%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM004-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:00:56 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 27
% Syntax : Number of formulae : 65 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 316 ( 10 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 433 ( 205 ~; 193 |; 0 &)
% ( 35 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 23 ( 23 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 156 ( 141 !; 0 ?; 156 :)
% Comments :
%------------------------------------------------------------------------------
tff(failure_node_type,type,
failure_node: ( $i * $i ) > $o ).
tff(or_type,type,
or: ( $i * $i ) > $i ).
tff(empty_type,type,
empty: $i ).
tff(parent_of_type,type,
parent_of: ( $i * $i ) > $i ).
tff(right_child_of_type,type,
right_child_of: $i > $i ).
tff(n_type,type,
n: $i ).
tff(left_child_of_type,type,
left_child_of: $i > $i ).
tff(negate_type,type,
negate: $i > $i ).
tff(atom_type,type,
atom: $i ).
tff(n_right_type,type,
n_right: $i ).
tff(n_left_type,type,
n_left: $i ).
tff(siblings_type,type,
siblings: ( $i * $i ) > $o ).
tff(contradictory_type,type,
contradictory: ( $i * $i ) > $o ).
tff(1,plain,
( ( n_right = right_child_of(n) )
<=> ( n_right = right_child_of(n) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
n_right = right_child_of(n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n_right_equals_right_child_of_n) ).
tff(3,plain,
n_right = right_child_of(n),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
right_child_of(n) = n_right,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( failure_node(right_child_of(n),or(empty,negate(atom)))
<=> failure_node(n_right,or(empty,negate(atom))) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( failure_node(n_right,or(empty,negate(atom)))
<=> failure_node(right_child_of(n),or(empty,negate(atom))) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( failure_node(n_right,or(empty,negate(atom)))
<=> failure_node(n_right,or(empty,negate(atom))) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
failure_node(n_right,or(empty,negate(atom))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n_right_is_not_atom) ).
tff(9,plain,
failure_node(n_right,or(empty,negate(atom))),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
failure_node(right_child_of(n),or(empty,negate(atom))),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
( ( n_left = left_child_of(n) )
<=> ( n_left = left_child_of(n) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
n_left = left_child_of(n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n_left_equals_left_child_of_n) ).
tff(13,plain,
n_left = left_child_of(n),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
left_child_of(n) = n_left,
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
( failure_node(left_child_of(n),or(empty,atom))
<=> failure_node(n_left,or(empty,atom)) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( failure_node(n_left,or(empty,atom))
<=> failure_node(left_child_of(n),or(empty,atom)) ),
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
( failure_node(n_left,or(empty,atom))
<=> failure_node(n_left,or(empty,atom)) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
failure_node(n_left,or(empty,atom)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n_left_is_atom) ).
tff(19,plain,
failure_node(n_left,or(empty,atom)),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
failure_node(left_child_of(n),or(empty,atom)),
inference(modus_ponens,[status(thm)],[19,16]) ).
tff(21,plain,
^ [X: $i] :
refl(( siblings(left_child_of(X),right_child_of(X))
<=> siblings(left_child_of(X),right_child_of(X)) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [X: $i] : siblings(left_child_of(X),right_child_of(X))
<=> ! [X: $i] : siblings(left_child_of(X),right_child_of(X)) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i] : siblings(left_child_of(X),right_child_of(X))
<=> ! [X: $i] : siblings(left_child_of(X),right_child_of(X)) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [X: $i] : siblings(left_child_of(X),right_child_of(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n_left_and_n_right_are_siblings) ).
tff(25,plain,
! [X: $i] : siblings(left_child_of(X),right_child_of(X)),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X: $i] : siblings(left_child_of(X),right_child_of(X)),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X: $i] : siblings(left_child_of(X),right_child_of(X)),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [X: $i] : siblings(left_child_of(X),right_child_of(X))
| siblings(left_child_of(n),right_child_of(n)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
siblings(left_child_of(n),right_child_of(n)),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
^ [X: $i] :
refl(( contradictory(X,negate(X))
<=> contradictory(X,negate(X)) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [X: $i] : contradictory(X,negate(X))
<=> ! [X: $i] : contradictory(X,negate(X)) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [X: $i] : contradictory(X,negate(X))
<=> ! [X: $i] : contradictory(X,negate(X)) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
! [X: $i] : contradictory(X,negate(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_contradicts_not_x) ).
tff(34,plain,
! [X: $i] : contradictory(X,negate(X)),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [X: $i] : contradictory(X,negate(X)),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [X: $i] : contradictory(X,negate(X)),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [X: $i] : contradictory(X,negate(X))
| contradictory(atom,negate(atom)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
contradictory(atom,negate(atom)),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
^ [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
refl(( ( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) )
<=> ( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) )
<=> ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) )
<=> ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
^ [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( failure_node(parent_of(X,Y),or(C,D))
| ~ failure_node(X,or(C,P)) )
<=> ( ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) ) )),
( ( failure_node(parent_of(X,Y),or(C,D))
| ~ failure_node(X,or(C,P))
| ~ failure_node(Y,or(D,Q)) )
<=> ( ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D))
| ~ failure_node(Y,or(D,Q)) ) )),
rewrite(( ( ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D))
| ~ failure_node(Y,or(D,Q)) )
<=> ( ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) ) )),
( ( failure_node(parent_of(X,Y),or(C,D))
| ~ failure_node(X,or(C,P))
| ~ failure_node(Y,or(D,Q)) )
<=> ( ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) ) )),
( ( failure_node(parent_of(X,Y),or(C,D))
| ~ failure_node(X,or(C,P))
| ~ failure_node(Y,or(D,Q))
| ~ contradictory(P,Q) )
<=> ( ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D))
| ~ contradictory(P,Q) ) )),
rewrite(( ( ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D))
| ~ contradictory(P,Q) )
<=> ( ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) ) )),
( ( failure_node(parent_of(X,Y),or(C,D))
| ~ failure_node(X,or(C,P))
| ~ failure_node(Y,or(D,Q))
| ~ contradictory(P,Q) )
<=> ( ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) ) )),
( ( failure_node(parent_of(X,Y),or(C,D))
| ~ failure_node(X,or(C,P))
| ~ failure_node(Y,or(D,Q))
| ~ contradictory(P,Q)
| ~ siblings(X,Y) )
<=> ( ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D))
| ~ siblings(X,Y) ) )),
rewrite(( ( ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D))
| ~ siblings(X,Y) )
<=> ( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) ) )),
( ( failure_node(parent_of(X,Y),or(C,D))
| ~ failure_node(X,or(C,P))
| ~ failure_node(Y,or(D,Q))
| ~ contradictory(P,Q)
| ~ siblings(X,Y) )
<=> ( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
( failure_node(parent_of(X,Y),or(C,D))
| ~ failure_node(X,or(C,P))
| ~ failure_node(Y,or(D,Q))
| ~ contradictory(P,Q)
| ~ siblings(X,Y) )
<=> ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
( failure_node(parent_of(X,Y),or(C,D))
| ~ failure_node(X,or(C,P))
| ~ failure_node(Y,or(D,Q))
| ~ contradictory(P,Q)
| ~ siblings(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',make_node) ).
tff(45,plain,
! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
( ( ~ ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) )
| ~ failure_node(left_child_of(n),or(empty,atom))
| failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty))
| ~ failure_node(right_child_of(n),or(empty,negate(atom)))
| ~ contradictory(atom,negate(atom))
| ~ siblings(left_child_of(n),right_child_of(n)) )
<=> ( ~ ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) )
| ~ failure_node(left_child_of(n),or(empty,atom))
| failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty))
| ~ failure_node(right_child_of(n),or(empty,negate(atom)))
| ~ contradictory(atom,negate(atom))
| ~ siblings(left_child_of(n),right_child_of(n)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ( ~ siblings(left_child_of(n),right_child_of(n))
| ~ contradictory(atom,negate(atom))
| ~ failure_node(right_child_of(n),or(empty,negate(atom)))
| ~ failure_node(left_child_of(n),or(empty,atom))
| failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty)) )
<=> ( ~ failure_node(left_child_of(n),or(empty,atom))
| failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty))
| ~ failure_node(right_child_of(n),or(empty,negate(atom)))
| ~ contradictory(atom,negate(atom))
| ~ siblings(left_child_of(n),right_child_of(n)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ( ~ ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) )
| ~ siblings(left_child_of(n),right_child_of(n))
| ~ contradictory(atom,negate(atom))
| ~ failure_node(right_child_of(n),or(empty,negate(atom)))
| ~ failure_node(left_child_of(n),or(empty,atom))
| failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty)) )
<=> ( ~ ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) )
| ~ failure_node(left_child_of(n),or(empty,atom))
| failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty))
| ~ failure_node(right_child_of(n),or(empty,negate(atom)))
| ~ contradictory(atom,negate(atom))
| ~ siblings(left_child_of(n),right_child_of(n)) ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ( ~ ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) )
| ~ siblings(left_child_of(n),right_child_of(n))
| ~ contradictory(atom,negate(atom))
| ~ failure_node(right_child_of(n),or(empty,negate(atom)))
| ~ failure_node(left_child_of(n),or(empty,atom))
| failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty)) )
<=> ( ~ ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) )
| ~ failure_node(left_child_of(n),or(empty,atom))
| failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty))
| ~ failure_node(right_child_of(n),or(empty,negate(atom)))
| ~ contradictory(atom,negate(atom))
| ~ siblings(left_child_of(n),right_child_of(n)) ) ),
inference(transitivity,[status(thm)],[51,49]) ).
tff(53,plain,
( ~ ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) )
| ~ siblings(left_child_of(n),right_child_of(n))
| ~ contradictory(atom,negate(atom))
| ~ failure_node(right_child_of(n),or(empty,negate(atom)))
| ~ failure_node(left_child_of(n),or(empty,atom))
| failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
( ~ siblings(X,Y)
| ~ contradictory(P,Q)
| ~ failure_node(Y,or(D,Q))
| ~ failure_node(X,or(C,P))
| failure_node(parent_of(X,Y),or(C,D)) )
| ~ failure_node(left_child_of(n),or(empty,atom))
| failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty))
| ~ failure_node(right_child_of(n),or(empty,negate(atom)))
| ~ contradictory(atom,negate(atom))
| ~ siblings(left_child_of(n),right_child_of(n)) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( ~ failure_node(left_child_of(n),or(empty,atom))
| failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty))
| ~ failure_node(right_child_of(n),or(empty,negate(atom))) ),
inference(unit_resolution,[status(thm)],[54,48,38,29]) ).
tff(56,plain,
failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty)),
inference(unit_resolution,[status(thm)],[55,20,10]) ).
tff(57,plain,
^ [Z: $i] :
refl(( ~ failure_node(Z,or(empty,empty))
<=> ~ failure_node(Z,or(empty,empty)) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [Z: $i] : ~ failure_node(Z,or(empty,empty))
<=> ! [Z: $i] : ~ failure_node(Z,or(empty,empty)) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [Z: $i] : ~ failure_node(Z,or(empty,empty))
<=> ! [Z: $i] : ~ failure_node(Z,or(empty,empty)) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,axiom,
! [Z: $i] : ~ failure_node(Z,or(empty,empty)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_is_there_an_empty_node) ).
tff(61,plain,
! [Z: $i] : ~ failure_node(Z,or(empty,empty)),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [Z: $i] : ~ failure_node(Z,or(empty,empty)),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [Z: $i] : ~ failure_node(Z,or(empty,empty)),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
( ~ ! [Z: $i] : ~ failure_node(Z,or(empty,empty))
| ~ failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
$false,
inference(unit_resolution,[status(thm)],[64,63,56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM004-1 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 12:21:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.37 % SZS status Unsatisfiable
% 0.18/0.37 % SZS output start Proof
% See solution above
% 0.18/0.38 % E exiting
%------------------------------------------------------------------------------