%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NLP262+1 : TPTP v9.0.0. Bugfixed v4.0.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:18:38 AM UTC 2025
% Result : Theorem 55.94s 56.12s
% Output : Proof 68.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 23
% Syntax : Number of formulae : 45 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 245 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 343 ( 157 ~; 141 |; 16 &)
% ( 26 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 108 ( 102 !; 0 ?; 108 :)
% Comments :
%------------------------------------------------------------------------------
tff(hypernym_type,type,
hypernym: ( $i * $i ) > $o ).
tff(n7846_type,type,
n7846: $i ).
tff(n9855630_type,type,
n9855630: $i ).
tff(n10560637_type,type,
n10560637: $i ).
tff(n9986904_type,type,
n9986904: $i ).
tff(n10126424_type,type,
n10126424: $i ).
tff(1,plain,
( ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
<=> ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( hypernym(X,Y)
& hypernym(Y,Z) )
<=> ~ ( ~ hypernym(Y,Z)
| ~ hypernym(X,Y) ) )),
( ~ ( hypernym(X,Y)
& hypernym(Y,Z) )
<=> ~ ~ ( ~ hypernym(Y,Z)
| ~ hypernym(X,Y) ) )),
rewrite(( ~ ~ ( ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
<=> ( ~ hypernym(Y,Z)
| ~ hypernym(X,Y) ) )),
( ~ ( hypernym(X,Y)
& hypernym(Y,Z) )
<=> ( ~ hypernym(Y,Z)
| ~ hypernym(X,Y) ) )),
( ( ~ ( hypernym(X,Y)
& hypernym(Y,Z) )
| hypernym(X,Z) )
<=> ( ~ hypernym(Y,Z)
| ~ hypernym(X,Y)
| hypernym(X,Z) ) )),
rewrite(( ( ~ hypernym(Y,Z)
| ~ hypernym(X,Y)
| hypernym(X,Z) )
<=> ( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) ) )),
( ( ~ ( hypernym(X,Y)
& hypernym(Y,Z) )
| hypernym(X,Z) )
<=> ( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(3,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( hypernym(X,Y)
& hypernym(Y,Z) )
| hypernym(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) ) ),
inference(quant_intro,[status(thm)],[2]) ).
tff(4,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( hypernym(X,Y)
& hypernym(Y,Z) )
| hypernym(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( hypernym(X,Y)
& hypernym(Y,Z) )
| hypernym(X,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(( ( ( hypernym(X,Y)
& hypernym(Y,Z) )
=> hypernym(X,Z) )
<=> ( ~ ( hypernym(X,Y)
& hypernym(Y,Z) )
| hypernym(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( hypernym(X,Y)
& hypernym(Y,Z) )
=> hypernym(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( hypernym(X,Y)
& hypernym(Y,Z) )
| hypernym(X,Z) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( hypernym(X,Y)
& hypernym(Y,Z) )
=> hypernym(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
tff(8,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( hypernym(X,Y)
& hypernym(Y,Z) )
| hypernym(X,Z) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( hypernym(X,Y)
& hypernym(Y,Z) )
| hypernym(X,Z) ),
inference(modus_ponens,[status(thm)],[8,4]) ).
tff(10,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( hypernym(X,Y)
& hypernym(Y,Z) )
| hypernym(X,Z) ),
inference(skolemize,[status(sab)],[9]) ).
tff(11,plain,
! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) ),
inference(modus_ponens,[status(thm)],[10,3]) ).
tff(12,plain,
! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) ),
inference(modus_ponens,[status(thm)],[11,1]) ).
tff(13,plain,
( hypernym(n9855630,n10560637)
<=> hypernym(n9855630,n10560637) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
hypernym(n9855630,n10560637),
file('/export/starexec/sandbox/benchmark/Axioms/NLP001+0.ax',kb886122) ).
tff(15,plain,
hypernym(n9855630,n10560637),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( hypernym(n10560637,n7846)
<=> hypernym(n10560637,n7846) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
hypernym(n10560637,n7846),
file('/export/starexec/sandbox/benchmark/Axioms/NLP001+0.ax',kb117091) ).
tff(18,plain,
hypernym(n10560637,n7846),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
| ~ hypernym(n9855630,n10560637)
| ~ hypernym(n10560637,n7846)
| hypernym(n9855630,n7846) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
| ~ hypernym(n9855630,n10560637)
| ~ hypernym(n10560637,n7846)
| hypernym(n9855630,n7846) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
( ( hypernym(n9855630,n7846)
| ~ hypernym(n10560637,n7846)
| ~ hypernym(n9855630,n10560637) )
<=> ( ~ hypernym(n9855630,n10560637)
| ~ hypernym(n10560637,n7846)
| hypernym(n9855630,n7846) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
| hypernym(n9855630,n7846)
| ~ hypernym(n10560637,n7846)
| ~ hypernym(n9855630,n10560637) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
| ~ hypernym(n9855630,n10560637)
| ~ hypernym(n10560637,n7846)
| hypernym(n9855630,n7846) ) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
| hypernym(n9855630,n7846)
| ~ hypernym(n10560637,n7846)
| ~ hypernym(n9855630,n10560637) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
| ~ hypernym(n9855630,n10560637)
| ~ hypernym(n10560637,n7846)
| hypernym(n9855630,n7846) ) ),
inference(transitivity,[status(thm)],[21,19]) ).
tff(23,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
| hypernym(n9855630,n7846)
| ~ hypernym(n10560637,n7846)
| ~ hypernym(n9855630,n10560637) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
| ~ hypernym(n9855630,n10560637)
| ~ hypernym(n10560637,n7846)
| hypernym(n9855630,n7846) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
hypernym(n9855630,n7846),
inference(unit_resolution,[status(thm)],[24,18,15,12]) ).
tff(26,plain,
( hypernym(n10126424,n9855630)
<=> hypernym(n10126424,n9855630) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
hypernym(n10126424,n9855630),
file('/export/starexec/sandbox/benchmark/Axioms/NLP001+0.ax',kb340304) ).
tff(28,plain,
hypernym(n10126424,n9855630),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( hypernym(n9986904,n10126424)
<=> hypernym(n9986904,n10126424) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
hypernym(n9986904,n10126424),
file('/export/starexec/sandbox/benchmark/Axioms/NLP001+0.ax',kb1049) ).
tff(31,plain,
hypernym(n9986904,n10126424),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
| hypernym(n9986904,n9855630)
| ~ hypernym(n10126424,n9855630)
| ~ hypernym(n9986904,n10126424) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
| hypernym(n9986904,n9855630)
| ~ hypernym(n10126424,n9855630)
| ~ hypernym(n9986904,n10126424) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
| hypernym(n9986904,n9855630)
| ~ hypernym(n10126424,n9855630)
| ~ hypernym(n9986904,n10126424) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
| hypernym(n9986904,n9855630)
| ~ hypernym(n10126424,n9855630)
| ~ hypernym(n9986904,n10126424) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
hypernym(n9986904,n9855630),
inference(unit_resolution,[status(thm)],[34,31,28,12]) ).
tff(36,plain,
( ~ hypernym(n9986904,n7846)
<=> ~ hypernym(n9986904,n7846) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
~ hypernym(n9986904,n7846),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypernym_transitiviy_1) ).
tff(38,plain,
~ hypernym(n9986904,n7846),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
| hypernym(n9986904,n7846)
| ~ hypernym(n9986904,n9855630)
| ~ hypernym(n9855630,n7846) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
| hypernym(n9986904,n7846)
| ~ hypernym(n9986904,n9855630)
| ~ hypernym(n9855630,n7846) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ( hypernym(n9986904,n7846)
| ~ hypernym(n9855630,n7846)
| ~ hypernym(n9986904,n9855630) )
<=> ( hypernym(n9986904,n7846)
| ~ hypernym(n9986904,n9855630)
| ~ hypernym(n9855630,n7846) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
| hypernym(n9986904,n7846)
| ~ hypernym(n9855630,n7846)
| ~ hypernym(n9986904,n9855630) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
| hypernym(n9986904,n7846)
| ~ hypernym(n9986904,n9855630)
| ~ hypernym(n9855630,n7846) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
| hypernym(n9986904,n7846)
| ~ hypernym(n9855630,n7846)
| ~ hypernym(n9986904,n9855630) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
| hypernym(n9986904,n7846)
| ~ hypernym(n9986904,n9855630)
| ~ hypernym(n9855630,n7846) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
| hypernym(n9986904,n7846)
| ~ hypernym(n9855630,n7846)
| ~ hypernym(n9986904,n9855630) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( hypernym(X,Z)
| ~ hypernym(Y,Z)
| ~ hypernym(X,Y) )
| hypernym(n9986904,n7846)
| ~ hypernym(n9986904,n9855630)
| ~ hypernym(n9855630,n7846) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
$false,
inference(unit_resolution,[status(thm)],[44,12,38,35,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NLP262+1 : TPTP v9.0.0. Bugfixed v4.0.1.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 23:59:04 EDT 2025
% 0.12/0.34 % CPUTime :
% 55.94/56.12 % SZS status Theorem
% 55.94/56.12 % SZS output start Proof
% See solution above
% 69.14/69.33 % E exiting
%------------------------------------------------------------------------------