
( ( sK1_SY0 @ SY185 )
& ( ( SY201 @ SY185 )
= SY206 ) ) ) ) )
& ? [SY113: $i > $i] :
( ( ! [SY114: $i] :
( ( SY199 @ SY114 )
=> ( SY200 @ ( SY113 @ SY114 ) ) )
=> ! [SY102: $i,SY103: $i] :
( ( ( SY199 @ SY102 )
& ( SY199 @ SY103 )
& ( ( SY113 @ SY102 )
= ( SY113 @ SY103 ) ) )
=> ( SY102 = SY103 ) ) )
& ( ! [SY117: $i] :
( ( SY199 @ SY117 )
=> ( SY200 @ ( SY113 @ SY117 ) ) )
=> ! [SY118: $i] :
( ( SY200 @ SY118 )
=> ? [SY106: $i] :
( ( SY199 @ SY106 )
& ( ( SY113 @ SY106 )
= SY118 ) ) ) ) )
& ( ( ^ [SY215: $i] :
( ( sK2_SY176 @ SY215 )
& ( SY200 @ SY215 ) ) )
= ( ^ [X: $i] : $false ) ) )
=> ? [SY217: $i > $i] :
( ! [SY218: $i] :
( ( ( sK1_SY0 @ SY218 )
| ( SY199 @ SY218 ) )
=> ( ( sK2_SY176 @ ( SY217 @ SY218 ) )
| ( SY200 @ ( SY217 @ SY218 ) ) ) )
=> ! [SY197: $i,SY198: $i] :
( ( ( ( sK1_SY0 @ SY197 )
| ( SY199 @ SY197 ) )
& ( ( sK1_SY0 @ SY198 )
| ( SY199 @ SY198 ) )
& ( ( SY217 @ SY197 )
= ( SY217 @ SY198 ) ) )
=> ( SY197 = SY198 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY221: $i > $o] :
( ( ? [SY201: $i > $i] :
( ( ! [SY202: $i] :
( ( sK1_SY0 @ SY202 )
=> ( sK2_SY176 @ ( SY201 @ SY202 ) ) )
=> ! [SY181: $i,SY182: $i] :
( ( ( sK1_SY0 @ SY181 )
& ( sK1_SY0 @ SY182 )
& ( ( SY201 @ SY181 )
= ( SY201 @ SY182 ) ) )
=> ( SY181 = SY182 ) ) )
& ( ! [SY205: $i] :
( ( sK1_SY0 @ SY205 )
=> ( sK2_SY176 @ ( SY201 @ SY205 ) ) )
=> ! [SY206: $i] :
( ( sK2_SY176 @ SY206 )
=> ? [SY185: $i] :
( ( sK1_SY0 @ SY185 )
& ( ( SY201 @ SY185 )
= SY206 ) ) ) ) )
& ? [SY229: $i > $i] :
( ( ! [SY230: $i] :
( ( sK3_SY199 @ SY230 )
=> ( SY221 @ ( SY229 @ SY230 ) ) )
=> ! [SY231: $i,SY232: $i] :
( ( ( sK3_SY199 @ SY231 )
& ( sK3_SY199 @ SY232 )
& ( ( SY229 @ SY231 )
= ( SY229 @ SY232 ) ) )
=> ( SY231 = SY232 ) ) )
& ( ! [SY233: $i] :
( ( sK3_SY199 @ SY233 )
=> ( SY221 @ ( SY229 @ SY233 ) ) )
=> ! [SY234: $i] :
( ( SY221 @ SY234 )
=> ? [SY235: $i] :
( ( sK3_SY199 @ SY235 )
& ( ( SY229 @ SY235 )
= SY234 ) ) ) ) )
& ( ( ^ [SY215: $i] :
( ( sK2_SY176 @ SY215 )
& ( SY221 @ SY215 ) ) )
= ( ^ [X: $i] : $false ) ) )
=> ? [SY238: $i > $i] :
( ! [SY239: $i] :
( ( ( sK1_SY0 @ SY239 )
| ( sK3_SY199 @ SY239 ) )
=> ( ( sK2_SY176 @ ( SY238 @ SY239 ) )
| ( SY221 @ ( SY238 @ SY239 ) ) ) )
=> ! [SY240: $i,SY241: $i] :
( ( ( ( sK1_SY0 @ SY240 )
| ( sK3_SY199 @ SY240 ) )
& ( ( sK1_SY0 @ SY241 )
| ( sK3_SY199 @ SY241 ) )
& ( ( SY238 @ SY240 )
= ( SY238 @ SY241 ) ) )
=> ( SY240 = SY241 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ( ? [SY201: $i > $i] :
( ( ! [SY202: $i] :
( ( sK1_SY0 @ SY202 )
=> ( sK2_SY176 @ ( SY201 @ SY202 ) ) )
=> ! [SY181: $i,SY182: $i] :
( ( ( sK1_SY0 @ SY181 )
& ( sK1_SY0 @ SY182 )
& ( ( SY201 @ SY181 )
= ( SY201 @ SY182 ) ) )
=> ( SY181 = SY182 ) ) )
& ( ! [SY205: $i] :
( ( sK1_SY0 @ SY205 )
=> ( sK2_SY176 @ ( SY201 @ SY205 ) ) )
=> ! [SY206: $i] :
( ( sK2_SY176 @ SY206 )
=> ? [SY185: $i] :
( ( sK1_SY0 @ SY185 )
& ( ( SY201 @ SY185 )
= SY206 ) ) ) ) )
& ? [SY249: $i > $i] :
( ( ! [SY250: $i] :
( ( sK3_SY199 @ SY250 )
=> ( sK4_SY221 @ ( SY249 @ SY250 ) ) )
=> ! [SY231: $i,SY232: $i] :
( ( ( sK3_SY199 @ SY231 )
& ( sK3_SY199 @ SY232 )
& ( ( SY249 @ SY231 )
= ( SY249 @ SY232 ) ) )
=> ( SY231 = SY232 ) ) )
& ( ! [SY253: $i] :
( ( sK3_SY199 @ SY253 )
=> ( sK4_SY221 @ ( SY249 @ SY253 ) ) )
=> ! [SY254: $i] :
( ( sK4_SY221 @ SY254 )
=> ? [SY235: $i] :
( ( sK3_SY199 @ SY235 )
& ( ( SY249 @ SY235 )
= SY254 ) ) ) ) )
& ( ( ^ [SY256: $i] :
( ( sK2_SY176 @ SY256 )
& ( sK4_SY221 @ SY256 ) ) )
= ( ^ [X: $i] : $false ) ) )
=> ? [SY258: $i > $i] :
( ! [SY259: $i] :
( ( ( sK1_SY0 @ SY259 )
| ( sK3_SY199 @ SY259 ) )
=> ( ( sK2_SY176 @ ( SY258 @ SY259 ) )
| ( sK4_SY221 @ ( SY258 @ SY259 ) ) ) )
=> ! [SY240: $i,SY241: $i] :
( ( ( ( sK1_SY0 @ SY240 )
| ( sK3_SY199 @ SY240 ) )
& ( ( sK1_SY0 @ SY241 )
| ( sK3_SY199 @ SY241 ) )
& ( ( SY258 @ SY240 )
= ( SY258 @ SY241 ) ) )
=> ( SY240 = SY241 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(11,plain,
( ( ? [SY258: $i > $i] :
( ! [SY259: $i] :
( ( ( sK1_SY0 @ SY259 )
| ( sK3_SY199 @ SY259 ) )
=> ( ( sK2_SY176 @ ( SY258 @ SY259 ) )
| ( sK4_SY221 @ ( SY258 @ SY259 ) ) ) )
=> ! [SY240: $i,SY241: $i] :
( ( ( ( sK1_SY0 @ SY240 )
| ( sK3_SY199 @ SY240 ) )
& ( ( sK1_SY0 @ SY241 )
| ( sK3_SY199 @ SY241 ) )
& ( ( SY258 @ SY240 )
= ( SY258 @ SY241 ) ) )
=> ( SY240 = SY241 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(12,plain,
( ( ~ ? [SY258: $i > $i] :
( ! [SY259: $i] :
( ( ( sK1_SY0 @ SY259 )
| ( sK3_SY199 @ SY259 ) )
=> ( ( sK2_SY176 @ ( SY258 @ SY259 ) )
| ( sK4_SY221 @ ( SY258 @ SY259 ) ) ) )
=> ! [SY240: $i,SY241: $i] :
( ( ( ( sK1_SY0 @ SY240 )
| ( sK3_SY199 @ SY240 ) )
& ( ( sK1_SY0 @ SY241 )
| ( sK3_SY199 @ SY241 ) )
& ( ( SY258 @ SY240 )
= ( SY258 @ SY241 ) ) )
=> ( SY240 = SY241 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [SY258: $i > $i,SY259: $i] :
( ~ ( sK1_SY0 @ SY259 )
| ( sK2_SY176 @ ( SY258 @ SY259 ) )
| ( sK4_SY221 @ ( SY258 @ SY259 ) ) )
& ! [SY258: $i > $i,SY259: $i] :
( ~ ( sK3_SY199 @ SY259 )
| ( sK2_SY176 @ ( SY258 @ SY259 ) )
| ( sK4_SY221 @ ( SY258 @ SY259 ) ) )
& ! [SY258: $i > $i] :
( ( ( sK1_SY0 @ ( sK5_SY240 @ SY258 ) )
| ( sK3_SY199 @ ( sK5_SY240 @ SY258 ) ) )
& ( ( sK1_SY0 @ ( sK6_SY262 @ SY258 ) )
| ( sK3_SY199 @ ( sK6_SY262 @ SY258 ) ) )
& ( ( SY258 @ ( sK5_SY240 @ SY258 ) )
= ( SY258 @ ( sK6_SY262 @ SY258 ) ) )
& ( ( sK5_SY240 @ SY258 )
!= ( sK6_SY262 @ SY258 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(19,plain,
( ( ! [SY258: $i > $i,SY259: $i] :
( ~ ( sK1_SY0 @ SY259 )
| ( sK2_SY176 @ ( SY258 @ SY259 ) )
| ( sK4_SY221 @ ( SY258 @ SY259 ) ) )
& ! [SY258: $i > $i,SY259: $i] :
( ~ ( sK3_SY199 @ SY259 )
| ( sK2_SY176 @ ( SY258 @ SY259 ) )
| ( sK4_SY221 @ ( SY258 @ SY259 ) ) )
& ! [SY258: $i > $i] :
( ( ( sK1_SY0 @ ( sK5_SY240 @ SY258 ) )
| ( sK3_SY199 @ ( sK5_SY240 @ SY258 ) ) )
& ( ( sK1_SY0 @ ( sK6_SY262 @ SY258 ) )
| ( sK3_SY199 @ ( sK6_SY262 @ SY258 ) ) )
& ( ( SY258 @ ( sK5_SY240 @ SY258 ) )
= ( SY258 @ ( sK6_SY262 @ SY258 ) ) )
& ( ( sK5_SY240 @ SY258 )
!= ( sK6_SY262 @ SY258 ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(23,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i > $i,SX1: $i] :
( ~ ( sK1_SY0 @ SX1 )
| ( sK2_SY176 @ ( SX0 @ SX1 ) )
| ( sK4_SY221 @ ( SX0 @ SX1 ) ) )
| ~ ! [SX0: $i > $i,SX1: $i] :
( ~ ( sK3_SY199 @ SX1 )
| ( sK2_SY176 @ ( SX0 @ SX1 ) )
| ( sK4_SY221 @ ( SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i > $i] :
~ ( ~ ~ ( ~ ~ ( ~ ( ( sK1_SY0 @ ( sK5_SY240 @ SX0 ) )
| ( sK3_SY199 @ ( sK5_SY240 @ SX0 ) ) )
| ~ ( ( sK1_SY0 @ ( sK6_SY262 @ SX0 ) )
| ( sK3_SY199 @ ( sK6_SY262 @ SX0 ) ) ) )
| ( ( SX0 @ ( sK5_SY240 @ SX0 ) )
!= ( SX0 @ ( sK6_SY262 @ SX0 ) ) ) )
| ~ ( ( ( sK5_SY240 @ SX0 )
!= ( sK6_SY262 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19,bijection,complement,disjoint,embedding,emptyset,equinumerous,excl_union,in,injection,intersection,is_a,is_function,meets,misses,setminus,singleton,subset,surjection,union,unord_pair]) ).
thf(28,plain,
( ( ~ ~ ( ~ ! [SX0: $i > $i,SX1: $i] :
( ~ ( sK1_SY0 @ SX1 )
| ( sK2_SY176 @ ( SX0 @ SX1 ) )
| ( sK4_SY221 @ ( SX0 @ SX1 ) ) )
| ~ ! [SX0: $i > $i,SX1: $i] :
( ~ ( sK3_SY199 @ SX1 )
| ( sK2_SY176 @ ( SX0 @ SX1 ) )
| ( sK4_SY221 @ ( SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i > $i] :
~ ( ~ ~ ( ~ ~ ( ~ ( ( sK1_SY0 @ ( sK5_SY240 @ SX0 ) )
| ( sK3_SY199 @ ( sK5_SY240 @ SX0 ) ) )
| ~ ( ( sK1_SY0 @ ( sK6_SY262 @ SX0 ) )
| ( sK3_SY199 @ ( sK6_SY262 @ SX0 ) ) ) )
| ( ( SX0 @ ( sK5_SY240 @ SX0 ) )
!= ( SX0 @ ( sK6_SY262 @ SX0 ) ) ) )
| ~ ( ( ( sK5_SY240 @ SX0 )
!= ( sK6_SY262 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(35,plain,
( ( ~ ! [SX0: $i > $i] :
~ ( ~ ~ ( ~ ~ ( ~ ( ( sK1_SY0 @ ( sK5_SY240 @ SX0 ) )
| ( sK3_SY199 @ ( sK5_SY240 @ SX0 ) ) )
| ~ ( ( sK1_SY0 @ ( sK6_SY262 @ SX0 ) )
| ( sK3_SY199 @ ( sK6_SY262 @ SX0 ) ) ) )
| ( ( SX0 @ ( sK5_SY240 @ SX0 ) )
!= ( SX0 @ ( sK6_SY262 @ SX0 ) ) ) )
| ~ ( ( ( sK5_SY240 @ SX0 )
!= ( sK6_SY262 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(43,plain,
( ( ! [SX0: $i > $i] :
~ ( ~ ~ ( ~ ~ ( ~ ( ( sK1_SY0 @ ( sK5_SY240 @ SX0 ) )
| ( sK3_SY199 @ ( sK5_SY240 @ SX0 ) ) )
| ~ ( ( sK1_SY0 @ ( sK6_SY262 @ SX0 ) )
| ( sK3_SY199 @ ( sK6_SY262 @ SX0 ) ) ) )
| ( ( SX0 @ ( sK5_SY240 @ SX0 ) )
!= ( SX0 @ ( sK6_SY262 @ SX0 ) ) ) )
| ~ ( ( ( sK5_SY240 @ SX0 )
!= ( sK6_SY262 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(50,plain,
! [SV3: $i > $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( sK1_SY0 @ ( sK5_SY240 @ SV3 ) )
| ( sK3_SY199 @ ( sK5_SY240 @ SV3 ) ) )
| ~ ( ( sK1_SY0 @ ( sK6_SY262 @ SV3 ) )
| ( sK3_SY199 @ ( sK6_SY262 @ SV3 ) ) ) )
| ( ( SV3 @ ( sK5_SY240 @ SV3 ) )
!= ( SV3 @ ( sK6_SY262 @ SV3 ) ) ) )
| ~ ( ( ( sK5_SY240 @ SV3 )
!= ( sK6_SY262 @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(62,plain,
! [SV3: $i > $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ( sK1_SY0 @ ( sK5_SY240 @ SV3 ) )
| ( sK3_SY199 @ ( sK5_SY240 @ SV3 ) ) )
| ~ ( ( sK1_SY0 @ ( sK6_SY262 @ SV3 ) )
| ( sK3_SY199 @ ( sK6_SY262 @ SV3 ) ) ) )
| ( ( SV3 @ ( sK5_SY240 @ SV3 ) )
!= ( SV3 @ ( sK6_SY262 @ SV3 ) ) ) )
| ~ ( ( ( sK5_SY240 @ SV3 )
!= ( sK6_SY262 @ SV3 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(75,plain,
! [SV3: $i > $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ( sK1_SY0 @ ( sK5_SY240 @ SV3 ) )
| ( sK3_SY199 @ ( sK5_SY240 @ SV3 ) ) )
| ~ ( ( sK1_SY0 @ ( sK6_SY262 @ SV3 ) )
| ( sK3_SY199 @ ( sK6_SY262 @ SV3 ) ) ) )
| ( ( SV3 @ ( sK5_SY240 @ SV3 ) )
!= ( SV3 @ ( sK6_SY262 @ SV3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(76,plain,
! [SV3: $i > $i] :
( ( ~ ( ( ( sK5_SY240 @ SV3 )
!= ( sK6_SY262 @ SV3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(89,plain,
! [SV3: $i > $i] :
( ( ~ ( ~ ~ ( ~ ( ( sK1_SY0 @ ( sK5_SY240 @ SV3 ) )
| ( sK3_SY199 @ ( sK5_SY240 @ SV3 ) ) )
| ~ ( ( sK1_SY0 @ ( sK6_SY262 @ SV3 ) )
| ( sK3_SY199 @ ( sK6_SY262 @ SV3 ) ) ) )
| ( ( SV3 @ ( sK5_SY240 @ SV3 ) )
!= ( SV3 @ ( sK6_SY262 @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(90,plain,
! [SV3: $i > $i] :
( ( ( sK5_SY240 @ SV3 )
!= ( sK6_SY262 @ SV3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(104,plain,
! [SV3: $i > $i] :
( ( ~ ~ ( ~ ( ( sK1_SY0 @ ( sK5_SY240 @ SV3 ) )
| ( sK3_SY199 @ ( sK5_SY240 @ SV3 ) ) )
| ~ ( ( sK1_SY0 @ ( sK6_SY262 @ SV3 ) )
| ( sK3_SY199 @ ( sK6_SY262 @ SV3 ) ) ) )
| ( ( SV3 @ ( sK5_SY240 @ SV3 ) )
!= ( SV3 @ ( sK6_SY262 @ SV3 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(105,plain,
! [SV3: $i > $i] :
( ( ( sK5_SY240 @ SV3 )
= ( sK6_SY262 @ SV3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(120,plain,
! [SV3: $i > $i] :
( ( ( SV3 @ ( sK5_SY240 @ SV3 ) )
!= ( SV3 @ ( sK6_SY262 @ SV3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[104]) ).
thf(138,plain,
! [SV3: $i > $i] :
( ( ( SV3 @ ( sK5_SY240 @ SV3 ) )
= ( SV3 @ ( sK6_SY262 @ SV3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(339,plain,
! [SV16: $i > $i] :
( ( ( sK5_SY240 @ SV16 )
= ( sK6_SY262 @ SV16 ) )
= $false ),
inference(rename,[status(thm)],[105]) ).
thf(342,plain,
! [SV17: $i > $i] :
( ( ( SV17 @ ( sK5_SY240 @ SV17 ) )
= ( SV17 @ ( sK6_SY262 @ SV17 ) ) )
= $true ),
inference(rename,[status(thm)],[138]) ).
thf(343,plain,
! [SV17: $i > $i,SV16: $i > $i] :
( ( ( ( SV17 @ ( sK5_SY240 @ SV17 ) )
= ( SV17 @ ( sK6_SY262 @ SV17 ) ) )
= ( ( sK5_SY240 @ SV16 )
= ( sK6_SY262 @ SV16 ) ) )
= $false ),
inference(res,[status(thm)],[342,339]) ).
thf(349,plain,
$false = $true,
inference(extuni,[status(esa)],[343:[bind(SV16,$thf( ^ [SX0: $i] : SX0 )),bind(SV17,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(350,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[349]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV420^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.20 % Computer : n018.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 15:48:52 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.09/0.53
% 1.09/0.53 No.of.Axioms: 0
% 1.09/0.53
% 1.09/0.53 Length.of.Defs: 3306
% 1.09/0.53
% 1.09/0.53 Contains.Choice.Funs: false
% 1.09/0.53 ..........
% 1.09/0.53
% 1.09/0.53 ********************************
% 1.09/0.53 * All subproblems solved! *
% 1.09/0.53 ********************************
% 1.09/0.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,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:349,loop_count:4,foatp_calls:2,translation:fof_experiment)
% 1.09/0.53
% 1.09/0.53 %**** Beginning of derivation protocol ****
% 1.09/0.53 % SZS output start CNFRefutation
% See solution above
% 1.09/0.53
% 1.09/0.53 %**** End of derivation protocol ****
% 1.09/0.53 %**** no. of clauses in derivation: 30 ****
% 1.09/0.53 %**** clause counter: 349 ****
% 1.09/0.53
% 1.09/0.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,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:349,loop_count:4,foatp_calls:2,translation:fof_experiment)
%------------------------------------------------------------------------------