%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM727^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n006.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 08:18:03 AM UTC 2026
% Result : Theorem 14.19s 4.47s
% Output : Refutation 12.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 85 ( 43 unt; 0 typ; 1 def)
% Number of atoms : 141 ( 140 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 900 ( 79 ~; 52 |; 0 &; 766 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 79 ( 0 ^; 76 !; 2 ?; 79 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% 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(z_decl,type,
z: frac ).
thf(ts_decl,type,
ts: nat > nat > nat ).
thf(num_decl,type,
num: frac > nat ).
thf(den_decl,type,
den: frac > nat ).
thf(sk1_decl,type,
sk1: nat > nat > nat ).
thf(sk1_def,definition,
( sk1
= ( @+[A: nat > nat > nat] :
! [B: nat,C: nat] :
( ( A @ C @ ( ts @ B @ C ) )
= B ) ) ) ).
thf(7,axiom,
! [A: nat,B: nat,C: nat] :
( ( ts @ ( ts @ A @ B ) @ C )
= ( ts @ A @ ( ts @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz31) ).
thf(23,plain,
! [A: nat,B: nat,C: nat] :
( ( ts @ ( ts @ A @ B ) @ C )
= ( ts @ A @ ( ts @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(24,plain,
! [C: nat,B: nat,A: nat] :
( ( ts @ ( ts @ A @ B ) @ C )
= ( ts @ A @ ( ts @ B @ C ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(25,plain,
! [C: nat,B: nat,A: nat] :
( ( ts @ ( ts @ A @ B ) @ C )
= ( ts @ A @ ( ts @ B @ C ) ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(3,axiom,
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e) ).
thf(10,plain,
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
( ( ts @ ( num @ y ) @ ( den @ x ) )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(6,axiom,
! [A: nat,B: nat] :
( ( ts @ A @ B )
= ( ts @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz29) ).
thf(20,plain,
! [A: nat,B: nat] :
( ( ts @ A @ B )
= ( ts @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21,plain,
! [B: nat,A: nat] :
( ( ts @ A @ B )
= ( ts @ B @ A ) ),
inference(cnf,[status(esa)],[20]) ).
thf(22,plain,
! [B: nat,A: nat] :
( ( ts @ A @ B )
= ( ts @ B @ A ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(49,plain,
! [B: nat,A: nat] :
( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( ts @ B @ A ) )
| ( ( ts @ ( num @ y ) @ ( den @ x ) )
!= ( ts @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11,22]) ).
thf(50,plain,
( ( ts @ ( den @ x ) @ ( num @ y ) )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ),
inference(pattern_uni,[status(thm)],[49:[bind(A,$thf( num @ y )),bind(B,$thf( den @ x ))]]) ).
thf(1,conjecture,
( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz39) ).
thf(2,negated_conjecture,
( ( ts @ ( num @ x ) @ ( den @ z ) )
!= ( ts @ ( num @ z ) @ ( den @ x ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
( ( ts @ ( num @ x ) @ ( den @ z ) )
!= ( ts @ ( num @ z ) @ ( den @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
( ( ts @ ( num @ z ) @ ( den @ x ) )
!= ( ts @ ( num @ x ) @ ( den @ z ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(63,plain,
( ( ( ts @ ( num @ x ) @ ( den @ z ) )
!= ( ts @ ( num @ x ) @ ( den @ y ) ) )
| ( ( ts @ ( den @ x ) @ ( num @ y ) )
!= ( ts @ ( num @ z ) @ ( den @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[50,9]) ).
thf(82,plain,
( ( ( num @ x )
!= ( num @ x ) )
| ( ( den @ z )
!= ( den @ y ) )
| ( ( den @ x )
!= ( num @ z ) )
| ( ( den @ x )
!= ( num @ y ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(84,plain,
( ( ( den @ z )
!= ( den @ y ) )
| ( ( den @ x )
!= ( num @ z ) )
| ( ( den @ x )
!= ( num @ y ) ) ),
inference(simp,[status(thm)],[82]) ).
thf(27,plain,
( ( ( ts @ ( num @ x ) @ ( den @ z ) )
!= ( ts @ ( num @ x ) @ ( den @ y ) ) )
| ( ( ts @ ( num @ z ) @ ( den @ x ) )
!= ( ts @ ( num @ y ) @ ( den @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,9]) ).
thf(30,plain,
( ( ( num @ x )
!= ( num @ x ) )
| ( ( den @ z )
!= ( den @ y ) )
| ( ( num @ z )
!= ( num @ y ) )
| ( ( den @ x )
!= ( den @ x ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(33,plain,
( ( ( den @ z )
!= ( den @ y ) )
| ( ( num @ z )
!= ( num @ y ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(4,axiom,
( ( ts @ ( num @ y ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f) ).
thf(12,plain,
( ( ts @ ( num @ y ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
( ( ts @ ( num @ z ) @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ z ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(55,plain,
! [B: nat,A: nat] :
( ( ( ts @ ( num @ y ) @ ( den @ z ) )
= ( ts @ B @ A ) )
| ( ( ts @ ( num @ z ) @ ( den @ y ) )
!= ( ts @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[13,22]) ).
thf(56,plain,
( ( ts @ ( den @ y ) @ ( num @ z ) )
= ( ts @ ( num @ y ) @ ( den @ z ) ) ),
inference(pattern_uni,[status(thm)],[55:[bind(A,$thf( num @ z )),bind(B,$thf( den @ y ))]]) ).
thf(191,plain,
! [C: nat,B: nat,A: nat] :
( ( ( ts @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ C )
= ( ts @ A @ ( ts @ B @ C ) ) )
| ( ( ts @ ( num @ z ) @ ( den @ y ) )
!= ( ts @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[13,25]) ).
thf(192,plain,
! [A: nat] :
( ( ts @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ A )
= ( ts @ ( num @ z ) @ ( ts @ ( den @ y ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[191:[bind(A,$thf( num @ z )),bind(B,$thf( den @ y )),bind(C,$thf( C ))]]) ).
thf(231,plain,
! [A: nat] :
( ( ts @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ A )
= ( ts @ ( num @ z ) @ ( ts @ ( den @ y ) @ A ) ) ),
inference(simp,[status(thm)],[192]) ).
thf(451,plain,
! [A: nat] :
( ( ts @ ( num @ y ) @ ( ts @ ( den @ z ) @ A ) )
= ( ts @ ( num @ z ) @ ( ts @ ( den @ y ) @ A ) ) ),
inference(rewrite,[status(thm)],[231,25]) ).
thf(500,plain,
! [A: nat] :
( ( ( ts @ ( num @ z ) @ ( ts @ ( num @ y ) @ ( den @ z ) ) )
= ( ts @ ( num @ y ) @ ( ts @ ( den @ z ) @ A ) ) )
| ( ( ts @ ( den @ y ) @ ( num @ z ) )
!= ( ts @ ( den @ y ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[56,451]) ).
thf(501,plain,
( ( ts @ ( num @ z ) @ ( ts @ ( num @ y ) @ ( den @ z ) ) )
= ( ts @ ( num @ y ) @ ( ts @ ( den @ z ) @ ( num @ z ) ) ) ),
inference(pattern_uni,[status(thm)],[500:[bind(A,$thf( num @ z ))]]) ).
thf(5,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( ts @ A @ C )
= ( ts @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz33b) ).
thf(14,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ts @ A @ C )
= ( ts @ B @ C ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,plain,
! [A: nat,B: nat] :
( ? [C: nat] :
( ( ts @ A @ C )
= ( ts @ B @ C ) )
=> ( A = B ) ),
inference(miniscope,[status(thm)],[14]) ).
thf(16,plain,
! [C: nat,B: nat,A: nat] :
( ( ( ts @ A @ C )
!= ( ts @ B @ C ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[15]) ).
thf(17,plain,
! [C: nat,B: nat,A: nat] :
( ( ( ts @ A @ C )
!= ( ts @ B @ C ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(18,plain,
? [A: nat > nat > nat] :
! [B: nat,C: nat] :
( ( A @ C @ ( ts @ B @ C ) )
= B ),
inference(detectInverse,[status(thm)],[17]) ).
thf(19,plain,
! [B: nat,A: nat] :
( ( sk1 @ B @ ( ts @ A @ B ) )
= A ),
inference(cnf,[status(esa)],[18]) ).
thf(147,plain,
! [B: nat,A: nat] :
( ( sk1 @ B @ ( ts @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[19]) ).
thf(152,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( ( sk1 @ D @ ( ts @ B @ A ) )
= C )
| ( ( ts @ A @ B )
!= ( ts @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[22,147]) ).
thf(153,plain,
! [B: nat,A: nat] :
( ( sk1 @ B @ ( ts @ B @ A ) )
= A ),
inference(pattern_uni,[status(thm)],[152:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(709,plain,
! [B: nat,A: nat] :
( ( ( sk1 @ B @ ( ts @ ( num @ y ) @ ( ts @ ( den @ z ) @ ( num @ z ) ) ) )
= A )
| ( ( ts @ ( num @ z ) @ ( ts @ ( num @ y ) @ ( den @ z ) ) )
!= ( ts @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[501,153]) ).
thf(710,plain,
( ( sk1 @ ( num @ z ) @ ( ts @ ( num @ y ) @ ( ts @ ( den @ z ) @ ( num @ z ) ) ) )
= ( ts @ ( num @ y ) @ ( den @ z ) ) ),
inference(pattern_uni,[status(thm)],[709:[bind(A,$thf( ts @ ( num @ y ) @ ( den @ z ) )),bind(B,$thf( num @ z ))]]) ).
thf(657,plain,
! [B: nat,A: nat] :
( ( ( sk1 @ B @ ( ts @ ( num @ y ) @ ( ts @ ( den @ z ) @ ( num @ z ) ) ) )
= A )
| ( ( ts @ ( num @ z ) @ ( ts @ ( num @ y ) @ ( den @ z ) ) )
!= ( ts @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[501,147]) ).
thf(658,plain,
( ( sk1 @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ y ) @ ( ts @ ( den @ z ) @ ( num @ z ) ) ) )
= ( num @ z ) ),
inference(pattern_uni,[status(thm)],[657:[bind(A,$thf( num @ z )),bind(B,$thf( ts @ ( num @ y ) @ ( den @ z ) ))]]) ).
thf(889,plain,
! [B: nat,A: nat] :
( ( ( sk1 @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ y ) @ ( ts @ B @ A ) ) )
= ( num @ z ) )
| ( ( ts @ A @ B )
!= ( ts @ ( den @ z ) @ ( num @ z ) ) ) ),
inference(paramod_ordered,[status(thm)],[22,658]) ).
thf(890,plain,
( ( sk1 @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ y ) @ ( ts @ ( num @ z ) @ ( den @ z ) ) ) )
= ( num @ z ) ),
inference(pattern_uni,[status(thm)],[889:[bind(A,$thf( den @ z )),bind(B,$thf( num @ z ))]]) ).
thf(150,plain,
! [B: nat,A: nat] :
( ( ( sk1 @ B @ ( ts @ ( num @ y ) @ ( den @ z ) ) )
= A )
| ( ( ts @ ( num @ z ) @ ( den @ y ) )
!= ( ts @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[13,147]) ).
thf(151,plain,
( ( sk1 @ ( den @ y ) @ ( ts @ ( num @ y ) @ ( den @ z ) ) )
= ( num @ z ) ),
inference(pattern_uni,[status(thm)],[150:[bind(A,$thf( num @ z )),bind(B,$thf( den @ y ))]]) ).
thf(156,plain,
! [B: nat,A: nat] :
( ( ( sk1 @ B @ ( ts @ ( num @ x ) @ ( den @ y ) ) )
= A )
| ( ( ts @ ( den @ x ) @ ( num @ y ) )
!= ( ts @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[50,147]) ).
thf(157,plain,
( ( sk1 @ ( num @ y ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) )
= ( den @ x ) ),
inference(pattern_uni,[status(thm)],[156:[bind(A,$thf( den @ x )),bind(B,$thf( num @ y ))]]) ).
thf(867,plain,
! [A: nat] :
( ( ( sk1 @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( ts @ ( den @ y ) @ A ) ) )
= ( num @ z ) )
| ( ( ts @ ( num @ y ) @ ( ts @ ( den @ z ) @ A ) )
!= ( ts @ ( num @ y ) @ ( ts @ ( den @ z ) @ ( num @ z ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[451,658]) ).
thf(868,plain,
( ( sk1 @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( ts @ ( den @ y ) @ ( num @ z ) ) ) )
= ( num @ z ) ),
inference(pattern_uni,[status(thm)],[867:[bind(A,$thf( num @ z ))]]) ).
thf(2024,plain,
( ( sk1 @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( ts @ ( num @ y ) @ ( den @ z ) ) ) )
= ( num @ z ) ),
inference(rewrite,[status(thm)],[868,56]) ).
thf(733,plain,
! [B: nat,A: nat] :
( ( ( ts @ ( num @ y ) @ ( ts @ B @ A ) )
= ( ts @ ( num @ z ) @ ( ts @ ( num @ y ) @ ( den @ z ) ) ) )
| ( ( ts @ A @ B )
!= ( ts @ ( den @ z ) @ ( num @ z ) ) ) ),
inference(paramod_ordered,[status(thm)],[22,501]) ).
thf(734,plain,
( ( ts @ ( num @ z ) @ ( ts @ ( num @ y ) @ ( den @ z ) ) )
= ( ts @ ( num @ y ) @ ( ts @ ( num @ z ) @ ( den @ z ) ) ) ),
inference(pattern_uni,[status(thm)],[733:[bind(A,$thf( den @ z )),bind(B,$thf( num @ z ))]]) ).
thf(29,plain,
( ( ( ts @ ( num @ x ) @ ( den @ z ) )
!= ( ts @ ( num @ x ) @ ( den @ y ) ) )
| ( ( num @ z )
!= ( num @ y ) )
| ( ( den @ x )
!= ( den @ x ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(32,plain,
( ( ( ts @ ( num @ x ) @ ( den @ z ) )
!= ( ts @ ( num @ x ) @ ( den @ y ) ) )
| ( ( num @ z )
!= ( num @ y ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(148,plain,
! [B: nat,A: nat] :
( ( ( sk1 @ B @ ( ts @ ( num @ y ) @ ( den @ z ) ) )
= A )
| ( ( ts @ ( den @ y ) @ ( num @ z ) )
!= ( ts @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[56,147]) ).
thf(149,plain,
( ( sk1 @ ( num @ z ) @ ( ts @ ( num @ y ) @ ( den @ z ) ) )
= ( den @ y ) ),
inference(pattern_uni,[status(thm)],[148:[bind(A,$thf( den @ y )),bind(B,$thf( num @ z ))]]) ).
thf(34,plain,
( ( ( ts @ ( num @ y ) @ ( den @ z ) )
!= ( ts @ ( num @ x ) @ ( den @ z ) ) )
| ( ( ts @ ( num @ z ) @ ( den @ y ) )
!= ( ts @ ( num @ z ) @ ( den @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,9]) ).
thf(39,plain,
( ( ( num @ y )
!= ( num @ x ) )
| ( ( den @ z )
!= ( den @ z ) )
| ( ( num @ z )
!= ( num @ z ) )
| ( ( den @ y )
!= ( den @ x ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(44,plain,
( ( ( num @ y )
!= ( num @ x ) )
| ( ( den @ y )
!= ( den @ x ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(390,plain,
( ( y != x )
| ( y != x ) ),
inference(simp,[status(thm)],[44]) ).
thf(391,plain,
y != x,
inference(simp,[status(thm)],[390]) ).
thf(158,plain,
! [B: nat,A: nat] :
( ( ( sk1 @ B @ ( ts @ ( num @ x ) @ ( den @ y ) ) )
= A )
| ( ( ts @ ( num @ y ) @ ( den @ x ) )
!= ( ts @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11,147]) ).
thf(159,plain,
( ( sk1 @ ( den @ x ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) )
= ( num @ y ) ),
inference(pattern_uni,[status(thm)],[158:[bind(A,$thf( num @ y )),bind(B,$thf( den @ x ))]]) ).
thf(28,plain,
( ( ( num @ x )
!= ( num @ x ) )
| ( ( den @ z )
!= ( den @ y ) )
| ( ( ts @ ( num @ z ) @ ( den @ x ) )
!= ( ts @ ( num @ y ) @ ( den @ x ) ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(31,plain,
( ( ( den @ z )
!= ( den @ y ) )
| ( ( ts @ ( num @ z ) @ ( den @ x ) )
!= ( ts @ ( num @ y ) @ ( den @ x ) ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(394,plain,
( ( ( den @ z )
!= ( den @ y ) )
| ( ( ts @ ( num @ z ) @ ( den @ x ) )
!= ( ts @ ( num @ x ) @ ( den @ y ) ) ) ),
inference(rewrite,[status(thm)],[31,11]) ).
thf(114,plain,
( ( ( ts @ ( num @ y ) @ ( den @ z ) )
!= ( ts @ ( num @ x ) @ ( den @ z ) ) )
| ( ( ts @ ( den @ y ) @ ( num @ z ) )
!= ( ts @ ( num @ z ) @ ( den @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[56,9]) ).
thf(137,plain,
( ( ( num @ y )
!= ( num @ x ) )
| ( ( den @ z )
!= ( den @ z ) )
| ( ( den @ y )
!= ( num @ z ) )
| ( ( den @ x )
!= ( num @ z ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(143,plain,
( ( ( num @ y )
!= ( num @ x ) )
| ( ( den @ y )
!= ( num @ z ) )
| ( ( den @ x )
!= ( num @ z ) ) ),
inference(simp,[status(thm)],[137]) ).
thf(35,plain,
( ( ( ts @ ( num @ y ) @ ( den @ z ) )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
| ( ( ts @ ( num @ z ) @ ( den @ y ) )
!= ( ts @ ( num @ y ) @ ( den @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,11]) ).
thf(40,plain,
( ( ( ts @ ( num @ y ) @ ( den @ z ) )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
| ( ( num @ z )
!= ( num @ y ) )
| ( ( den @ y )
!= ( den @ x ) ) ),
inference(simp,[status(thm)],[35]) ).
thf(26,plain,
( ( ( num @ z )
!= ( num @ x ) )
| ( ( den @ z )
!= ( den @ x ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(162,plain,
( ( z != y )
| ( z != y ) ),
inference(simp,[status(thm)],[33]) ).
thf(163,plain,
z != y,
inference(simp,[status(thm)],[162]) ).
thf(61,plain,
( ( z != x )
| ( z != x ) ),
inference(simp,[status(thm)],[26]) ).
thf(62,plain,
z != x,
inference(simp,[status(thm)],[61]) ).
thf(2561,plain,
$false,
inference(e,[status(thm)],[25,84,33,710,9,13,451,890,50,8,151,10,56,153,14,157,20,2024,147,734,32,17,149,22,44,391,12,159,394,658,11,143,40,26,23,163,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM727^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % 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
% 0.10/0.21 % Computer : n006.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 12:45:09 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 1.01/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/0.98 % [INFO] Parsing done (175ms).
% 1.18/0.99 % [INFO] Running in sequential loop mode.
% 1.77/1.39 % [INFO] eprover registered as external prover.
% 1.95/1.40 % [INFO] Scanning for conjecture ...
% 1.95/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.10/1.52 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.10/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.10/1.55 % [INFO] Type checking passed.
% 2.10/1.56 % [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 ...
% 14.19/4.46 % External prover 'e' found a proof!
% 14.19/4.46 % [INFO] Killing All external provers ...
% 14.19/4.47 % Time passed: 4107ms (effective reasoning time: 3466ms)
% 14.19/4.47 % 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)>
% 14.19/4.47 % Axioms used in derivation (5): e, satz29, satz31, f, satz33b
% 14.19/4.47 % No. of inferences in proof: 84
% 14.19/4.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4107 ms resp. 3466 ms w/o parsing
% 12.38/4.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.38/4.54 % [INFO] Killing All external provers ...
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