%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM768^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n002.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 08:18:09 AM UTC 2026
% Result : Theorem 24.32s 5.42s
% Output : Refutation 20.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 111 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 320 ( 119 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 2252 ( 138 ~; 79 |; 0 &;2019 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 303 ( 75 ^; 228 !; 0 ?; 303 :)
% Comments :
%------------------------------------------------------------------------------
thf(frac_type,type,
frac: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(x_decl,type,
x: frac ).
thf(y_decl,type,
y: frac ).
thf(some_decl,type,
some: ( nat > $o ) > $o ).
thf(ts_decl,type,
ts: nat > nat > nat ).
thf(num_decl,type,
num: frac > nat ).
thf(den_decl,type,
den: frac > nat ).
thf(pl_decl,type,
pl: nat > nat > nat ).
thf(eq_decl,type,
eq: frac > frac > $o ).
thf(pf_decl,type,
pf: frac > frac > frac ).
thf(fr_decl,type,
fr: nat > nat > frac ).
thf(ind_decl,type,
ind: ( nat > $o ) > nat ).
thf(amone_decl,type,
amone: ( nat > $o ) > $o ).
thf(3,axiom,
( some
@ ^ [A: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(14,plain,
( some
@ ^ [A: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [A: nat,B: nat] :
( ( ts @ A @ B )
= ( ts @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz29) ).
thf(27,plain,
! [A: nat,B: nat] :
( ( ts @ A @ B )
= ( ts @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(28,plain,
! [B: nat,A: nat] :
( ( ts @ A @ B )
= ( ts @ B @ A ) ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [B: nat,A: nat] :
( ( ts @ A @ B )
= ( ts @ B @ A ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(12,axiom,
! [A: frac,B: nat] : ( eq @ ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz40a) ).
thf(34,plain,
! [A: frac,B: nat] : ( eq @ ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(35,plain,
! [B: nat,A: frac] : ( eq @ ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) ) @ A ),
inference(cnf,[status(esa)],[34]) ).
thf(1,conjecture,
( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [A: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ A ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz67c) ).
thf(2,negated_conjecture,
~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [A: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ A ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [A: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ A ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(152,plain,
! [B: nat,A: frac] :
( ~ $true
| ( ( eq @ ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) ) @ A )
!= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [C: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ C ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) ) ),
inference(paramod_ordered,[status(thm)],[35,13]) ).
thf(153,plain,
! [B: nat,A: frac] :
( ( eq @ ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) ) @ A )
!= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [C: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ C ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) ),
inference(simp,[status(thm)],[152]) ).
thf(160,plain,
! [B: nat,A: frac] :
( ( ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) )
!= ( pf @ y
@ ( fr
@ ( ind
@ ^ [C: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ C ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[153]) ).
thf(161,plain,
! [A: nat] :
( ( fr @ ( ts @ ( num @ x ) @ A ) @ ( ts @ ( den @ x ) @ A ) )
!= ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(279,plain,
! [C: nat,B: nat,A: nat] :
( ( ( fr @ ( ts @ ( num @ x ) @ C ) @ ( ts @ A @ B ) )
!= ( pf @ y
@ ( fr
@ ( ind
@ ^ [D: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ D ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
| ( ( ts @ B @ A )
!= ( ts @ ( den @ x ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,161]) ).
thf(280,plain,
! [A: nat] :
( ( fr @ ( ts @ ( num @ x ) @ A ) @ ( ts @ A @ ( den @ x ) ) )
!= ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) ),
inference(pattern_uni,[status(thm)],[279:[bind(A,$thf( A )),bind(B,$thf( den @ x )),bind(C,$thf( A ))]]) ).
thf(7,axiom,
! [A: frac,B: nat] : ( eq @ A @ ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz40) ).
thf(23,plain,
! [A: frac,B: nat] : ( eq @ A @ ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(24,plain,
! [B: nat,A: frac] : ( eq @ A @ ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(64,plain,
! [B: nat,A: frac] :
( ~ $true
| ( ( eq @ A @ ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) ) )
!= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [C: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ C ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) ) ),
inference(paramod_ordered,[status(thm)],[24,13]) ).
thf(65,plain,
! [B: nat,A: frac] :
( ( eq @ A @ ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) ) )
!= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [C: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ C ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) ),
inference(simp,[status(thm)],[64]) ).
thf(66,plain,
! [B: nat,A: frac] :
( ( A
!= ( pf @ y
@ ( fr
@ ( ind
@ ^ [C: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ C ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
| ( ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) )
!= x ) ),
inference(simp,[status(thm)],[65]) ).
thf(67,plain,
! [A: nat] :
( ( fr
@ ( ts
@ ( num
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
@ A )
@ ( ts
@ ( den
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
@ A ) )
!= x ),
inference(simp,[status(thm)],[66]) ).
thf(84,plain,
! [C: nat,B: nat,A: nat] :
( ( ( fr @ ( ts @ A @ B )
@ ( ts
@ ( den
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [D: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ D ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
@ C ) )
!= x )
| ( ( ts @ B @ A )
!= ( ts
@ ( num
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [D: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ D ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
@ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,67]) ).
thf(85,plain,
! [A: nat] :
( ( fr
@ ( ts @ A
@ ( num
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) ) )
@ ( ts
@ ( den
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
@ A ) )
!= x ),
inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( A )),bind(B,$thf( num @ ( pf @ y @ ( fr @ ( ind @ ^ [D: nat] : ( ( ts @ ( num @ x ) @ ( den @ y ) ) = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ D ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )),bind(C,$thf( A ))]]) ).
thf(11,axiom,
! [A: nat > $o] :
( ~ ( ( amone @ A )
=> ~ ( some @ A ) )
=> ( A @ ( ind @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oneax) ).
thf(32,plain,
! [A: nat > $o] :
( ~ ( ( amone @ A )
=> ~ ( some @ A ) )
=> ( A @ ( ind @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(33,plain,
! [A: nat > $o] :
( ~ ( amone @ A )
| ~ ( some @ A )
| ( A @ ( ind @ A ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(56,plain,
! [D: nat,C: frac,B: nat,A: nat] :
( ( eq @ C @ ( fr @ ( ts @ ( num @ C ) @ D ) @ ( ts @ B @ A ) ) )
| ( ( ts @ A @ B )
!= ( ts @ ( den @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[29,24]) ).
thf(57,plain,
! [B: frac,A: nat] : ( eq @ B @ ( fr @ ( ts @ ( num @ B ) @ A ) @ ( ts @ A @ ( den @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[56:[bind(A,$thf( den @ E )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( B ))]]) ).
thf(68,plain,
! [B: frac,A: nat] : ( eq @ B @ ( fr @ ( ts @ ( num @ B ) @ A ) @ ( ts @ A @ ( den @ B ) ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(168,plain,
! [D: frac,C: nat,B: nat,A: nat] :
( ( eq @ D @ ( fr @ ( ts @ B @ A ) @ ( ts @ C @ ( den @ D ) ) ) )
| ( ( ts @ A @ B )
!= ( ts @ ( num @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,68]) ).
thf(169,plain,
! [B: frac,A: nat] : ( eq @ B @ ( fr @ ( ts @ A @ ( num @ B ) ) @ ( ts @ A @ ( den @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[168:[bind(A,$thf( num @ E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E ))]]) ).
thf(188,plain,
! [B: frac,A: nat] : ( eq @ B @ ( fr @ ( ts @ A @ ( num @ B ) ) @ ( ts @ A @ ( den @ B ) ) ) ),
inference(simp,[status(thm)],[169]) ).
thf(744,plain,
( ~ ( amone
@ ^ [A: nat] : $false )
| ~ ( some
@ ^ [A: nat] : $false )
| $false ),
inference(prim_subst,[status(thm)],[33:[bind(A,$thf( ^ [B: nat] : $false ))]]) ).
thf(765,plain,
( ~ ( amone
@ ^ [A: nat] : $false )
| ~ ( some
@ ^ [A: nat] : $false ) ),
inference(simp,[status(thm)],[744]) ).
thf(144,plain,
! [D: nat,C: frac,B: nat,A: nat] :
( ( eq @ ( fr @ ( ts @ ( num @ C ) @ D ) @ ( ts @ B @ A ) ) @ C )
| ( ( ts @ A @ B )
!= ( ts @ ( den @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[29,35]) ).
thf(145,plain,
! [B: frac,A: nat] : ( eq @ ( fr @ ( ts @ ( num @ B ) @ A ) @ ( ts @ A @ ( den @ B ) ) ) @ B ),
inference(pattern_uni,[status(thm)],[144:[bind(A,$thf( den @ E )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( B ))]]) ).
thf(162,plain,
! [B: frac,A: nat] : ( eq @ ( fr @ ( ts @ ( num @ B ) @ A ) @ ( ts @ A @ ( den @ B ) ) ) @ B ),
inference(simp,[status(thm)],[145]) ).
thf(281,plain,
! [C: nat,B: nat,A: nat] :
( ( ( fr @ ( ts @ A @ B ) @ ( ts @ ( den @ x ) @ C ) )
!= ( pf @ y
@ ( fr
@ ( ind
@ ^ [D: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ D ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
| ( ( ts @ B @ A )
!= ( ts @ ( num @ x ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,161]) ).
thf(282,plain,
! [A: nat] :
( ( fr @ ( ts @ A @ ( num @ x ) ) @ ( ts @ ( den @ x ) @ A ) )
!= ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) ),
inference(pattern_uni,[status(thm)],[281:[bind(A,$thf( A )),bind(B,$thf( num @ x )),bind(C,$thf( A ))]]) ).
thf(5,axiom,
! [A: frac,B: frac,C: frac] :
( ( eq @ A @ B )
=> ( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz39) ).
thf(17,plain,
! [A: frac,B: frac,C: frac] :
( ( eq @ A @ B )
=> ( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,plain,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ! [C: frac] :
( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
inference(miniscope,[status(thm)],[17]) ).
thf(19,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ B @ C )
| ( eq @ A @ C ) ),
inference(cnf,[status(esa)],[18]) ).
thf(122,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ B @ C )
| ~ $true
| ( ( eq @ A @ C )
!= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [D: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ D ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) ) ),
inference(paramod_ordered,[status(thm)],[19,13]) ).
thf(123,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ B @ C )
| ( ( eq @ A @ C )
!= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [D: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ D ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) ) ),
inference(simp,[status(thm)],[122]) ).
thf(124,plain,
! [A: frac] :
( ~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ A )
| ~ ( eq @ A @ x ) ),
inference(pattern_uni,[status(thm)],[123:[bind(A,$thf( pf @ y @ ( fr @ ( ind @ ^ [D: nat] : ( ( ts @ ( num @ x ) @ ( den @ y ) ) = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ D ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )),bind(B,$thf( B )),bind(C,$thf( x ))]]) ).
thf(143,plain,
! [A: frac] :
( ~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ A )
| ~ ( eq @ A @ x ) ),
inference(simp,[status(thm)],[124]) ).
thf(235,plain,
! [C: frac,B: nat,A: frac] :
( ~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [D: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ D ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ C )
| ~ $true
| ( ( eq @ ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) ) @ A )
!= ( eq @ C @ x ) ) ),
inference(paramod_ordered,[status(thm)],[35,143]) ).
thf(236,plain,
! [C: frac,B: nat,A: frac] :
( ~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [D: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ D ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ C )
| ( ( eq @ ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) ) @ A )
!= ( eq @ C @ x ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(237,plain,
! [A: nat] :
~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ ( fr @ ( ts @ ( num @ x ) @ A ) @ ( ts @ ( den @ x ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[236:[bind(A,$thf( x )),bind(B,$thf( J )),bind(C,$thf( fr @ ( ts @ ( num @ x ) @ J ) @ ( ts @ ( den @ x ) @ J ) ))]]) ).
thf(268,plain,
! [A: nat] :
~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ ( fr @ ( ts @ ( num @ x ) @ A ) @ ( ts @ ( den @ x ) @ A ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(247,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ B @ C )
| ~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [E: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ E ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ D )
| ~ $true
| ( ( eq @ A @ C )
!= ( eq @ D @ x ) ) ),
inference(paramod_ordered,[status(thm)],[19,143]) ).
thf(248,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ B @ C )
| ~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [E: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ E ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ D )
| ( ( eq @ A @ C )
!= ( eq @ D @ x ) ) ),
inference(simp,[status(thm)],[247]) ).
thf(249,plain,
! [B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ B @ x )
| ~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [C: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ C ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ A ) ),
inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( x )),bind(D,$thf( A ))]]) ).
thf(883,plain,
! [A: nat > $o] :
( ~ ( amone @ A )
| ~ ( some @ A )
| ~ $true
| ~ ( some
@ ^ [B: nat] : $false )
| ( ( A @ ( ind @ A ) )
!= ( amone
@ ^ [B: nat] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[33,765]) ).
thf(884,plain,
! [A: nat > $o] :
( ~ ( amone @ A )
| ~ ( some @ A )
| ~ ( some
@ ^ [B: nat] : $false )
| ( ( A @ ( ind @ A ) )
!= ( amone
@ ^ [B: nat] : $false ) ) ),
inference(simp,[status(thm)],[883]) ).
thf(892,plain,
( ~ ( amone
@ ^ [A: nat] :
( amone
@ ^ [B: nat] : $false ) )
| ~ ( some
@ ^ [A: nat] :
( amone
@ ^ [B: nat] : $false ) )
| ~ ( some
@ ^ [A: nat] : $false ) ),
inference(pre_uni,[status(thm)],[884:[bind(A,$thf( ^ [B: nat] : ( amone @ ^ [C: nat] : $false ) ))]]) ).
thf(58,plain,
! [D: nat,C: frac,B: nat,A: nat] :
( ( eq @ C @ ( fr @ ( ts @ B @ A ) @ ( ts @ ( den @ C ) @ D ) ) )
| ( ( ts @ A @ B )
!= ( ts @ ( num @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[29,24]) ).
thf(59,plain,
! [B: frac,A: nat] : ( eq @ B @ ( fr @ ( ts @ A @ ( num @ B ) ) @ ( ts @ ( den @ B ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[58:[bind(A,$thf( num @ E )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( B ))]]) ).
thf(69,plain,
! [B: frac,A: nat] : ( eq @ B @ ( fr @ ( ts @ A @ ( num @ B ) ) @ ( ts @ ( den @ B ) @ A ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(8,axiom,
! [A: frac] : ( eq @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz37) ).
thf(25,plain,
! [A: frac] : ( eq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( eq @ A @ B )
=> ( ( eq @ C @ D )
=> ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz56) ).
thf(20,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( eq @ A @ B )
=> ( ( eq @ C @ D )
=> ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21,plain,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ! [C: frac,D: frac] :
( ( eq @ C @ D )
=> ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(miniscope,[status(thm)],[20]) ).
thf(22,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ C @ D )
| ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(347,plain,
! [E: frac,D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ C @ D )
| ~ $true
| ~ ( eq @ E @ x )
| ( ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
!= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [F: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ F ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ E ) ) ),
inference(paramod_ordered,[status(thm)],[22,143]) ).
thf(348,plain,
! [E: frac,D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ C @ D )
| ~ ( eq @ E @ x )
| ( ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
!= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [F: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ F ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ E ) ) ),
inference(simp,[status(thm)],[347]) ).
thf(349,plain,
! [B: frac,A: frac] :
( ~ ( eq @ y @ A )
| ~ ( eq
@ ( fr
@ ( ind
@ ^ [C: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ C ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) )
@ B )
| ~ ( eq @ ( pf @ A @ B ) @ x ) ),
inference(pattern_uni,[status(thm)],[348:[bind(A,$thf( y )),bind(B,$thf( Y )),bind(C,$thf( fr @ ( ind @ ^ [F: nat] : ( ( ts @ ( num @ x ) @ ( den @ y ) ) = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ F ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) )),bind(D,$thf( Z )),bind(E,$thf( pf @ Y @ Z ))]]) ).
thf(393,plain,
! [B: frac,A: frac] :
( ~ ( eq @ y @ A )
| ~ ( eq
@ ( fr
@ ( ind
@ ^ [C: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ C ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) )
@ B )
| ~ ( eq @ ( pf @ A @ B ) @ x ) ),
inference(simp,[status(thm)],[349]) ).
thf(394,plain,
! [D: frac,C: nat,B: nat,A: nat] :
( ( eq @ ( fr @ ( ts @ B @ A ) @ ( ts @ C @ ( den @ D ) ) ) @ D )
| ( ( ts @ A @ B )
!= ( ts @ ( num @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,162]) ).
thf(395,plain,
! [B: frac,A: nat] : ( eq @ ( fr @ ( ts @ A @ ( num @ B ) ) @ ( ts @ A @ ( den @ B ) ) ) @ B ),
inference(pattern_uni,[status(thm)],[394:[bind(A,$thf( num @ E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E ))]]) ).
thf(430,plain,
! [B: frac,A: nat] : ( eq @ ( fr @ ( ts @ A @ ( num @ B ) ) @ ( ts @ A @ ( den @ B ) ) ) @ B ),
inference(simp,[status(thm)],[395]) ).
thf(400,plain,
! [D: frac,C: nat,B: nat,A: nat] :
( ( eq @ ( fr @ ( ts @ ( num @ D ) @ C ) @ ( ts @ A @ B ) ) @ D )
| ( ( ts @ B @ A )
!= ( ts @ C @ ( den @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,162]) ).
thf(401,plain,
! [B: frac,A: nat] : ( eq @ ( fr @ ( ts @ ( num @ B ) @ A ) @ ( ts @ ( den @ B ) @ A ) ) @ B ),
inference(pattern_uni,[status(thm)],[400:[bind(A,$thf( den @ E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E ))]]) ).
thf(423,plain,
! [B: frac,A: nat] : ( eq @ ( fr @ ( ts @ ( num @ B ) @ A ) @ ( ts @ ( den @ B ) @ A ) ) @ B ),
inference(simp,[status(thm)],[401]) ).
thf(26,plain,
! [A: frac] : ( eq @ A @ A ),
inference(cnf,[status(esa)],[25]) ).
thf(46,plain,
! [A: frac] :
( ~ $true
| ( ( eq @ A @ A )
!= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) ) ),
inference(paramod_ordered,[status(thm)],[26,13]) ).
thf(47,plain,
! [A: frac] :
( ( eq @ A @ A )
!= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) ),
inference(simp,[status(thm)],[46]) ).
thf(48,plain,
! [A: frac] :
( ( A
!= ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[47]) ).
thf(49,plain,
( ( pf @ y
@ ( fr
@ ( ind
@ ^ [A: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ A ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
!= x ),
inference(simp,[status(thm)],[48]) ).
thf(146,plain,
! [D: nat,C: frac,B: nat,A: nat] :
( ( eq @ ( fr @ ( ts @ B @ A ) @ ( ts @ ( den @ C ) @ D ) ) @ C )
| ( ( ts @ A @ B )
!= ( ts @ ( num @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[29,35]) ).
thf(147,plain,
! [B: frac,A: nat] : ( eq @ ( fr @ ( ts @ A @ ( num @ B ) ) @ ( ts @ ( den @ B ) @ A ) ) @ B ),
inference(pattern_uni,[status(thm)],[146:[bind(A,$thf( num @ E )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( B ))]]) ).
thf(163,plain,
! [B: frac,A: nat] : ( eq @ ( fr @ ( ts @ A @ ( num @ B ) ) @ ( ts @ ( den @ B ) @ A ) ) @ B ),
inference(simp,[status(thm)],[147]) ).
thf(452,plain,
! [C: frac,B: frac,A: nat] :
( ~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [D: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ D ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ C )
| ~ $true
| ( ( eq @ ( fr @ ( ts @ A @ ( num @ B ) ) @ ( ts @ ( den @ B ) @ A ) ) @ B )
!= ( eq @ C @ x ) ) ),
inference(paramod_ordered,[status(thm)],[163,143]) ).
thf(453,plain,
! [C: frac,B: frac,A: nat] :
( ~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [D: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ D ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ C )
| ( ( eq @ ( fr @ ( ts @ A @ ( num @ B ) ) @ ( ts @ ( den @ B ) @ A ) ) @ B )
!= ( eq @ C @ x ) ) ),
inference(simp,[status(thm)],[452]) ).
thf(454,plain,
! [A: nat] :
~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ ( fr @ ( ts @ A @ ( num @ x ) ) @ ( ts @ ( den @ x ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[453:[bind(A,$thf( J )),bind(B,$thf( x )),bind(C,$thf( fr @ ( ts @ J @ ( num @ x ) ) @ ( ts @ ( den @ x ) @ J ) ))]]) ).
thf(466,plain,
! [A: nat] :
~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ ( fr @ ( ts @ A @ ( num @ x ) ) @ ( ts @ ( den @ x ) @ A ) ) ),
inference(simp,[status(thm)],[454]) ).
thf(298,plain,
! [C: nat,B: nat,A: nat] :
( ( ( fr @ ( ts @ A @ B ) @ ( ts @ C @ ( den @ x ) ) )
!= ( pf @ y
@ ( fr
@ ( ind
@ ^ [D: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ D ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
| ( ( ts @ B @ A )
!= ( ts @ ( num @ x ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,280]) ).
thf(299,plain,
! [A: nat] :
( ( fr @ ( ts @ A @ ( num @ x ) ) @ ( ts @ A @ ( den @ x ) ) )
!= ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) ),
inference(pattern_uni,[status(thm)],[298:[bind(A,$thf( A )),bind(B,$thf( num @ x )),bind(C,$thf( A ))]]) ).
thf(4,axiom,
! [A: nat,B: nat] :
( amone
@ ^ [C: nat] :
( A
= ( pl @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz8b) ).
thf(15,plain,
! [A: nat,B: nat] :
( amone
@ ^ [C: nat] :
( A
= ( pl @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,plain,
! [B: nat,A: nat] :
( amone
@ ^ [C: nat] :
( A
= ( pl @ B @ C ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(10,axiom,
! [A: nat,B: nat,C: nat] : ( eq @ ( pf @ ( fr @ A @ C ) @ ( fr @ B @ C ) ) @ ( fr @ ( pl @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz57) ).
thf(30,plain,
! [A: nat,B: nat,C: nat] : ( eq @ ( pf @ ( fr @ A @ C ) @ ( fr @ B @ C ) ) @ ( fr @ ( pl @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,plain,
! [C: nat,B: nat,A: nat] : ( eq @ ( pf @ ( fr @ A @ C ) @ ( fr @ B @ C ) ) @ ( fr @ ( pl @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[30]) ).
thf(1059,plain,
! [C: frac,B: frac,A: frac] :
( ~ $true
| ~ ( eq
@ ( fr
@ ( ind
@ ^ [D: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ D ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) )
@ C )
| ~ ( eq @ ( pf @ B @ C ) @ x )
| ( ( eq @ A @ A )
!= ( eq @ y @ B ) ) ),
inference(paramod_ordered,[status(thm)],[26,393]) ).
thf(1060,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq
@ ( fr
@ ( ind
@ ^ [D: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ D ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) )
@ C )
| ~ ( eq @ ( pf @ B @ C ) @ x )
| ( ( eq @ A @ A )
!= ( eq @ y @ B ) ) ),
inference(simp,[status(thm)],[1059]) ).
thf(1061,plain,
! [A: frac] :
( ~ ( eq
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) )
@ A )
| ~ ( eq @ ( pf @ y @ A ) @ x ) ),
inference(pattern_uni,[status(thm)],[1060:[bind(A,$thf( y )),bind(B,$thf( y ))]]) ).
thf(1180,plain,
! [A: frac] :
( ~ ( eq
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) )
@ A )
| ~ ( eq @ ( pf @ y @ A ) @ x ) ),
inference(simp,[status(thm)],[1061]) ).
thf(86,plain,
! [C: nat,B: nat,A: nat] :
( ( ( fr
@ ( ts
@ ( num
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [D: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ D ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
@ C )
@ ( ts @ A @ B ) )
!= x )
| ( ( ts @ B @ A )
!= ( ts
@ ( den
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [D: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ D ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
@ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,67]) ).
thf(87,plain,
! [A: nat] :
( ( fr
@ ( ts
@ ( num
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
@ A )
@ ( ts @ A
@ ( den
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) ) ) )
!= x ),
inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( A )),bind(B,$thf( den @ ( pf @ y @ ( fr @ ( ind @ ^ [D: nat] : ( ( ts @ ( num @ x ) @ ( den @ y ) ) = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ D ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )),bind(C,$thf( A ))]]) ).
thf(412,plain,
! [C: frac,B: frac,A: nat] :
( ~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [D: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ D ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ C )
| ~ $true
| ( ( eq @ ( fr @ ( ts @ ( num @ B ) @ A ) @ ( ts @ A @ ( den @ B ) ) ) @ B )
!= ( eq @ C @ x ) ) ),
inference(paramod_ordered,[status(thm)],[162,143]) ).
thf(413,plain,
! [C: frac,B: frac,A: nat] :
( ~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [D: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ D ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ C )
| ( ( eq @ ( fr @ ( ts @ ( num @ B ) @ A ) @ ( ts @ A @ ( den @ B ) ) ) @ B )
!= ( eq @ C @ x ) ) ),
inference(simp,[status(thm)],[412]) ).
thf(414,plain,
! [A: nat] :
~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ ( fr @ ( ts @ ( num @ x ) @ A ) @ ( ts @ A @ ( den @ x ) ) ) ),
inference(pattern_uni,[status(thm)],[413:[bind(A,$thf( I )),bind(B,$thf( x )),bind(C,$thf( fr @ ( ts @ ( num @ x ) @ I ) @ ( ts @ I @ ( den @ x ) ) ))]]) ).
thf(432,plain,
! [A: nat] :
~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [B: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ B ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ ( fr @ ( ts @ ( num @ x ) @ A ) @ ( ts @ A @ ( den @ x ) ) ) ),
inference(simp,[status(thm)],[414]) ).
thf(1568,plain,
$false,
inference(e,[status(thm)],[14,280,85,33,188,765,162,282,143,268,249,892,69,24,25,20,29,393,13,430,161,17,32,34,423,22,27,49,466,299,35,67,16,31,1180,87,26,23,432,30,19,15,163,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM768^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % 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
% 0.10/0.20 % Computer : n002.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 12:56:52 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.65/0.51 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.86/0.62 % [INFO] Parsing done (106ms).
% 0.86/0.63 % [INFO] Running in sequential loop mode.
% 1.37/0.82 % [INFO] eprover registered as external prover.
% 1.37/0.82 % [INFO] Scanning for conjecture ...
% 1.37/0.87 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 1.37/0.89 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.61/0.91 % [INFO] Problem is higher-order (TPTP THF).
% 1.61/0.91 % [INFO] Type checking passed.
% 1.61/0.91 % [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 ...
% 24.32/5.41 % External prover 'e' found a proof!
% 24.32/5.41 % [INFO] Killing All external provers ...
% 24.32/5.41 % Time passed: 5119ms (effective reasoning time: 4786ms)
% 24.32/5.41 % 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)>
% 24.32/5.42 % Axioms used in derivation (10): satz29, satz40a, satz39, m, oneax, satz56, satz40, satz57, satz8b, satz37
% 24.32/5.42 % No. of inferences in proof: 111
% 24.32/5.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5119 ms resp. 4786 ms w/o parsing
% 20.58/5.54 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.58/5.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------