%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP210^4 : TPTP v9.3.1. Bugfixed v9.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 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 Sep 30 08:07:12 AM UTC 2026
% Result : Theorem 76.93s 20.25s
% Output : Refutation 76.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 3
% Syntax : Number of formulae : 59 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 354 ( 151 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 838 ( 74 ~; 50 |; 81 &; 633 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 12 ( 11 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 78 ( 59 ^; 19 !; 0 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(code_natural_type,type,
code_natural: $tType ).
thf(code_integer_type,type,
code_integer: $tType ).
thf(code_term_type,type,
code_term: $tType ).
thf(product_unit_type,type,
product_unit: $tType ).
thf(assn_type,type,
assn: $tType ).
thf(literal_type,type,
literal: $tType ).
thf(char_type,type,
char: $tType ).
thf(rat_type,type,
rat: $tType ).
thf(num_type,type,
num: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(abs_assn_decl,type,
abs_assn: ( ( product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat ) ) > $o ) > assn ).
thf(rep_assn_decl,type,
rep_assn: assn > ( product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat ) ) > $o ).
thf(x_decl,type,
x: assn ).
thf(y_decl,type,
y: assn ).
thf(sk67_decl,type,
sk67: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat ) ).
thf(1,conjecture,
( ( ( x
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) )
& ( x != y ) )
= ( ( x
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) )
& ( y
!= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( ( x
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) )
& ( x != y ) )
!= ( ( x
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) )
& ( y
!= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
( ( ( x
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) )
& ( x != y ) )
!= ( ( x
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) )
& ( y
!= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,plain,
( ( ( x
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) )
& ( y
!= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) ) ) )
!= ( ( x
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) )
& ( x != y ) ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(57,plain,
( ( ( x
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) )
!= ( x
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) ) )
| ( ( y
!= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) ) )
!= ( x != y ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(71,plain,
( ( y
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) ) )
!= ( x = y ) ),
inference(simp,[status(thm)],[57]) ).
thf(129,plain,
( ( y
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) ) )
| ( x = y ) ),
inference(bool_ext,[status(thm)],[71]) ).
thf(139,plain,
( ( ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) )
= y )
| ( y = x ) ),
inference(lifteq,[status(thm)],[129]) ).
thf(59,plain,
( ( ( x
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) )
& ( y
!= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) ) ) )
| ( ( x
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) )
& ( x != y ) ) ),
inference(bool_ext,[status(thm)],[14]) ).
thf(75,plain,
( ( ( x
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) )
| ( x
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) ) )
& ( ( x
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) )
| ( x != y ) )
& ( ( y
!= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) ) )
| ( x
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) ) )
& ( ( y
!= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) ) )
| ( x != y ) ) ),
inference(cnf,[status(esa)],[59]) ).
thf(76,plain,
( ( x
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) )
| ( x
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) ) ),
inference(cnfConj,[status(thm)],[75]) ).
thf(80,plain,
( ( ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) )
= x )
| ( ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) )
= x ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(81,plain,
( ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) )
= x ),
inference(simp,[status(thm)],[80]) ).
thf(179,plain,
( ( y = x )
| ( y = x )
| ( ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) )
!= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[139,81]) ).
thf(180,plain,
( ( y = x )
| ( ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) )
!= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) ) ),
inference(simp,[status(thm)],[179]) ).
thf(186,plain,
( ( y = x )
| ( ( ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) )
!= ( ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) ) ),
inference(simp,[status(thm)],[180]) ).
thf(7,axiom,
! [A: assn,B: assn] :
( ( ( rep_assn @ A )
= ( rep_assn @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_Rep__assn__inject) ).
thf(24,plain,
! [A: assn,B: assn] :
( ( ( rep_assn @ A )
= ( rep_assn @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(25,plain,
! [B: assn,A: assn] :
( ( ( rep_assn @ A )
= ( rep_assn @ B ) )
= ( A = B ) ),
inference(cnf,[status(esa)],[24]) ).
thf(26,plain,
! [B: assn,A: assn] :
( ( ( rep_assn @ A )
= ( rep_assn @ B ) )
= ( A = B ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(505,plain,
! [B: assn,A: assn] :
( ( ( ( rep_assn @ A )
= ( rep_assn @ B ) )
!= ( x = y ) )
| ( ( A = B )
!= ( y
= ( abs_assn
@ ^ [C: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ C )
& ( rep_assn @ x @ C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,71]) ).
thf(506,plain,
( ( ( rep_assn @ y )
= ( rep_assn
@ ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) ) ) )
!= ( x = y ) ),
inference(pattern_uni,[status(thm)],[505:[bind(A,$thf( y )),bind(B,$thf( abs_assn @ ^ [C: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] : ( ( rep_assn @ y @ C ) & ( rep_assn @ x @ C ) ) ))]]) ).
thf(520,plain,
( ( ( rep_assn @ y )
= ( rep_assn
@ ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) ) ) )
| ( x = y ) ),
inference(bool_ext,[status(thm)],[506]) ).
thf(564,plain,
( ( ( rep_assn
@ ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) ) )
= ( rep_assn @ y ) )
| ( y = x ) ),
inference(lifteq,[status(thm)],[520]) ).
thf(504,plain,
! [B: assn,A: assn] :
( ( ( A = B )
!= ( x = y ) )
| ( ( ( rep_assn @ A )
= ( rep_assn @ B ) )
!= ( y
= ( abs_assn
@ ^ [C: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ C )
& ( rep_assn @ x @ C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,71]) ).
thf(511,plain,
! [B: assn,A: assn] :
( ( A != x )
| ( B != y )
| ( ( ( rep_assn @ A )
= ( rep_assn @ B ) )
!= ( y
= ( abs_assn
@ ^ [C: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ C )
& ( rep_assn @ x @ C ) ) ) ) ) ),
inference(simp,[status(thm)],[504]) ).
thf(517,plain,
( ( ( rep_assn @ x )
= ( rep_assn @ y ) )
!= ( y
= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) ) ) ),
inference(simp,[status(thm)],[511]) ).
thf(606,plain,
( ( y = x )
| ( ( y = y )
!= ( ( rep_assn @ x )
= ( rep_assn @ y ) ) )
| ( ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) )
!= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[139,517]) ).
thf(607,plain,
( ( y = x )
| ( ( rep_assn @ x )
!= ( rep_assn @ y ) )
| ( ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) )
!= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) ) ) ),
inference(simp,[status(thm)],[606]) ).
thf(608,plain,
( ( y = x )
| ( ( rep_assn @ x )
!= ( rep_assn @ y ) ) ),
inference(pattern_uni,[status(thm)],[607:[]]) ).
thf(618,plain,
( ( ( rep_assn @ y )
!= ( rep_assn @ x ) )
| ( y = x ) ),
inference(lifteq,[status(thm)],[608]) ).
thf(9,axiom,
! [A: assn] :
( ( abs_assn @ ( rep_assn @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_Rep__assn__inverse) ).
thf(30,plain,
! [A: assn] :
( ( abs_assn @ ( rep_assn @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(31,plain,
! [A: assn] :
( ( abs_assn @ ( rep_assn @ A ) )
= A ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [A: assn] :
( ( abs_assn @ ( rep_assn @ A ) )
= A ),
inference(lifteq,[status(thm)],[31]) ).
thf(79,plain,
( ( y
!= ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) ) )
| ( x != y ) ),
inference(cnfConj,[status(thm)],[75]) ).
thf(84,plain,
( ( ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) )
!= y )
| ( y != x ) ),
inference(lifteq,[status(thm)],[79]) ).
thf(105,plain,
! [A: assn] :
( ( A != y )
| ( y != x )
| ( ( abs_assn @ ( rep_assn @ A ) )
!= ( abs_assn
@ ^ [B: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ B )
& ( rep_assn @ x @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,84]) ).
thf(124,plain,
( ( y != x )
| ( ( ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) )
!= ( rep_assn @ y ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(919,plain,
( ( ( rep_assn @ y )
!= ( rep_assn @ x ) )
| ( y != x )
| ( ( rep_assn @ y )
!= ( ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ x @ A ) ) ) )
| ( y != y ) ),
inference(paramod_ordered,[status(thm)],[618,124]) ).
thf(920,plain,
( ( ( rep_assn @ y )
!= ( rep_assn @ x ) )
| ( y != x )
| ( y != y ) ),
inference(simp,[status(thm)],[919]) ).
thf(921,plain,
( ( ( rep_assn @ y )
!= ( rep_assn @ x ) )
| ( y != x ) ),
inference(pattern_uni,[status(thm)],[920:[]]) ).
thf(1535,plain,
( ( ( rep_assn @ y )
!= ( rep_assn @ x ) )
| ( ( rep_assn @ y )
!= ( rep_assn @ x ) )
| ( x != x )
| ( y != y ) ),
inference(paramod_ordered,[status(thm)],[618,921]) ).
thf(1536,plain,
( ( ( rep_assn @ y )
!= ( rep_assn @ x ) )
| ( y != y ) ),
inference(simp,[status(thm)],[1535]) ).
thf(1537,plain,
( ( rep_assn @ y )
!= ( rep_assn @ x ) ),
inference(pattern_uni,[status(thm)],[1536:[]]) ).
thf(1559,plain,
( ( ( rep_assn
@ ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) ) )
= ( rep_assn @ y ) )
| ( ( rep_assn @ x )
!= ( rep_assn @ x ) )
| ( y != y ) ),
inference(paramod_ordered,[status(thm)],[564,1537]) ).
thf(1560,plain,
( ( ( rep_assn
@ ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) ) )
= ( rep_assn @ y ) )
| ( y != y ) ),
inference(simp,[status(thm)],[1559]) ).
thf(1561,plain,
( ( rep_assn
@ ( abs_assn
@ ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) ) )
= ( rep_assn @ y ) ),
inference(pattern_uni,[status(thm)],[1560:[]]) ).
thf(1571,plain,
( ( ( rep_assn @ y )
= ( rep_assn @ y ) )
!= ( x = y ) ),
inference(rewrite,[status(thm)],[506,1561]) ).
thf(1572,plain,
x != y,
inference(simp,[status(thm)],[1571]) ).
thf(1624,plain,
y != x,
inference(lifteq,[status(thm)],[1572]) ).
thf(20421,plain,
( ( ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ y @ A )
& ( rep_assn @ x @ A ) ) )
!= ( ^ [A: product_prod @ ( heap_ext @ product_unit ) @ ( set @ nat )] :
( ( rep_assn @ x @ A )
& ( rep_assn @ y @ A ) ) ) ),
inference(simplifyReflect,[status(thm)],[186,1624]) ).
thf(20423,plain,
( ( ( rep_assn @ y @ sk67 )
& ( rep_assn @ x @ sk67 ) )
!= ( ( rep_assn @ x @ sk67 )
& ( rep_assn @ y @ sk67 ) ) ),
inference(func_ext,[status(esa)],[20421]) ).
thf(20521,plain,
( ( ( rep_assn @ y @ sk67 )
& ( rep_assn @ x @ sk67 ) )
| ( ( rep_assn @ x @ sk67 )
& ( rep_assn @ y @ sk67 ) ) ),
inference(bool_ext,[status(thm)],[20423]) ).
thf(20715,plain,
( ( ( rep_assn @ y @ sk67 )
| ( rep_assn @ x @ sk67 ) )
& ( ( rep_assn @ y @ sk67 )
| ( rep_assn @ y @ sk67 ) )
& ( ( rep_assn @ x @ sk67 )
| ( rep_assn @ x @ sk67 ) )
& ( ( rep_assn @ x @ sk67 )
| ( rep_assn @ y @ sk67 ) ) ),
inference(cnf,[status(esa)],[20521]) ).
thf(20717,plain,
( ( rep_assn @ y @ sk67 )
| ( rep_assn @ y @ sk67 ) ),
inference(cnfConj,[status(thm)],[20715]) ).
thf(20719,plain,
rep_assn @ y @ sk67,
inference(simp,[status(thm)],[20717]) ).
thf(20731,plain,
( ( $true
& ( rep_assn @ x @ sk67 ) )
!= ( ( rep_assn @ x @ sk67 )
& $true ) ),
inference(rewrite,[status(thm)],[20423,20719]) ).
thf(20732,plain,
$false,
inference(simp,[status(thm)],[20731]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP210^4 : TPTP v9.3.1. Bugfixed v9.2.1.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.06/0.12 % Computer : n012.cluster.edu
% 0.06/0.12 % Model : x86_64 x86_64
% 0.06/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.12 % Memory : 8046.5625MB
% 0.06/0.12 % OS : Linux 6.8.0-71-generic
% 0.06/0.12 % CPULimit : 300
% 0.06/0.12 % WCLimit : 300
% 0.06/0.12 % DateTime : Tue Sep 29 20:13:48 UTC 2026
% 0.06/0.12 % CPUTime :
% 0.06/0.12 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.39/0.40 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.87/1.33 % [INFO] Parsing done (924ms).
% 3.87/1.34 % [INFO] Running in sequential loop mode.
% 4.27/1.51 % [INFO] eprover registered as external prover.
% 4.27/1.52 % [INFO] Scanning for conjecture ...
% 5.34/1.84 % [INFO] Found a conjecture (or negated_conjecture) and 8622 axioms. Running axiom selection ...
% 5.72/1.96 % [INFO] Axiom selection finished. Selected 10 axioms (removed 8612 axioms).
% 5.72/1.98 % [INFO] Problem is higher-order (TPTP THF).
% 5.72/1.98 % [INFO] Type checking passed.
% 5.72/1.98 % [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 ...
% 76.93/20.24 % [INFO] Killing All external provers ...
% 76.93/20.25 % Time passed: 20054ms (effective reasoning time: 18901ms)
% 76.93/20.25 % 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)>
% 76.93/20.25 % Axioms used in derivation (2): fact_0_Rep__assn__inject, fact_1_Rep__assn__inverse
% 76.93/20.25 % No. of inferences in proof: 59
% 76.93/20.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 20054 ms resp. 18901 ms w/o parsing
% 76.19/20.30 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 76.19/20.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------