%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MSC007^1.003.004 : TPTP v9.3.1. Released v5.4.0.
% 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 : n015.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 08:15:36 AM UTC 2026
% Result : Theorem 27.19s 7.30s
% Output : Refutation 27.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 182 ( 52 unt; 0 typ; 1 def)
% Number of atoms : 565 ( 554 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 1668 ( 413 ~; 545 |; 7 &; 701 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 83 ( 83 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 9 usr; 10 con; 0-2 aty)
% Number of variables : 216 ( 0 ^; 208 !; 7 ?; 216 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(hole_type,type,
hole: $tType ).
thf(pigeon_type,type,
pigeon: $tType ).
thf(hole1_decl,type,
hole1: hole ).
thf(hole2_decl,type,
hole2: hole ).
thf(hole3_decl,type,
hole3: hole ).
thf(pigeon1_decl,type,
pigeon1: pigeon ).
thf(pigeon2_decl,type,
pigeon2: pigeon ).
thf(pigeon3_decl,type,
pigeon3: pigeon ).
thf(pigeon4_decl,type,
pigeon4: pigeon ).
thf(pigeon_hole_decl,type,
pigeon_hole: pigeon > hole ).
thf(sk1_decl,type,
sk1: hole > pigeon ).
thf(sk1_def,definition,
( sk1
= ( @+[A: hole > pigeon] :
! [B: pigeon] :
( ( A @ ( pigeon_hole @ B ) )
= B ) ) ) ).
thf(1,conjecture,
? [A: pigeon,B: pigeon] :
( ( ( pigeon_hole @ A )
= ( pigeon_hole @ B ) )
& ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sharing_a_hole) ).
thf(2,negated_conjecture,
~ ? [A: pigeon,B: pigeon] :
( ( ( pigeon_hole @ A )
= ( pigeon_hole @ B ) )
& ( A != B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ? [A: pigeon,B: pigeon] :
( ( ( pigeon_hole @ A )
= ( pigeon_hole @ B ) )
& ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: hole > $o] :
( ( ( A @ hole1 )
& ( A @ hole2 )
& ( A @ hole3 ) )
=> ! [B: hole] : ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',holecover) ).
thf(15,plain,
! [A: hole > $o] :
( ( ( A @ hole1 )
& ( A @ hole2 )
& ( A @ hole3 ) )
=> ! [B: hole] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,plain,
! [B: hole,A: hole > $o] :
( ~ ( A @ hole1 )
| ~ ( A @ hole2 )
| ~ ( A @ hole3 )
| ( A @ B ) ),
inference(cnf,[status(esa)],[15]) ).
thf(102,plain,
! [B: hole > $o,A: hole] :
( ~ ~ ( B @ hole1 )
| ~ ~ ( B @ hole2 )
| ~ ~ ( B @ hole3 )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[16:[bind(A,$thf( ^ [D: hole] : ~ ( C @ D ) ))]]) ).
thf(136,plain,
! [B: hole > $o,A: hole] :
( ( B @ hole1 )
| ( B @ hole2 )
| ( B @ hole3 )
| ~ ( B @ A ) ),
inference(cnf,[status(esa)],[102]) ).
thf(137,plain,
! [B: hole > $o,A: hole] :
( ( B @ hole1 )
| ( B @ hole2 )
| ( B @ hole3 )
| ~ ( B @ A ) ),
inference(simp,[status(thm)],[136]) ).
thf(181,plain,
! [D: hole > $o,C: hole,B: hole > $o,A: hole] :
( ( B @ hole1 )
| ( B @ hole2 )
| ~ ( B @ A )
| ( D @ hole1 )
| ( D @ hole2 )
| ( D @ hole3 )
| ~ $true
| ( ( B @ hole3 )
!= ( D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[137,137]) ).
thf(182,plain,
! [D: hole > $o,C: hole,B: hole > $o,A: hole] :
( ( B @ hole1 )
| ( B @ hole2 )
| ~ ( B @ A )
| ( D @ hole1 )
| ( D @ hole2 )
| ( D @ hole3 )
| ( ( B @ hole3 )
!= ( D @ C ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(209,plain,
! [C: hole > $o,B: hole,A: hole] :
( ( A = hole1 )
| ( A = hole2 )
| ( A != A )
| ( C @ hole1 )
| ( C @ hole2 )
| ( C @ hole3 )
| ( ( A = hole3 )
!= ( C @ B ) ) ),
inference(replace_leibeq,[status(thm)],[182:[bind(A,$thf( A )),bind(B,$thf( (=) @ hole @ A ))]]) ).
thf(217,plain,
! [C: hole > $o,B: hole,A: hole] :
( ( A = hole1 )
| ( A = hole2 )
| ( A != A )
| ( C @ hole1 )
| ( C @ hole2 )
| ( C @ hole3 )
| ( ( A = hole3 )
!= ( C @ B ) ) ),
inference(lifteq,[status(thm)],[209]) ).
thf(219,plain,
! [A: hole > hole] :
( ( ( A @ hole3 )
= hole3 )
| ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 ) ),
inference(pre_uni,[status(thm)],[217:[bind(A,$thf( D @ hole3 )),bind(B,$thf( hole3 )),bind(C,$thf( ^ [E: hole] : ( ( D @ E ) = E ) ))]]) ).
thf(251,plain,
! [A: hole > hole] :
( ( ( A @ hole3 )
= hole3 )
| ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 ) ),
inference(lifteq,[status(thm)],[219]) ).
thf(252,plain,
! [A: hole > hole] :
( ( ( A @ hole3 )
= hole3 )
| ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 ) ),
inference(simp,[status(thm)],[251]) ).
thf(11,plain,
! [B: pigeon,A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
! [B: pigeon,A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(6,axiom,
pigeon2 != pigeon3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pigeon2pigeon3) ).
thf(26,plain,
pigeon2 != pigeon3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(27,plain,
pigeon2 != pigeon3,
inference(polarity_switch,[status(thm)],[26]) ).
thf(28,plain,
pigeon3 != pigeon2,
inference(lifteq,[status(thm)],[27]) ).
thf(63,plain,
! [B: pigeon,A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ B ) )
| ( A != pigeon2 )
| ( B != pigeon3 ) ),
inference(paramod_ordered,[status(thm)],[12,28]) ).
thf(64,plain,
! [A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ pigeon3 ) )
| ( A != pigeon2 ) ),
inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( A )),bind(B,$thf( pigeon3 ))]]) ).
thf(69,plain,
( ( pigeon_hole @ pigeon3 )
!= ( pigeon_hole @ pigeon2 ) ),
inference(simp,[status(thm)],[64]) ).
thf(367,plain,
! [A: hole > hole] :
( ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
!= hole3 )
| ( ( A @ hole3 )
!= ( pigeon_hole @ pigeon3 ) ) ),
inference(paramod_ordered,[status(thm)],[252,69]) ).
thf(417,plain,
( ( ( pigeon_hole @ pigeon3 )
= hole2 )
| ( ( pigeon_hole @ pigeon3 )
= hole1 )
| ( ( pigeon_hole @ pigeon3 )
= hole2 )
| ( ( pigeon_hole @ pigeon3 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
!= hole3 ) ),
inference(pre_uni,[status(thm)],[367:[bind(A,$thf( ^ [B: hole] : ( pigeon_hole @ pigeon3 ) ))]]) ).
thf(444,plain,
( ( ( pigeon_hole @ pigeon3 )
= hole2 )
| ( ( pigeon_hole @ pigeon3 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
!= hole3 ) ),
inference(simp,[status(thm)],[417]) ).
thf(858,plain,
! [A: hole > hole] :
( ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 )
| ( ( pigeon_hole @ pigeon3 )
= hole2 )
| ( ( pigeon_hole @ pigeon3 )
= hole1 )
| ( hole3 != hole3 )
| ( ( A @ hole3 )
!= ( pigeon_hole @ pigeon2 ) ) ),
inference(paramod_ordered,[status(thm)],[252,444]) ).
thf(859,plain,
! [A: hole > hole] :
( ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 )
| ( ( pigeon_hole @ pigeon3 )
= hole2 )
| ( ( pigeon_hole @ pigeon3 )
= hole1 )
| ( ( A @ hole3 )
!= ( pigeon_hole @ pigeon2 ) ) ),
inference(simp,[status(thm)],[858]) ).
thf(894,plain,
( ( ( pigeon_hole @ pigeon2 )
= hole2 )
| ( ( pigeon_hole @ pigeon2 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
= hole2 )
| ( ( pigeon_hole @ pigeon2 )
= hole1 )
| ( ( pigeon_hole @ pigeon3 )
= hole2 )
| ( ( pigeon_hole @ pigeon3 )
= hole1 ) ),
inference(pre_uni,[status(thm)],[859:[bind(A,$thf( ^ [B: hole] : ( pigeon_hole @ pigeon2 ) ))]]) ).
thf(921,plain,
( ( ( pigeon_hole @ pigeon2 )
= hole2 )
| ( ( pigeon_hole @ pigeon2 )
= hole1 )
| ( ( pigeon_hole @ pigeon3 )
= hole2 )
| ( ( pigeon_hole @ pigeon3 )
= hole1 ) ),
inference(simp,[status(thm)],[894]) ).
thf(13,plain,
? [A: hole > pigeon] :
! [B: pigeon] :
( ( A @ ( pigeon_hole @ B ) )
= B ),
inference(detectInverse,[status(thm)],[12]) ).
thf(14,plain,
! [A: pigeon] :
( ( sk1 @ ( pigeon_hole @ A ) )
= A ),
inference(cnf,[status(esa)],[13]) ).
thf(38,plain,
! [A: pigeon] :
( ( sk1 @ ( pigeon_hole @ A ) )
= A ),
inference(lifteq,[status(thm)],[14]) ).
thf(1859,plain,
! [A: pigeon] :
( ( ( pigeon_hole @ pigeon2 )
= hole2 )
| ( ( pigeon_hole @ pigeon2 )
= hole1 )
| ( ( pigeon_hole @ pigeon3 )
= hole1 )
| ( ( sk1 @ hole2 )
= A )
| ( ( pigeon_hole @ pigeon3 )
!= ( pigeon_hole @ A ) ) ),
inference(paramod_ordered,[status(thm)],[921,38]) ).
thf(1860,plain,
( ( ( pigeon_hole @ pigeon2 )
= hole2 )
| ( ( pigeon_hole @ pigeon2 )
= hole1 )
| ( ( pigeon_hole @ pigeon3 )
= hole1 )
| ( ( sk1 @ hole2 )
= pigeon3 ) ),
inference(pattern_uni,[status(thm)],[1859:[bind(A,$thf( pigeon3 ))]]) ).
thf(7,axiom,
pigeon1 != pigeon4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pigeon1pigeon4) ).
thf(29,plain,
pigeon1 != pigeon4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(30,plain,
pigeon1 != pigeon4,
inference(polarity_switch,[status(thm)],[29]) ).
thf(31,plain,
pigeon4 != pigeon1,
inference(lifteq,[status(thm)],[30]) ).
thf(49,plain,
! [B: pigeon,A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ B ) )
| ( B != pigeon1 )
| ( A != pigeon4 ) ),
inference(paramod_ordered,[status(thm)],[12,31]) ).
thf(50,plain,
! [A: pigeon] :
( ( ( pigeon_hole @ pigeon4 )
!= ( pigeon_hole @ A ) )
| ( A != pigeon1 ) ),
inference(pattern_uni,[status(thm)],[49:[bind(A,$thf( pigeon4 ))]]) ).
thf(76,plain,
( ( pigeon_hole @ pigeon4 )
!= ( pigeon_hole @ pigeon1 ) ),
inference(simp,[status(thm)],[50]) ).
thf(178,plain,
! [B: pigeon,A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ B ) )
| ( ( pigeon_hole @ A )
!= ( pigeon_hole @ pigeon1 ) )
| ( B != pigeon4 ) ),
inference(paramod_ordered,[status(thm)],[12,76]) ).
thf(179,plain,
! [A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ pigeon4 ) )
| ( ( pigeon_hole @ A )
!= ( pigeon_hole @ pigeon1 ) ) ),
inference(pattern_uni,[status(thm)],[178:[bind(A,$thf( A )),bind(B,$thf( pigeon4 ))]]) ).
thf(99,plain,
! [B: hole,A: hole > $o] :
( ~ ( A @ hole1 )
| ~ ( A @ hole2 )
| ~ ( A @ hole3 )
| ( ( A @ B )
!= ( ~ ( A @ hole1 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[16]) ).
thf(124,plain,
! [B: hole,A: hole > $o] :
( ~ ( A @ hole1 )
| ~ ( A @ hole2 )
| ~ ( A @ hole3 )
| ( ( A @ B )
!= ( ~ ( A @ hole1 ) ) ) ),
inference(simp,[status(thm)],[99]) ).
thf(4,axiom,
pigeon1 != pigeon2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pigeon1pigeon2) ).
thf(20,plain,
pigeon1 != pigeon2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(21,plain,
pigeon1 != pigeon2,
inference(polarity_switch,[status(thm)],[20]) ).
thf(22,plain,
pigeon2 != pigeon1,
inference(lifteq,[status(thm)],[21]) ).
thf(45,plain,
! [B: pigeon,A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ B ) )
| ( B != pigeon1 )
| ( A != pigeon2 ) ),
inference(paramod_ordered,[status(thm)],[12,22]) ).
thf(46,plain,
! [A: pigeon] :
( ( ( pigeon_hole @ pigeon2 )
!= ( pigeon_hole @ A ) )
| ( A != pigeon1 ) ),
inference(pattern_uni,[status(thm)],[45:[bind(A,$thf( pigeon2 ))]]) ).
thf(74,plain,
( ( pigeon_hole @ pigeon2 )
!= ( pigeon_hole @ pigeon1 ) ),
inference(simp,[status(thm)],[46]) ).
thf(172,plain,
! [B: pigeon,A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ B ) )
| ( ( pigeon_hole @ A )
!= ( pigeon_hole @ pigeon1 ) )
| ( B != pigeon2 ) ),
inference(paramod_ordered,[status(thm)],[12,74]) ).
thf(173,plain,
! [A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ pigeon2 ) )
| ( ( pigeon_hole @ A )
!= ( pigeon_hole @ pigeon1 ) ) ),
inference(pattern_uni,[status(thm)],[172:[bind(A,$thf( A )),bind(B,$thf( pigeon2 ))]]) ).
thf(95,plain,
! [B: hole,A: hole > $o] :
( ~ ( A @ hole1 )
| ~ ( A @ hole2 )
| ( A @ B )
| ( ( A @ hole3 )
!= ( A @ hole1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[16]) ).
thf(122,plain,
! [B: hole,A: hole > $o] :
( ~ ( A @ hole1 )
| ~ ( A @ hole2 )
| ( A @ B )
| ( ( A @ hole3 )
!= ( A @ hole1 ) ) ),
inference(pre_uni,[status(thm)],[95:[]]) ).
thf(123,plain,
! [B: hole,A: hole > $o] :
( ( A @ B )
| ~ ( A @ hole2 )
| ~ ( A @ hole1 )
| ( ( A @ hole3 )
!= ( A @ hole1 ) ) ),
inference(pre_uni,[status(thm)],[122:[]]) ).
thf(8,axiom,
pigeon2 != pigeon4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pigeon2pigeon4) ).
thf(32,plain,
pigeon2 != pigeon4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(33,plain,
pigeon2 != pigeon4,
inference(polarity_switch,[status(thm)],[32]) ).
thf(34,plain,
pigeon4 != pigeon2,
inference(lifteq,[status(thm)],[33]) ).
thf(41,plain,
! [B: pigeon,A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ B ) )
| ( B != pigeon2 )
| ( A != pigeon4 ) ),
inference(paramod_ordered,[status(thm)],[12,34]) ).
thf(42,plain,
! [A: pigeon] :
( ( ( pigeon_hole @ pigeon4 )
!= ( pigeon_hole @ A ) )
| ( A != pigeon2 ) ),
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( pigeon4 ))]]) ).
thf(72,plain,
( ( pigeon_hole @ pigeon4 )
!= ( pigeon_hole @ pigeon2 ) ),
inference(simp,[status(thm)],[42]) ).
thf(93,plain,
! [D: hole,C: hole > $o,B: hole,A: hole > $o] :
( ~ ( A @ hole1 )
| ~ ( A @ hole2 )
| ~ ( A @ hole3 )
| ~ ( C @ hole1 )
| ~ ( C @ hole2 )
| ~ $true
| ( C @ D )
| ( ( A @ B )
!= ( C @ hole3 ) ) ),
inference(paramod_ordered,[status(thm)],[16,16]) ).
thf(94,plain,
! [D: hole,C: hole > $o,B: hole,A: hole > $o] :
( ~ ( A @ hole1 )
| ~ ( A @ hole2 )
| ~ ( A @ hole3 )
| ~ ( C @ hole1 )
| ~ ( C @ hole2 )
| ( C @ D )
| ( ( A @ B )
!= ( C @ hole3 ) ) ),
inference(simp,[status(thm)],[93]) ).
thf(125,plain,
! [D: hole,C: hole > $o,B: hole,A: hole > $o] :
( ~ ( A @ hole1 )
| ~ ( A @ hole2 )
| ~ ( A @ hole3 )
| ~ ( C @ hole1 )
| ~ ( C @ hole2 )
| ( C @ D )
| ( ( A @ B )
!= ( C @ hole3 ) ) ),
inference(pre_uni,[status(thm)],[94:[]]) ).
thf(126,plain,
! [D: hole,C: hole > $o,B: hole,A: hole > $o] :
( ( C @ D )
| ~ ( C @ hole2 )
| ~ ( C @ hole1 )
| ~ ( A @ hole3 )
| ~ ( A @ hole2 )
| ~ ( A @ hole1 )
| ( ( A @ B )
!= ( C @ hole3 ) ) ),
inference(pre_uni,[status(thm)],[125:[]]) ).
thf(375,plain,
! [A: hole > hole] :
( ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
!= hole3 )
| ( ( A @ hole3 )
!= ( pigeon_hole @ pigeon4 ) ) ),
inference(paramod_ordered,[status(thm)],[252,72]) ).
thf(415,plain,
( ( ( pigeon_hole @ pigeon4 )
= hole2 )
| ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( pigeon_hole @ pigeon4 )
= hole2 )
| ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
!= hole3 ) ),
inference(pre_uni,[status(thm)],[375:[bind(A,$thf( ^ [B: hole] : ( pigeon_hole @ pigeon4 ) ))]]) ).
thf(442,plain,
( ( ( pigeon_hole @ pigeon4 )
= hole2 )
| ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
!= hole3 ) ),
inference(simp,[status(thm)],[415]) ).
thf(9,axiom,
pigeon3 != pigeon4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pigeon3pigeon4) ).
thf(35,plain,
pigeon3 != pigeon4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(36,plain,
pigeon3 != pigeon4,
inference(polarity_switch,[status(thm)],[35]) ).
thf(37,plain,
pigeon4 != pigeon3,
inference(lifteq,[status(thm)],[36]) ).
thf(53,plain,
! [B: pigeon,A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ B ) )
| ( B != pigeon3 )
| ( A != pigeon4 ) ),
inference(paramod_ordered,[status(thm)],[12,37]) ).
thf(54,plain,
! [A: pigeon] :
( ( ( pigeon_hole @ pigeon4 )
!= ( pigeon_hole @ A ) )
| ( A != pigeon3 ) ),
inference(pattern_uni,[status(thm)],[53:[bind(A,$thf( pigeon4 ))]]) ).
thf(78,plain,
( ( pigeon_hole @ pigeon4 )
!= ( pigeon_hole @ pigeon3 ) ),
inference(simp,[status(thm)],[54]) ).
thf(744,plain,
( ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
!= hole3 )
| ( ( pigeon_hole @ pigeon3 )
!= hole2 )
| ( ( pigeon_hole @ pigeon4 )
!= ( pigeon_hole @ pigeon4 ) ) ),
inference(paramod_ordered,[status(thm)],[442,78]) ).
thf(745,plain,
( ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
!= hole3 )
| ( ( pigeon_hole @ pigeon3 )
!= hole2 ) ),
inference(pattern_uni,[status(thm)],[744:[]]) ).
thf(2689,plain,
( ( ( pigeon_hole @ pigeon2 )
!= hole3 )
| ( ( pigeon_hole @ pigeon3 )
!= hole2 )
| ( ( pigeon_hole @ pigeon3 )
!= hole1 )
| ( ( pigeon_hole @ pigeon4 )
!= ( pigeon_hole @ pigeon4 ) ) ),
inference(paramod_ordered,[status(thm)],[745,78]) ).
thf(2690,plain,
( ( ( pigeon_hole @ pigeon2 )
!= hole3 )
| ( ( pigeon_hole @ pigeon3 )
!= hole2 )
| ( ( pigeon_hole @ pigeon3 )
!= hole1 ) ),
inference(pattern_uni,[status(thm)],[2689:[]]) ).
thf(17,plain,
! [A: hole] :
( ( hole1 != hole1 )
| ( hole1 != hole2 )
| ( hole1 != hole3 )
| ( hole1 = A ) ),
inference(replace_leibeq,[status(thm)],[16:[bind(A,$thf( (=) @ hole @ hole1 ))]]) ).
thf(18,plain,
! [A: hole] :
( ( hole1 != hole1 )
| ( hole2 != hole1 )
| ( hole3 != hole1 )
| ( hole1 = A ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(19,plain,
! [A: hole] :
( ( hole2 != hole1 )
| ( hole3 != hole1 )
| ( hole1 = A ) ),
inference(simp,[status(thm)],[18]) ).
thf(259,plain,
! [A: hole] :
( ( hole2 != hole1 )
| ( hole3 != hole1 )
| ( ( pigeon_hole @ pigeon2 )
!= hole1 )
| ( A
!= ( pigeon_hole @ pigeon3 ) ) ),
inference(paramod_ordered,[status(thm)],[19,69]) ).
thf(260,plain,
( ( hole2 != hole1 )
| ( hole3 != hole1 )
| ( ( pigeon_hole @ pigeon2 )
!= hole1 ) ),
inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( pigeon_hole @ pigeon3 ))]]) ).
thf(363,plain,
! [A: hole] :
( ( hole2 != hole1 )
| ( hole3 != hole1 )
| ( hole2 != hole1 )
| ( hole3 != hole1 )
| ( hole1 != hole1 )
| ( A
!= ( pigeon_hole @ pigeon2 ) ) ),
inference(paramod_ordered,[status(thm)],[19,260]) ).
thf(364,plain,
! [A: hole] :
( ( hole2 != hole1 )
| ( hole3 != hole1 )
| ( A
!= ( pigeon_hole @ pigeon2 ) ) ),
inference(simp,[status(thm)],[363]) ).
thf(365,plain,
( ( hole2 != hole1 )
| ( hole3 != hole1 ) ),
inference(pattern_uni,[status(thm)],[364:[bind(A,$thf( pigeon_hole @ pigeon2 ))]]) ).
thf(759,plain,
( ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
!= hole3 )
| ( ( pigeon_hole @ pigeon1 )
!= hole2 )
| ( ( pigeon_hole @ pigeon4 )
!= ( pigeon_hole @ pigeon4 ) ) ),
inference(paramod_ordered,[status(thm)],[442,76]) ).
thf(760,plain,
( ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
!= hole3 )
| ( ( pigeon_hole @ pigeon1 )
!= hole2 ) ),
inference(pattern_uni,[status(thm)],[759:[]]) ).
thf(761,plain,
( ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
!= hole3 )
| ( ( pigeon_hole @ pigeon2 )
!= hole2 )
| ( ( pigeon_hole @ pigeon4 )
!= ( pigeon_hole @ pigeon4 ) ) ),
inference(paramod_ordered,[status(thm)],[442,72]) ).
thf(762,plain,
( ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
!= hole3 )
| ( ( pigeon_hole @ pigeon2 )
!= hole2 ) ),
inference(pattern_uni,[status(thm)],[761:[]]) ).
thf(2670,plain,
( ( ( pigeon_hole @ pigeon2 )
!= hole3 )
| ( ( pigeon_hole @ pigeon3 )
!= hole2 )
| ( ( pigeon_hole @ pigeon2 )
!= hole1 )
| ( ( pigeon_hole @ pigeon4 )
!= ( pigeon_hole @ pigeon4 ) ) ),
inference(paramod_ordered,[status(thm)],[745,72]) ).
thf(2671,plain,
( ( ( pigeon_hole @ pigeon2 )
!= hole3 )
| ( ( pigeon_hole @ pigeon3 )
!= hole2 )
| ( ( pigeon_hole @ pigeon2 )
!= hole1 ) ),
inference(pattern_uni,[status(thm)],[2670:[]]) ).
thf(101,plain,
! [B: hole,A: hole > $o] :
( ~ ( A @ hole1 )
| ~ ( A @ hole2 )
| ~ ( A @ hole3 )
| ( ( A @ B )
!= ( ~ ( A @ hole3 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[16]) ).
thf(120,plain,
! [B: hole,A: hole > $o] :
( ~ ( A @ hole1 )
| ~ ( A @ hole2 )
| ~ ( A @ hole3 )
| ( ( A @ B )
!= ( ~ ( A @ hole3 ) ) ) ),
inference(simp,[status(thm)],[101]) ).
thf(5,axiom,
pigeon1 != pigeon3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pigeon1pigeon3) ).
thf(23,plain,
pigeon1 != pigeon3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,plain,
pigeon1 != pigeon3,
inference(polarity_switch,[status(thm)],[23]) ).
thf(25,plain,
pigeon3 != pigeon1,
inference(lifteq,[status(thm)],[24]) ).
thf(256,plain,
! [B: pigeon,A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ B ) )
| ( ( pigeon_hole @ A )
!= ( pigeon_hole @ pigeon3 ) )
| ( B != pigeon4 ) ),
inference(paramod_ordered,[status(thm)],[12,78]) ).
thf(257,plain,
! [A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ pigeon4 ) )
| ( ( pigeon_hole @ A )
!= ( pigeon_hole @ pigeon3 ) ) ),
inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( A )),bind(B,$thf( pigeon4 ))]]) ).
thf(852,plain,
( ( ( pigeon_hole @ pigeon3 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
!= hole3 )
| ( ( pigeon_hole @ pigeon2 )
!= hole2 )
| ( ( pigeon_hole @ pigeon3 )
!= ( pigeon_hole @ pigeon3 ) ) ),
inference(paramod_ordered,[status(thm)],[444,69]) ).
thf(853,plain,
( ( ( pigeon_hole @ pigeon3 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
!= hole3 )
| ( ( pigeon_hole @ pigeon2 )
!= hole2 ) ),
inference(pattern_uni,[status(thm)],[852:[]]) ).
thf(57,plain,
! [B: pigeon,A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ B ) )
| ( B != pigeon1 )
| ( A != pigeon3 ) ),
inference(paramod_ordered,[status(thm)],[12,25]) ).
thf(58,plain,
! [A: pigeon] :
( ( ( pigeon_hole @ pigeon3 )
!= ( pigeon_hole @ A ) )
| ( A != pigeon1 ) ),
inference(pattern_uni,[status(thm)],[57:[bind(A,$thf( pigeon3 ))]]) ).
thf(80,plain,
( ( pigeon_hole @ pigeon3 )
!= ( pigeon_hole @ pigeon1 ) ),
inference(simp,[status(thm)],[58]) ).
thf(374,plain,
! [A: hole > hole] :
( ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 )
| ( ( pigeon_hole @ pigeon1 )
!= hole3 )
| ( ( A @ hole3 )
!= ( pigeon_hole @ pigeon3 ) ) ),
inference(paramod_ordered,[status(thm)],[252,80]) ).
thf(418,plain,
( ( ( pigeon_hole @ pigeon3 )
= hole2 )
| ( ( pigeon_hole @ pigeon3 )
= hole1 )
| ( ( pigeon_hole @ pigeon3 )
= hole2 )
| ( ( pigeon_hole @ pigeon3 )
= hole1 )
| ( ( pigeon_hole @ pigeon1 )
!= hole3 ) ),
inference(pre_uni,[status(thm)],[374:[bind(A,$thf( ^ [B: hole] : ( pigeon_hole @ pigeon3 ) ))]]) ).
thf(445,plain,
( ( ( pigeon_hole @ pigeon3 )
= hole2 )
| ( ( pigeon_hole @ pigeon3 )
= hole1 )
| ( ( pigeon_hole @ pigeon1 )
!= hole3 ) ),
inference(simp,[status(thm)],[418]) ).
thf(1287,plain,
! [A: hole > hole] :
( ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 )
| ( ( pigeon_hole @ pigeon3 )
= hole2 )
| ( ( pigeon_hole @ pigeon3 )
= hole1 )
| ( hole3 != hole3 )
| ( ( A @ hole3 )
!= ( pigeon_hole @ pigeon1 ) ) ),
inference(paramod_ordered,[status(thm)],[252,445]) ).
thf(1288,plain,
! [A: hole > hole] :
( ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 )
| ( ( pigeon_hole @ pigeon3 )
= hole2 )
| ( ( pigeon_hole @ pigeon3 )
= hole1 )
| ( ( A @ hole3 )
!= ( pigeon_hole @ pigeon1 ) ) ),
inference(simp,[status(thm)],[1287]) ).
thf(1365,plain,
( ( ( pigeon_hole @ pigeon1 )
= hole2 )
| ( ( pigeon_hole @ pigeon1 )
= hole1 )
| ( ( pigeon_hole @ pigeon1 )
= hole2 )
| ( ( pigeon_hole @ pigeon1 )
= hole1 )
| ( ( pigeon_hole @ pigeon3 )
= hole2 )
| ( ( pigeon_hole @ pigeon3 )
= hole1 ) ),
inference(pre_uni,[status(thm)],[1288:[bind(A,$thf( ^ [B: hole] : ( pigeon_hole @ pigeon1 ) ))]]) ).
thf(1379,plain,
( ( ( pigeon_hole @ pigeon1 )
= hole2 )
| ( ( pigeon_hole @ pigeon1 )
= hole1 )
| ( ( pigeon_hole @ pigeon3 )
= hole2 )
| ( ( pigeon_hole @ pigeon3 )
= hole1 ) ),
inference(simp,[status(thm)],[1365]) ).
thf(368,plain,
! [A: hole > hole] :
( ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 )
| ( ( pigeon_hole @ pigeon3 )
!= hole3 )
| ( ( A @ hole3 )
!= ( pigeon_hole @ pigeon4 ) ) ),
inference(paramod_ordered,[status(thm)],[252,78]) ).
thf(421,plain,
( ( ( pigeon_hole @ pigeon4 )
= hole2 )
| ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( pigeon_hole @ pigeon4 )
= hole2 )
| ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( pigeon_hole @ pigeon3 )
!= hole3 ) ),
inference(pre_uni,[status(thm)],[368:[bind(A,$thf( ^ [B: hole] : ( pigeon_hole @ pigeon4 ) ))]]) ).
thf(448,plain,
( ( ( pigeon_hole @ pigeon4 )
= hole2 )
| ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( pigeon_hole @ pigeon3 )
!= hole3 ) ),
inference(simp,[status(thm)],[421]) ).
thf(89,plain,
! [D: hole,C: hole > $o,B: hole,A: hole > $o] :
( ~ ( A @ hole1 )
| ~ ( A @ hole2 )
| ~ ( A @ hole3 )
| ~ $true
| ~ ( C @ hole2 )
| ~ ( C @ hole3 )
| ( C @ D )
| ( ( A @ B )
!= ( C @ hole1 ) ) ),
inference(paramod_ordered,[status(thm)],[16,16]) ).
thf(90,plain,
! [D: hole,C: hole > $o,B: hole,A: hole > $o] :
( ~ ( A @ hole1 )
| ~ ( A @ hole2 )
| ~ ( A @ hole3 )
| ~ ( C @ hole2 )
| ~ ( C @ hole3 )
| ( C @ D )
| ( ( A @ B )
!= ( C @ hole1 ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(132,plain,
! [D: hole,C: hole > $o,B: hole,A: hole > $o] :
( ~ ( A @ hole1 )
| ~ ( A @ hole2 )
| ~ ( A @ hole3 )
| ~ ( C @ hole2 )
| ~ ( C @ hole3 )
| ( C @ D )
| ( ( A @ B )
!= ( C @ hole1 ) ) ),
inference(pre_uni,[status(thm)],[90:[]]) ).
thf(133,plain,
! [D: hole,C: hole > $o,B: hole,A: hole > $o] :
( ( C @ D )
| ~ ( C @ hole3 )
| ~ ( C @ hole2 )
| ~ ( A @ hole3 )
| ~ ( A @ hole2 )
| ~ ( A @ hole1 )
| ( ( A @ B )
!= ( C @ hole1 ) ) ),
inference(pre_uni,[status(thm)],[132:[]]) ).
thf(774,plain,
! [A: hole > hole] :
( ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 )
| ( ( pigeon_hole @ pigeon4 )
= hole2 )
| ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( hole3 != hole3 )
| ( ( A @ hole3 )
!= ( pigeon_hole @ pigeon2 ) ) ),
inference(paramod_ordered,[status(thm)],[252,442]) ).
thf(775,plain,
! [A: hole > hole] :
( ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 )
| ( ( pigeon_hole @ pigeon4 )
= hole2 )
| ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( A @ hole3 )
!= ( pigeon_hole @ pigeon2 ) ) ),
inference(simp,[status(thm)],[774]) ).
thf(805,plain,
( ( ( pigeon_hole @ pigeon2 )
= hole2 )
| ( ( pigeon_hole @ pigeon2 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
= hole2 )
| ( ( pigeon_hole @ pigeon2 )
= hole1 )
| ( ( pigeon_hole @ pigeon4 )
= hole2 )
| ( ( pigeon_hole @ pigeon4 )
= hole1 ) ),
inference(pre_uni,[status(thm)],[775:[bind(A,$thf( ^ [B: hole] : ( pigeon_hole @ pigeon2 ) ))]]) ).
thf(820,plain,
( ( ( pigeon_hole @ pigeon2 )
= hole2 )
| ( ( pigeon_hole @ pigeon2 )
= hole1 )
| ( ( pigeon_hole @ pigeon4 )
= hole2 )
| ( ( pigeon_hole @ pigeon4 )
= hole1 ) ),
inference(simp,[status(thm)],[805]) ).
thf(392,plain,
! [C: hole > $o,B: hole,A: hole > hole] :
( ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 )
| ( C @ hole1 )
| ( C @ hole2 )
| ( C @ hole3 )
| ~ ( C @ B )
| ( ( A @ hole3 )
!= hole3 ) ),
inference(paramod_ordered,[status(thm)],[252,137]) ).
thf(404,plain,
! [B: hole,A: hole > hole] :
( ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 )
| ( B = hole1 )
| ( B = hole2 )
| ( B = hole3 )
| ( B != B )
| ( ( A @ hole3 )
!= hole3 ) ),
inference(replace_leibeq,[status(thm)],[392:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( (=) @ hole @ B ))]]) ).
thf(407,plain,
! [B: hole,A: hole > hole] :
( ( B = hole1 )
| ( B = hole2 )
| ( B = hole3 )
| ( B != B )
| ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 )
| ( ( A @ hole3 )
!= hole3 ) ),
inference(lifteq,[status(thm)],[404]) ).
thf(429,plain,
! [A: hole] :
( ( hole3 = hole1 )
| ( hole3 = hole2 )
| ( hole3 = hole1 )
| ( hole3 = hole2 )
| ( A = hole3 )
| ( A = hole2 )
| ( A = hole1 ) ),
inference(pre_uni,[status(thm)],[407:[bind(A,$thf( ^ [C: hole] : hole3 ))]]) ).
thf(456,plain,
! [A: hole] :
( ( hole3 = hole1 )
| ( hole3 = hole2 )
| ( A = hole3 )
| ( A = hole2 )
| ( A = hole1 ) ),
inference(simp,[status(thm)],[429]) ).
thf(100,plain,
! [B: hole,A: hole > $o] :
( ~ ( A @ hole1 )
| ~ ( A @ hole2 )
| ~ ( A @ hole3 )
| ( ( A @ B )
!= ( ~ ( A @ hole2 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[16]) ).
thf(134,plain,
! [B: hole,A: hole > $o] :
( ~ ( A @ hole1 )
| ~ ( A @ hole2 )
| ~ ( A @ hole3 )
| ( ( A @ B )
!= ( ~ ( A @ hole2 ) ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(91,plain,
! [D: hole,C: hole > $o,B: hole,A: hole > $o] :
( ~ ( A @ hole1 )
| ~ ( A @ hole2 )
| ~ ( A @ hole3 )
| ~ ( C @ hole1 )
| ~ $true
| ~ ( C @ hole3 )
| ( C @ D )
| ( ( A @ B )
!= ( C @ hole2 ) ) ),
inference(paramod_ordered,[status(thm)],[16,16]) ).
thf(92,plain,
! [D: hole,C: hole > $o,B: hole,A: hole > $o] :
( ~ ( A @ hole1 )
| ~ ( A @ hole2 )
| ~ ( A @ hole3 )
| ~ ( C @ hole1 )
| ~ ( C @ hole3 )
| ( C @ D )
| ( ( A @ B )
!= ( C @ hole2 ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(127,plain,
! [D: hole,C: hole > $o,B: hole,A: hole > $o] :
( ~ ( A @ hole1 )
| ~ ( A @ hole2 )
| ~ ( A @ hole3 )
| ~ ( C @ hole1 )
| ~ ( C @ hole3 )
| ( C @ D )
| ( ( A @ B )
!= ( C @ hole2 ) ) ),
inference(pre_uni,[status(thm)],[92:[]]) ).
thf(128,plain,
! [D: hole,C: hole > $o,B: hole,A: hole > $o] :
( ( C @ D )
| ~ ( C @ hole3 )
| ~ ( C @ hole1 )
| ~ ( A @ hole3 )
| ~ ( A @ hole2 )
| ~ ( A @ hole1 )
| ( ( A @ B )
!= ( C @ hole2 ) ) ),
inference(pre_uni,[status(thm)],[127:[]]) ).
thf(297,plain,
! [B: pigeon,A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ B ) )
| ( ( pigeon_hole @ A )
!= ( pigeon_hole @ pigeon1 ) )
| ( B != pigeon3 ) ),
inference(paramod_ordered,[status(thm)],[12,80]) ).
thf(298,plain,
! [A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ pigeon3 ) )
| ( ( pigeon_hole @ A )
!= ( pigeon_hole @ pigeon1 ) ) ),
inference(pattern_uni,[status(thm)],[297:[bind(A,$thf( A )),bind(B,$thf( pigeon3 ))]]) ).
thf(2668,plain,
( ( ( pigeon_hole @ pigeon2 )
!= hole3 )
| ( ( pigeon_hole @ pigeon3 )
!= hole2 )
| ( ( pigeon_hole @ pigeon1 )
!= hole1 )
| ( ( pigeon_hole @ pigeon4 )
!= ( pigeon_hole @ pigeon4 ) ) ),
inference(paramod_ordered,[status(thm)],[745,76]) ).
thf(2669,plain,
( ( ( pigeon_hole @ pigeon2 )
!= hole3 )
| ( ( pigeon_hole @ pigeon3 )
!= hole2 )
| ( ( pigeon_hole @ pigeon1 )
!= hole1 ) ),
inference(pattern_uni,[status(thm)],[2668:[]]) ).
thf(97,plain,
! [B: hole,A: hole > $o] :
( ~ ( A @ hole1 )
| ~ ( A @ hole2 )
| ( A @ B )
| ( ( A @ hole3 )
!= ( A @ hole2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[16]) ).
thf(129,plain,
! [B: hole,A: hole > $o] :
( ~ ( A @ hole1 )
| ~ ( A @ hole2 )
| ( A @ B )
| ( ( A @ hole3 )
!= ( A @ hole2 ) ) ),
inference(pre_uni,[status(thm)],[97:[]]) ).
thf(130,plain,
! [B: hole,A: hole > $o] :
( ( A @ B )
| ~ ( A @ hole2 )
| ~ ( A @ hole1 )
| ( ( A @ hole3 )
!= ( A @ hole2 ) ) ),
inference(pre_uni,[status(thm)],[129:[]]) ).
thf(369,plain,
! [A: hole > hole] :
( ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 )
| ( ( pigeon_hole @ pigeon1 )
!= hole3 )
| ( ( A @ hole3 )
!= ( pigeon_hole @ pigeon2 ) ) ),
inference(paramod_ordered,[status(thm)],[252,74]) ).
thf(423,plain,
( ( ( pigeon_hole @ pigeon2 )
= hole2 )
| ( ( pigeon_hole @ pigeon2 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
= hole2 )
| ( ( pigeon_hole @ pigeon2 )
= hole1 )
| ( ( pigeon_hole @ pigeon1 )
!= hole3 ) ),
inference(pre_uni,[status(thm)],[369:[bind(A,$thf( ^ [B: hole] : ( pigeon_hole @ pigeon2 ) ))]]) ).
thf(450,plain,
( ( ( pigeon_hole @ pigeon2 )
= hole2 )
| ( ( pigeon_hole @ pigeon2 )
= hole1 )
| ( ( pigeon_hole @ pigeon1 )
!= hole3 ) ),
inference(simp,[status(thm)],[423]) ).
thf(2000,plain,
! [A: hole > hole] :
( ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
= hole2 )
| ( ( pigeon_hole @ pigeon2 )
= hole1 )
| ( hole3 != hole3 )
| ( ( A @ hole3 )
!= ( pigeon_hole @ pigeon1 ) ) ),
inference(paramod_ordered,[status(thm)],[252,450]) ).
thf(2001,plain,
! [A: hole > hole] :
( ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
= hole2 )
| ( ( pigeon_hole @ pigeon2 )
= hole1 )
| ( ( A @ hole3 )
!= ( pigeon_hole @ pigeon1 ) ) ),
inference(simp,[status(thm)],[2000]) ).
thf(2079,plain,
( ( ( pigeon_hole @ pigeon1 )
= hole2 )
| ( ( pigeon_hole @ pigeon1 )
= hole1 )
| ( ( pigeon_hole @ pigeon1 )
= hole2 )
| ( ( pigeon_hole @ pigeon1 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
= hole2 )
| ( ( pigeon_hole @ pigeon2 )
= hole1 ) ),
inference(pre_uni,[status(thm)],[2001:[bind(A,$thf( ^ [B: hole] : ( pigeon_hole @ pigeon1 ) ))]]) ).
thf(2101,plain,
( ( ( pigeon_hole @ pigeon1 )
= hole2 )
| ( ( pigeon_hole @ pigeon1 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
= hole2 )
| ( ( pigeon_hole @ pigeon2 )
= hole1 ) ),
inference(simp,[status(thm)],[2079]) ).
thf(166,plain,
! [B: pigeon,A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ B ) )
| ( ( pigeon_hole @ A )
!= ( pigeon_hole @ pigeon2 ) )
| ( B != pigeon4 ) ),
inference(paramod_ordered,[status(thm)],[12,72]) ).
thf(167,plain,
! [A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ pigeon4 ) )
| ( ( pigeon_hole @ A )
!= ( pigeon_hole @ pigeon2 ) ) ),
inference(pattern_uni,[status(thm)],[166:[bind(A,$thf( A )),bind(B,$thf( pigeon4 ))]]) ).
thf(1187,plain,
! [A: pigeon] :
( ( ( pigeon_hole @ pigeon2 )
= hole2 )
| ( ( pigeon_hole @ pigeon2 )
= hole1 )
| ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( sk1 @ hole2 )
= A )
| ( ( pigeon_hole @ pigeon4 )
!= ( pigeon_hole @ A ) ) ),
inference(paramod_ordered,[status(thm)],[820,38]) ).
thf(1188,plain,
( ( ( pigeon_hole @ pigeon2 )
= hole2 )
| ( ( pigeon_hole @ pigeon2 )
= hole1 )
| ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( sk1 @ hole2 )
= pigeon4 ) ),
inference(pattern_uni,[status(thm)],[1187:[bind(A,$thf( pigeon4 ))]]) ).
thf(373,plain,
! [A: hole > hole] :
( ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 )
| ( ( pigeon_hole @ pigeon1 )
!= hole3 )
| ( ( A @ hole3 )
!= ( pigeon_hole @ pigeon4 ) ) ),
inference(paramod_ordered,[status(thm)],[252,76]) ).
thf(436,plain,
( ( ( pigeon_hole @ pigeon4 )
= hole2 )
| ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( pigeon_hole @ pigeon4 )
= hole2 )
| ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( pigeon_hole @ pigeon1 )
!= hole3 ) ),
inference(pre_uni,[status(thm)],[373:[bind(A,$thf( ^ [B: hole] : ( pigeon_hole @ pigeon4 ) ))]]) ).
thf(463,plain,
( ( ( pigeon_hole @ pigeon4 )
= hole2 )
| ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( pigeon_hole @ pigeon1 )
!= hole3 ) ),
inference(simp,[status(thm)],[436]) ).
thf(86,plain,
! [B: pigeon,A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ B ) )
| ( ( pigeon_hole @ A )
!= ( pigeon_hole @ pigeon2 ) )
| ( B != pigeon3 ) ),
inference(paramod_ordered,[status(thm)],[12,69]) ).
thf(87,plain,
! [A: pigeon] :
( ( ( pigeon_hole @ A )
!= ( pigeon_hole @ pigeon3 ) )
| ( ( pigeon_hole @ A )
!= ( pigeon_hole @ pigeon2 ) ) ),
inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( A )),bind(B,$thf( pigeon3 ))]]) ).
thf(770,plain,
! [A: pigeon] :
( ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
!= hole3 )
| ( ( sk1 @ hole2 )
= A )
| ( ( pigeon_hole @ pigeon4 )
!= ( pigeon_hole @ A ) ) ),
inference(paramod_ordered,[status(thm)],[442,38]) ).
thf(771,plain,
( ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( pigeon_hole @ pigeon2 )
!= hole3 )
| ( ( sk1 @ hole2 )
= pigeon4 ) ),
inference(pattern_uni,[status(thm)],[770:[bind(A,$thf( pigeon4 ))]]) ).
thf(1420,plain,
! [A: hole > hole] :
( ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 )
| ( ( pigeon_hole @ pigeon4 )
= hole2 )
| ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( hole3 != hole3 )
| ( ( A @ hole3 )
!= ( pigeon_hole @ pigeon3 ) ) ),
inference(paramod_ordered,[status(thm)],[252,448]) ).
thf(1421,plain,
! [A: hole > hole] :
( ( ( A @ hole2 )
= hole2 )
| ( ( A @ hole1 )
= hole1 )
| ( ( A @ hole3 )
= hole2 )
| ( ( A @ hole3 )
= hole1 )
| ( ( pigeon_hole @ pigeon4 )
= hole2 )
| ( ( pigeon_hole @ pigeon4 )
= hole1 )
| ( ( A @ hole3 )
!= ( pigeon_hole @ pigeon3 ) ) ),
inference(simp,[status(thm)],[1420]) ).
thf(1503,plain,
( ( ( pigeon_hole @ pigeon3 )
= hole2 )
| ( ( pigeon_hole @ pigeon3 )
= hole1 )
| ( ( pigeon_hole @ pigeon3 )
= hole2 )
| ( ( pigeon_hole @ pigeon3 )
= hole1 )
| ( ( pigeon_hole @ pigeon4 )
= hole2 )
| ( ( pigeon_hole @ pigeon4 )
= hole1 ) ),
inference(pre_uni,[status(thm)],[1421:[bind(A,$thf( ^ [B: hole] : ( pigeon_hole @ pigeon3 ) ))]]) ).
thf(1523,plain,
( ( ( pigeon_hole @ pigeon3 )
= hole2 )
| ( ( pigeon_hole @ pigeon3 )
= hole1 )
| ( ( pigeon_hole @ pigeon4 )
= hole2 )
| ( ( pigeon_hole @ pigeon4 )
= hole1 ) ),
inference(simp,[status(thm)],[1503]) ).
thf(513,plain,
! [B: pigeon,A: hole] :
( ( hole3 = hole1 )
| ( hole3 = hole2 )
| ( A = hole2 )
| ( A = hole1 )
| ( ( sk1 @ hole3 )
= B )
| ( A
!= ( pigeon_hole @ B ) ) ),
inference(paramod_ordered,[status(thm)],[456,38]) ).
thf(514,plain,
! [A: pigeon] :
( ( hole3 = hole1 )
| ( hole3 = hole2 )
| ( ( pigeon_hole @ A )
= hole2 )
| ( ( pigeon_hole @ A )
= hole1 )
| ( ( sk1 @ hole3 )
= A ) ),
inference(pattern_uni,[status(thm)],[513:[bind(A,$thf( pigeon_hole @ C )),bind(B,$thf( C ))]]) ).
thf(575,plain,
! [A: pigeon] :
( ( hole3 = hole1 )
| ( hole3 = hole2 )
| ( ( pigeon_hole @ A )
= hole2 )
| ( ( pigeon_hole @ A )
= hole1 )
| ( ( sk1 @ hole3 )
= A ) ),
inference(simp,[status(thm)],[514]) ).
thf(2909,plain,
! [F: hole,E: hole > $o,D: hole,C: hole > $o,B: hole,A: hole > $o] :
( ~ ( A @ hole2 )
| ~ ( A @ hole1 )
| ( ( A @ hole3 )
!= ( A @ hole1 ) )
| ( E @ F )
| ~ ( E @ hole2 )
| ~ $true
| ~ ( C @ hole3 )
| ~ ( C @ hole2 )
| ~ ( C @ hole1 )
| ( ( C @ D )
!= ( E @ hole3 ) )
| ( ( A @ B )
!= ( E @ hole1 ) ) ),
inference(paramod_ordered,[status(thm)],[123,126]) ).
thf(2910,plain,
! [F: hole,E: hole > $o,D: hole,C: hole > $o,B: hole,A: hole > $o] :
( ~ ( A @ hole2 )
| ~ ( A @ hole1 )
| ( ( A @ hole3 )
!= ( A @ hole1 ) )
| ( E @ F )
| ~ ( E @ hole2 )
| ~ ( C @ hole3 )
| ~ ( C @ hole2 )
| ~ ( C @ hole1 )
| ( ( C @ D )
!= ( E @ hole3 ) )
| ( ( A @ B )
!= ( E @ hole1 ) ) ),
inference(simp,[status(thm)],[2909]) ).
thf(3024,plain,
! [E: hole,D: hole,C: hole > $o,B: hole,A: hole > $o] :
( ~ ( A @ hole2 )
| ~ ( A @ hole1 )
| ( ( A @ hole3 )
!= ( A @ hole1 ) )
| ( hole2 = E )
| ( hole2 != hole2 )
| ~ ( C @ hole3 )
| ~ ( C @ hole2 )
| ~ ( C @ hole1 )
| ( ( C @ D )
!= ( hole2 = hole3 ) )
| ( ( A @ B )
!= ( hole2 = hole1 ) ) ),
inference(replace_leibeq,[status(thm)],[2910:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( (=) @ hole @ hole2 ))]]) ).
thf(3118,plain,
! [E: hole,D: hole,C: hole > $o,B: hole,A: hole > $o] :
( ( hole2 = E )
| ( hole2 != hole2 )
| ~ ( A @ hole2 )
| ~ ( A @ hole1 )
| ( ( A @ hole3 )
!= ( A @ hole1 ) )
| ~ ( C @ hole3 )
| ~ ( C @ hole2 )
| ~ ( C @ hole1 )
| ( ( C @ D )
!= ( hole2 = hole3 ) )
| ( ( A @ B )
!= ( hole2 = hole1 ) ) ),
inference(lifteq,[status(thm)],[3024]) ).
thf(3195,plain,
! [A: hole] :
( ( hole2 != hole3 )
| ( hole2 != hole3 )
| ( hole2 != hole3 )
| ( hole2 != hole1 )
| ( hole2 != hole1 )
| ( hole2 = A ) ),
inference(pre_uni,[status(thm)],[3118:[bind(A,$thf( ^ [F: hole] : ( hole2 = hole1 ) )),bind(B,$thf( A )),bind(C,$thf( ^ [F: hole] : ( hole2 = hole3 ) )),bind(D,$thf( C )),bind(E,$thf( E ))]]) ).
thf(3340,plain,
! [A: hole] :
( ( hole3 != hole2 )
| ( hole3 != hole2 )
| ( hole3 != hole2 )
| ( hole2 != hole1 )
| ( hole2 != hole1 )
| ( hole2 = A ) ),
inference(lifteq,[status(thm)],[3195]) ).
thf(3341,plain,
! [A: hole] :
( ( hole3 != hole2 )
| ( hole2 != hole1 )
| ( hole2 = A ) ),
inference(simp,[status(thm)],[3340]) ).
thf(9510,plain,
$false,
inference(e,[status(thm)],[10,1860,179,124,173,22,123,72,126,2690,69,365,760,762,2671,120,37,25,257,853,1379,20,448,78,29,133,74,820,137,28,38,252,456,134,128,921,298,745,444,32,34,12,445,76,2669,130,2101,80,167,35,1188,16,463,31,450,87,771,26,1523,23,575,15,442,3341]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MSC007^1.003.004 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.08 % 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
% 0.10/0.22 % Computer : n015.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 11:23:17 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 0.85/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.16/0.98 % [INFO] Parsing done (182ms).
% 1.16/0.99 % [INFO] Running in sequential loop mode.
% 1.73/1.39 % [INFO] eprover registered as external prover.
% 1.73/1.40 % [INFO] Scanning for conjecture ...
% 1.92/1.48 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.08/1.52 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.08/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.08/1.53 % [INFO] Type checking passed.
% 2.08/1.53 % [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 ...
% 26.82/7.29 % External prover 'e' found a proof!
% 26.82/7.29 % [INFO] Killing All external provers ...
% 26.82/7.29 % Time passed: 6933ms (effective reasoning time: 6296ms)
% 26.82/7.29 % 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)>
% 26.82/7.30 % Axioms used in derivation (7): holecover, pigeon1pigeon4, pigeon3pigeon4, pigeon1pigeon2, pigeon2pigeon4, pigeon1pigeon3, pigeon2pigeon3
% 26.82/7.30 % No. of inferences in proof: 181
% 27.19/7.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6933 ms resp. 6296 ms w/o parsing
% 27.64/7.44 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 27.64/7.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------