%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEG002^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/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 07:49:22 AM UTC 2026
% Result : Theorem 14.63s 3.35s
% Output : Refutation 14.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 24
% Syntax : Number of formulae : 126 ( 56 unt; 0 typ; 18 def)
% Number of atoms : 445 ( 111 equ; 0 cnn)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 1028 ( 184 ~; 114 |; 55 &; 642 @)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 9 con; 0-2 aty)
% Number of variables : 138 ( 22 ^; 93 !; 12 ?; 138 :)
% ( 0 !>; 0 ?*; 0 @-; 11 @+)
% Comments :
%------------------------------------------------------------------------------
thf(reg_type,type,
reg: $tType ).
thf(c_decl,type,
c: reg > reg > $o ).
thf(dc_decl,type,
dc: reg > reg > $o ).
thf(p_decl,type,
p: reg > reg > $o ).
thf(o_decl,type,
o: reg > reg > $o ).
thf(ec_decl,type,
ec: reg > reg > $o ).
thf(pp_decl,type,
pp: reg > reg > $o ).
thf(tpp_decl,type,
tpp: reg > reg > $o ).
thf(ntpp_decl,type,
ntpp: reg > reg > $o ).
thf(catalunya_decl,type,
catalunya: reg ).
thf(france_decl,type,
france: reg ).
thf(spain_decl,type,
spain: reg ).
thf(paris_decl,type,
paris: reg ).
thf(sk1_decl,type,
sk1: reg ).
thf(sk2_decl,type,
sk2: reg ).
thf(sk3_decl,type,
sk3: reg > reg ).
thf(sk4_decl,type,
sk4: reg > reg ).
thf(sk5_decl,type,
sk5: reg > reg ).
thf(sk6_decl,type,
sk6: reg > reg ).
thf(sk7_decl,type,
sk7: reg > reg ).
thf(sk8_decl,type,
sk8: reg > reg ).
thf(sk9_decl,type,
sk9: reg ).
thf(sk10_decl,type,
sk10: reg > reg ).
thf(sk11_decl,type,
sk11: reg > reg ).
thf(dc_def,definition,
( dc
= ( ^ [A: reg,B: reg] :
~ ( c @ A @ B ) ) ) ).
thf(p_def,definition,
( p
= ( ^ [A: reg,B: reg] :
! [C: reg] :
( ( c @ C @ A )
=> ( c @ C @ B ) ) ) ) ).
thf(o_def,definition,
( o
= ( ^ [A: reg,B: reg] :
? [C: reg] :
( ( p @ C @ A )
& ( p @ C @ B ) ) ) ) ).
thf(ec_def,definition,
( ec
= ( ^ [A: reg,B: reg] :
( ( c @ A @ B )
& ~ ( o @ A @ B ) ) ) ) ).
thf(pp_def,definition,
( pp
= ( ^ [A: reg,B: reg] :
( ( p @ A @ B )
& ~ ( p @ B @ A ) ) ) ) ).
thf(tpp_def,definition,
( tpp
= ( ^ [A: reg,B: reg] :
( ( pp @ A @ B )
& ? [C: reg] :
( ( ec @ C @ A )
& ( ec @ C @ B ) ) ) ) ) ).
thf(ntpp_def,definition,
( ntpp
= ( ^ [A: reg,B: reg] :
( ( pp @ A @ B )
& ~ ? [C: reg] :
( ( ec @ C @ A )
& ( ec @ C @ B ) ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: reg] :
~ ( ( c @ A @ spain )
=> ( c @ A @ catalunya ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: reg] :
( ( c @ A @ catalunya )
& ~ ? [B: reg] :
( ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ A ) )
& ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ catalunya ) ) )
& ( c @ A @ spain )
& ~ ? [B: reg] :
( ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ A ) )
& ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ spain ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: reg] :
@+[B: reg] :
~ ( ( c @ B @ A )
=> ( c @ B @ sk2 ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: reg] :
@+[B: reg] :
~ ( ( c @ B @ A )
=> ( c @ B @ catalunya ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: reg] :
@+[B: reg] :
~ ( ( c @ B @ A )
=> ( c @ B @ sk2 ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: reg] :
@+[B: reg] :
~ ( ( c @ B @ A )
=> ( c @ B @ spain ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: reg] :
@+[B: reg] :
~ ( ( c @ B @ A )
=> ( c @ B @ spain ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: reg] :
@+[B: reg] :
~ ( ( c @ B @ A )
=> ( c @ B @ france ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: reg] :
~ ( ( c @ A @ france )
=> ( c @ A @ paris ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: reg] :
@+[B: reg] :
( ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ A ) )
& ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ paris ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: reg] :
@+[B: reg] :
( ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ A ) )
& ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ france ) ) ) ) ) ).
thf(3,axiom,
! [A: reg] : ( c @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_reflexive) ).
thf(10,plain,
! [A: reg] : ( c @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
tpp @ catalunya @ spain,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(14,plain,
( ! [A: reg] :
( ( c @ A @ catalunya )
=> ( c @ A @ spain ) )
& ~ ! [A: reg] :
( ( c @ A @ spain )
=> ( c @ A @ catalunya ) )
& ? [A: reg] :
( ( c @ A @ catalunya )
& ~ ? [B: reg] :
( ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ A ) )
& ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ catalunya ) ) )
& ( c @ A @ spain )
& ~ ? [B: reg] :
( ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ A ) )
& ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ spain ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,plain,
! [C: reg,B: reg,A: reg] :
( ( ~ ( c @ A @ catalunya )
| ( c @ A @ spain ) )
& ( c @ sk1 @ spain )
& ~ ( c @ sk1 @ catalunya )
& ( c @ sk2 @ catalunya )
& ( ( c @ ( sk3 @ B ) @ B )
| ( c @ ( sk4 @ B ) @ B ) )
& ( ( c @ ( sk3 @ B ) @ B )
| ~ ( c @ ( sk4 @ B ) @ catalunya ) )
& ( ~ ( c @ ( sk3 @ B ) @ sk2 )
| ( c @ ( sk4 @ B ) @ B ) )
& ( ~ ( c @ ( sk3 @ B ) @ sk2 )
| ~ ( c @ ( sk4 @ B ) @ catalunya ) )
& ( c @ sk2 @ spain )
& ( ( c @ ( sk5 @ C ) @ C )
| ( c @ ( sk6 @ C ) @ C ) )
& ( ( c @ ( sk5 @ C ) @ C )
| ~ ( c @ ( sk6 @ C ) @ spain ) )
& ( ~ ( c @ ( sk5 @ C ) @ sk2 )
| ( c @ ( sk6 @ C ) @ C ) )
& ( ~ ( c @ ( sk5 @ C ) @ sk2 )
| ~ ( c @ ( sk6 @ C ) @ spain ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(20,plain,
! [A: reg] :
( ( c @ ( sk3 @ A ) @ A )
| ( c @ ( sk4 @ A ) @ A ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(29,plain,
! [A: reg] :
( ( c @ ( sk3 @ A ) @ A )
| ( c @ ( sk4 @ A ) @ A ) ),
inference(simp,[status(thm)],[20]) ).
thf(11,plain,
! [A: reg] : ( c @ A @ A ),
inference(cnf,[status(esa)],[10]) ).
thf(24,plain,
! [A: reg] :
( ~ ( c @ A @ catalunya )
| ( c @ A @ spain ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(346,plain,
! [B: reg,A: reg] :
( ~ $true
| ( c @ B @ spain )
| ( ( c @ A @ A )
!= ( c @ B @ catalunya ) ) ),
inference(paramod_ordered,[status(thm)],[11,24]) ).
thf(347,plain,
! [B: reg,A: reg] :
( ( c @ B @ spain )
| ( ( c @ A @ A )
!= ( c @ B @ catalunya ) ) ),
inference(simp,[status(thm)],[346]) ).
thf(348,plain,
c @ catalunya @ spain,
inference(pattern_uni,[status(thm)],[347:[bind(A,$thf( catalunya )),bind(B,$thf( catalunya ))]]) ).
thf(7,axiom,
ntpp @ paris @ france,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(44,plain,
( ! [A: reg] :
( ( c @ A @ paris )
=> ( c @ A @ france ) )
& ~ ! [A: reg] :
( ( c @ A @ france )
=> ( c @ A @ paris ) )
& ~ ? [A: reg] :
( ( c @ A @ paris )
& ~ ? [B: reg] :
( ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ A ) )
& ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ paris ) ) )
& ( c @ A @ france )
& ~ ? [B: reg] :
( ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ A ) )
& ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ france ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(45,plain,
! [F: reg,E: reg,D: reg,C: reg,B: reg,A: reg] :
( ( ~ ( c @ A @ paris )
| ( c @ A @ france ) )
& ( c @ sk9 @ france )
& ~ ( c @ sk9 @ paris )
& ( ~ ( c @ B @ paris )
| ~ ( c @ C @ ( sk10 @ B ) )
| ( c @ C @ B )
| ~ ( c @ B @ france )
| ~ ( c @ E @ ( sk11 @ B ) )
| ( c @ E @ B ) )
& ( ~ ( c @ B @ paris )
| ~ ( c @ C @ ( sk10 @ B ) )
| ( c @ C @ B )
| ~ ( c @ B @ france )
| ~ ( c @ F @ ( sk11 @ B ) )
| ( c @ F @ france ) )
& ( ~ ( c @ B @ paris )
| ~ ( c @ D @ ( sk10 @ B ) )
| ( c @ D @ paris )
| ~ ( c @ B @ france )
| ~ ( c @ E @ ( sk11 @ B ) )
| ( c @ E @ B ) )
& ( ~ ( c @ B @ paris )
| ~ ( c @ D @ ( sk10 @ B ) )
| ( c @ D @ paris )
| ~ ( c @ B @ france )
| ~ ( c @ F @ ( sk11 @ B ) )
| ( c @ F @ france ) ) ),
inference(cnf,[status(esa)],[44]) ).
thf(52,plain,
c @ sk9 @ france,
inference(cnfConj,[status(thm)],[45]) ).
thf(4,axiom,
! [A: reg,B: reg] :
( ( c @ A @ B )
=> ( c @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_symmetric) ).
thf(12,plain,
! [A: reg,B: reg] :
( ( c @ A @ B )
=> ( c @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [B: reg,A: reg] :
( ~ ( c @ A @ B )
| ( c @ B @ A ) ),
inference(cnf,[status(esa)],[12]) ).
thf(131,plain,
! [B: reg,A: reg] :
( ~ $true
| ( c @ B @ A )
| ( ( c @ sk9 @ france )
!= ( c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[52,13]) ).
thf(132,plain,
! [B: reg,A: reg] :
( ( c @ B @ A )
| ( ( c @ sk9 @ france )
!= ( c @ A @ B ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(133,plain,
c @ france @ sk9,
inference(pattern_uni,[status(thm)],[132:[bind(A,$thf( sk9 )),bind(B,$thf( france ))]]) ).
thf(19,plain,
c @ sk2 @ catalunya,
inference(cnfConj,[status(thm)],[15]) ).
thf(50,plain,
~ ( c @ sk9 @ paris ),
inference(cnfConj,[status(thm)],[45]) ).
thf(67,plain,
( ~ $true
| ( ( c @ sk9 @ paris )
!= ( c @ sk2 @ catalunya ) ) ),
inference(paramod_ordered,[status(thm)],[19,50]) ).
thf(68,plain,
( ( c @ sk9 @ paris )
!= ( c @ sk2 @ catalunya ) ),
inference(simp,[status(thm)],[67]) ).
thf(70,plain,
( ( sk9 != sk2 )
| ( paris != catalunya ) ),
inference(simp,[status(thm)],[68]) ).
thf(1,conjecture,
( ( dc @ catalunya @ paris )
& ( dc @ spain @ paris ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( ( dc @ catalunya @ paris )
& ( dc @ spain @ paris ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ( ~ ( c @ catalunya @ paris )
& ~ ( c @ spain @ paris ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
( ( c @ catalunya @ paris )
| ( c @ spain @ paris ) ),
inference(cnf,[status(esa)],[8]) ).
thf(25,plain,
c @ sk2 @ spain,
inference(cnfConj,[status(thm)],[15]) ).
thf(128,plain,
! [B: reg,A: reg] :
( ~ $true
| ( c @ B @ A )
| ( ( c @ sk2 @ spain )
!= ( c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[25,13]) ).
thf(129,plain,
! [B: reg,A: reg] :
( ( c @ B @ A )
| ( ( c @ sk2 @ spain )
!= ( c @ A @ B ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(130,plain,
c @ spain @ sk2,
inference(pattern_uni,[status(thm)],[129:[bind(A,$thf( sk2 )),bind(B,$thf( spain ))]]) ).
thf(22,plain,
c @ sk1 @ spain,
inference(cnfConj,[status(thm)],[15]) ).
thf(143,plain,
! [B: reg,A: reg] :
( ~ $true
| ( c @ B @ A )
| ( ( c @ sk1 @ spain )
!= ( c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[22,13]) ).
thf(144,plain,
! [B: reg,A: reg] :
( ( c @ B @ A )
| ( ( c @ sk1 @ spain )
!= ( c @ A @ B ) ) ),
inference(simp,[status(thm)],[143]) ).
thf(145,plain,
c @ spain @ sk1,
inference(pattern_uni,[status(thm)],[144:[bind(A,$thf( sk1 )),bind(B,$thf( spain ))]]) ).
thf(6,axiom,
ec @ spain @ france,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(37,plain,
( ( c @ spain @ france )
& ~ ? [A: reg] :
( ! [B: reg] :
( ( c @ B @ A )
=> ( c @ B @ spain ) )
& ! [B: reg] :
( ( c @ B @ A )
=> ( c @ B @ france ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(38,plain,
! [A: reg] :
( ( c @ spain @ france )
& ( ( c @ ( sk7 @ A ) @ A )
| ( c @ ( sk8 @ A ) @ A ) )
& ( ( c @ ( sk7 @ A ) @ A )
| ~ ( c @ ( sk8 @ A ) @ france ) )
& ( ~ ( c @ ( sk7 @ A ) @ spain )
| ( c @ ( sk8 @ A ) @ A ) )
& ( ~ ( c @ ( sk7 @ A ) @ spain )
| ~ ( c @ ( sk8 @ A ) @ france ) ) ),
inference(cnf,[status(esa)],[37]) ).
thf(43,plain,
c @ spain @ france,
inference(cnfConj,[status(thm)],[38]) ).
thf(161,plain,
! [B: reg,A: reg] :
( ~ $true
| ( c @ B @ A )
| ( ( c @ spain @ france )
!= ( c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[43,13]) ).
thf(162,plain,
! [B: reg,A: reg] :
( ( c @ B @ A )
| ( ( c @ spain @ france )
!= ( c @ A @ B ) ) ),
inference(simp,[status(thm)],[161]) ).
thf(163,plain,
c @ france @ spain,
inference(pattern_uni,[status(thm)],[162:[bind(A,$thf( spain )),bind(B,$thf( france ))]]) ).
thf(65,plain,
( ~ $true
| ( ( c @ sk9 @ paris )
!= ( c @ sk1 @ spain ) ) ),
inference(paramod_ordered,[status(thm)],[22,50]) ).
thf(66,plain,
( ( c @ sk9 @ paris )
!= ( c @ sk1 @ spain ) ),
inference(simp,[status(thm)],[65]) ).
thf(69,plain,
( ( sk9 != sk1 )
| ( paris != spain ) ),
inference(simp,[status(thm)],[66]) ).
thf(95,plain,
! [A: reg] :
( ~ $true
| ( ( c @ A @ A )
!= ( c @ sk9 @ paris ) ) ),
inference(paramod_ordered,[status(thm)],[11,50]) ).
thf(96,plain,
! [A: reg] :
( ( c @ A @ A )
!= ( c @ sk9 @ paris ) ),
inference(simp,[status(thm)],[95]) ).
thf(99,plain,
! [A: reg] :
( ( A != sk9 )
| ( A != paris ) ),
inference(simp,[status(thm)],[96]) ).
thf(101,plain,
sk9 != paris,
inference(simp,[status(thm)],[99]) ).
thf(406,plain,
! [B: reg,A: reg] :
( ~ $true
| ( c @ B @ A )
| ( ( c @ catalunya @ spain )
!= ( c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[348,13]) ).
thf(407,plain,
! [B: reg,A: reg] :
( ( c @ B @ A )
| ( ( c @ catalunya @ spain )
!= ( c @ A @ B ) ) ),
inference(simp,[status(thm)],[406]) ).
thf(408,plain,
c @ spain @ catalunya,
inference(pattern_uni,[status(thm)],[407:[bind(A,$thf( catalunya )),bind(B,$thf( spain ))]]) ).
thf(109,plain,
( ~ $true
| ( ( c @ sk9 @ paris )
!= ( c @ sk9 @ france ) ) ),
inference(paramod_ordered,[status(thm)],[52,50]) ).
thf(110,plain,
( ( c @ sk9 @ paris )
!= ( c @ sk9 @ france ) ),
inference(simp,[status(thm)],[109]) ).
thf(113,plain,
( ( sk9 != sk9 )
| ( paris != france ) ),
inference(simp,[status(thm)],[110]) ).
thf(115,plain,
paris != france,
inference(simp,[status(thm)],[113]) ).
thf(17,plain,
~ ( c @ sk1 @ catalunya ),
inference(cnfConj,[status(thm)],[15]) ).
thf(155,plain,
! [B: reg,A: reg] :
( ~ ( c @ A @ B )
| ~ $true
| ( ( c @ B @ A )
!= ( c @ sk1 @ catalunya ) ) ),
inference(paramod_ordered,[status(thm)],[13,17]) ).
thf(156,plain,
! [B: reg,A: reg] :
( ~ ( c @ A @ B )
| ( ( c @ B @ A )
!= ( c @ sk1 @ catalunya ) ) ),
inference(simp,[status(thm)],[155]) ).
thf(157,plain,
~ ( c @ catalunya @ sk1 ),
inference(pattern_uni,[status(thm)],[156:[bind(A,$thf( catalunya )),bind(B,$thf( sk1 ))]]) ).
thf(57,plain,
( ~ $true
| ( ( c @ sk2 @ catalunya )
!= ( c @ sk1 @ catalunya ) ) ),
inference(paramod_ordered,[status(thm)],[19,17]) ).
thf(58,plain,
( ( c @ sk2 @ catalunya )
!= ( c @ sk1 @ catalunya ) ),
inference(simp,[status(thm)],[57]) ).
thf(59,plain,
( ( sk2 != sk1 )
| ( catalunya != catalunya ) ),
inference(simp,[status(thm)],[58]) ).
thf(60,plain,
sk2 != sk1,
inference(simp,[status(thm)],[59]) ).
thf(97,plain,
! [A: reg] :
( ~ $true
| ( ( c @ A @ A )
!= ( c @ sk1 @ catalunya ) ) ),
inference(paramod_ordered,[status(thm)],[11,17]) ).
thf(98,plain,
! [A: reg] :
( ( c @ A @ A )
!= ( c @ sk1 @ catalunya ) ),
inference(simp,[status(thm)],[97]) ).
thf(100,plain,
! [A: reg] :
( ( A != sk1 )
| ( A != catalunya ) ),
inference(simp,[status(thm)],[98]) ).
thf(102,plain,
sk1 != catalunya,
inference(simp,[status(thm)],[100]) ).
thf(413,plain,
( ~ $true
| ( ( c @ catalunya @ sk1 )
!= ( c @ catalunya @ spain ) ) ),
inference(paramod_ordered,[status(thm)],[348,157]) ).
thf(414,plain,
( ( c @ catalunya @ sk1 )
!= ( c @ catalunya @ spain ) ),
inference(simp,[status(thm)],[413]) ).
thf(421,plain,
( ( catalunya != catalunya )
| ( sk1 != spain ) ),
inference(simp,[status(thm)],[414]) ).
thf(425,plain,
sk1 != spain,
inference(simp,[status(thm)],[421]) ).
thf(77,plain,
( ( c @ catalunya @ paris )
| ~ $true
| ( ( c @ sk9 @ paris )
!= ( c @ spain @ paris ) ) ),
inference(paramod_ordered,[status(thm)],[9,50]) ).
thf(78,plain,
( ( c @ catalunya @ paris )
| ( ( c @ sk9 @ paris )
!= ( c @ spain @ paris ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(82,plain,
( ( c @ catalunya @ paris )
| ( sk9 != spain )
| ( paris != paris ) ),
inference(simp,[status(thm)],[78]) ).
thf(86,plain,
( ( c @ catalunya @ paris )
| ( sk9 != spain ) ),
inference(simp,[status(thm)],[82]) ).
thf(146,plain,
! [B: reg,A: reg] :
( ( sk9 != spain )
| ~ $true
| ( c @ B @ A )
| ( ( c @ catalunya @ paris )
!= ( c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[86,13]) ).
thf(147,plain,
! [B: reg,A: reg] :
( ( sk9 != spain )
| ( c @ B @ A )
| ( ( c @ catalunya @ paris )
!= ( c @ A @ B ) ) ),
inference(simp,[status(thm)],[146]) ).
thf(148,plain,
( ( sk9 != spain )
| ( c @ paris @ catalunya ) ),
inference(pattern_uni,[status(thm)],[147:[bind(A,$thf( catalunya )),bind(B,$thf( paris ))]]) ).
thf(61,plain,
( ~ $true
| ( ( c @ sk1 @ spain )
!= ( c @ sk1 @ catalunya ) ) ),
inference(paramod_ordered,[status(thm)],[22,17]) ).
thf(62,plain,
( ( c @ sk1 @ spain )
!= ( c @ sk1 @ catalunya ) ),
inference(simp,[status(thm)],[61]) ).
thf(63,plain,
( ( sk1 != sk1 )
| ( spain != catalunya ) ),
inference(simp,[status(thm)],[62]) ).
thf(64,plain,
spain != catalunya,
inference(simp,[status(thm)],[63]) ).
thf(152,plain,
! [B: reg,A: reg] :
( ~ $true
| ( c @ B @ A )
| ( ( c @ sk2 @ catalunya )
!= ( c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19,13]) ).
thf(153,plain,
! [B: reg,A: reg] :
( ( c @ B @ A )
| ( ( c @ sk2 @ catalunya )
!= ( c @ A @ B ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(154,plain,
c @ catalunya @ sk2,
inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( sk2 )),bind(B,$thf( catalunya ))]]) ).
thf(71,plain,
( ~ $true
| ( ( c @ sk9 @ paris )
!= ( c @ sk2 @ spain ) ) ),
inference(paramod_ordered,[status(thm)],[25,50]) ).
thf(72,plain,
( ( c @ sk9 @ paris )
!= ( c @ sk2 @ spain ) ),
inference(simp,[status(thm)],[71]) ).
thf(75,plain,
( ( sk9 != sk2 )
| ( paris != spain ) ),
inference(simp,[status(thm)],[72]) ).
thf(149,plain,
! [B: reg,A: reg] :
( ~ ( c @ A @ B )
| ~ $true
| ( ( c @ B @ A )
!= ( c @ sk9 @ paris ) ) ),
inference(paramod_ordered,[status(thm)],[13,50]) ).
thf(150,plain,
! [B: reg,A: reg] :
( ~ ( c @ A @ B )
| ( ( c @ B @ A )
!= ( c @ sk9 @ paris ) ) ),
inference(simp,[status(thm)],[149]) ).
thf(151,plain,
~ ( c @ paris @ sk9 ),
inference(pattern_uni,[status(thm)],[150:[bind(A,$thf( paris )),bind(B,$thf( sk9 ))]]) ).
thf(245,plain,
( ( sk9 != spain )
| ~ $true
| ( ( c @ catalunya @ sk1 )
!= ( c @ catalunya @ paris ) ) ),
inference(paramod_ordered,[status(thm)],[86,157]) ).
thf(246,plain,
( ( sk9 != spain )
| ( ( c @ catalunya @ sk1 )
!= ( c @ catalunya @ paris ) ) ),
inference(simp,[status(thm)],[245]) ).
thf(269,plain,
( ( sk9 != spain )
| ( catalunya != catalunya )
| ( sk1 != paris ) ),
inference(simp,[status(thm)],[246]) ).
thf(273,plain,
( ( sk9 != spain )
| ( sk1 != paris ) ),
inference(simp,[status(thm)],[269]) ).
thf(339,plain,
! [A: reg] :
( ( sk9 != spain )
| ~ $true
| ( c @ A @ spain )
| ( ( c @ paris @ catalunya )
!= ( c @ A @ catalunya ) ) ),
inference(paramod_ordered,[status(thm)],[148,24]) ).
thf(340,plain,
! [A: reg] :
( ( sk9 != spain )
| ( c @ A @ spain )
| ( ( c @ paris @ catalunya )
!= ( c @ A @ catalunya ) ) ),
inference(simp,[status(thm)],[339]) ).
thf(341,plain,
( ( sk9 != spain )
| ( c @ paris @ spain ) ),
inference(pattern_uni,[status(thm)],[340:[bind(A,$thf( paris ))]]) ).
thf(88,plain,
( ( sk9 != spain )
| ~ $true
| ( ( c @ sk9 @ paris )
!= ( c @ catalunya @ paris ) ) ),
inference(paramod_ordered,[status(thm)],[86,50]) ).
thf(89,plain,
( ( sk9 != spain )
| ( ( c @ sk9 @ paris )
!= ( c @ catalunya @ paris ) ) ),
inference(simp,[status(thm)],[88]) ).
thf(92,plain,
( ( sk9 != spain )
| ( sk9 != catalunya )
| ( paris != paris ) ),
inference(simp,[status(thm)],[89]) ).
thf(94,plain,
( ( sk9 != spain )
| ( sk9 != catalunya ) ),
inference(simp,[status(thm)],[92]) ).
thf(9892,plain,
$false,
inference(e,[status(thm)],[10,29,348,133,70,9,13,130,145,50,163,69,101,408,115,24,37,25,52,14,157,60,102,425,148,64,17,22,44,12,86,154,11,43,8,75,151,19,273,341,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEG002^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.06/0.13 % Computer : n012.cluster.edu
% 0.06/0.13 % Model : x86_64 x86_64
% 0.06/0.13 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.13 % Memory : 8046.5625MB
% 0.06/0.13 % OS : Linux 6.8.0-71-generic
% 0.06/0.13 % CPULimit : 300
% 0.06/0.13 % WCLimit : 300
% 0.06/0.13 % DateTime : Tue Sep 29 18:33:18 UTC 2026
% 0.06/0.13 % CPUTime :
% 0.06/0.13 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.39/0.43 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.53/0.53 % [INFO] Parsing done (99ms).
% 0.75/0.54 % [INFO] Running in sequential loop mode.
% 1.01/0.73 % [INFO] eprover registered as external prover.
% 1.01/0.73 % [INFO] Scanning for conjecture ...
% 1.01/0.79 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 1.23/0.81 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.23/0.81 % [INFO] Problem is higher-order (TPTP THF).
% 1.23/0.81 % [INFO] Type checking passed.
% 1.23/0.81 % [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 ...
% 14.63/3.34 % External prover 'e' found a proof!
% 14.63/3.34 % [INFO] Killing All external provers ...
% 14.63/3.35 % Time passed: 3138ms (effective reasoning time: 2805ms)
% 14.63/3.35 % 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)>
% 14.63/3.35 % Axioms used in derivation (5): c_symmetric, ax1, ax2, ax3, c_reflexive
% 14.63/3.35 % No. of inferences in proof: 108
% 14.63/3.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3138 ms resp. 2805 ms w/o parsing
% 14.63/3.39 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.63/3.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------