TSTP Solution File: SET787-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET787-2 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 : Tue Sep 20 05:08:01 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 75
% Syntax : Number of formulae : 156 ( 31 unt; 11 typ; 0 def)
% Number of atoms : 672 ( 82 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 913 ( 411 ~; 437 |; 0 &)
% ( 65 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 25 ( 25 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 7 >; 5 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 421 ( 387 !; 0 ?; 421 :)
% Comments :
%------------------------------------------------------------------------------
tff(unionE_sk1_type,type,
unionE_sk1: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(eptset_type,type,
eptset: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(pow_type,type,
pow: $i > $i ).
tff(un_type,type,
un: ( $i * $i ) > $i ).
tff(union_type,type,
union: $i > $i ).
tff(subset_type,type,
subset: ( $i * $i ) > $o ).
tff(1,plain,
( member(sk2,union(cons(a,cons(b,eptset))))
<=> member(sk2,union(cons(a,cons(b,eptset)))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
member(sk2,union(cons(a,cons(b,eptset)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',un_eq_Union_2_c1) ).
tff(3,plain,
member(sk2,union(cons(a,cons(b,eptset)))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ member(U,union(V))
| member(U,unionE_sk1(U,V)) )
<=> ( ~ member(U,union(V))
| member(U,unionE_sk1(U,V)) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(U,unionE_sk1(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(U,unionE_sk1(U,V)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(U,unionE_sk1(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(U,unionE_sk1(U,V)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(U,unionE_sk1(U,V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).
tff(8,plain,
! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(U,unionE_sk1(U,V)) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(U,unionE_sk1(U,V)) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(U,unionE_sk1(U,V)) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(U,unionE_sk1(U,V)) )
| ~ member(sk2,union(cons(a,cons(b,eptset))))
| member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset)))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(U,unionE_sk1(U,V)) )
| ~ member(sk2,union(cons(a,cons(b,eptset))))
| member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(U,unionE_sk1(U,V)) )
| ~ member(sk2,union(cons(a,cons(b,eptset))))
| member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(U,unionE_sk1(U,V)) )
| ~ member(sk2,union(cons(a,cons(b,eptset))))
| member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset)))) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset)))),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( ~ member(sk2,un(a,b))
<=> ~ member(sk2,un(a,b)) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
~ member(sk2,un(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',un_eq_Union_2_c2) ).
tff(17,plain,
~ member(sk2,un(a,b)),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( member(W,V)
| ~ member(W,U)
| ~ member(U,pow(V)) )
<=> ( member(W,V)
| ~ member(W,U)
| ~ member(U,pow(V)) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [W: $i,V: $i,U: $i] :
( member(W,V)
| ~ member(W,U)
| ~ member(U,pow(V)) )
<=> ! [W: $i,V: $i,U: $i] :
( member(W,V)
| ~ member(W,U)
| ~ member(U,pow(V)) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [W: $i,V: $i,U: $i] :
( member(W,V)
| ~ member(W,U)
| ~ member(U,pow(V)) )
<=> ! [W: $i,V: $i,U: $i] :
( member(W,V)
| ~ member(W,U)
| ~ member(U,pow(V)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
^ [W: $i,V: $i,U: $i] :
trans(
monotonicity(
rewrite(
( ( ~ member(U,pow(V))
| ~ member(W,U) )
<=> ( ~ member(W,U)
| ~ member(U,pow(V)) ) )),
( ( ~ member(U,pow(V))
| ~ member(W,U)
| member(W,V) )
<=> ( ~ member(W,U)
| ~ member(U,pow(V))
| member(W,V) ) )),
rewrite(
( ( ~ member(W,U)
| ~ member(U,pow(V))
| member(W,V) )
<=> ( member(W,V)
| ~ member(W,U)
| ~ member(U,pow(V)) ) )),
( ( ~ member(U,pow(V))
| ~ member(W,U)
| member(W,V) )
<=> ( member(W,V)
| ~ member(W,U)
| ~ member(U,pow(V)) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ member(U,pow(V))
| ~ member(W,U)
| member(W,V) )
<=> ! [W: $i,V: $i,U: $i] :
( member(W,V)
| ~ member(W,U)
| ~ member(U,pow(V)) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [W: $i,V: $i,U: $i] :
( ~ member(U,pow(V))
| ~ member(W,U)
| member(W,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause118) ).
tff(24,plain,
! [W: $i,V: $i,U: $i] :
( member(W,V)
| ~ member(W,U)
| ~ member(U,pow(V)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [W: $i,V: $i,U: $i] :
( member(W,V)
| ~ member(W,U)
| ~ member(U,pow(V)) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [W: $i,V: $i,U: $i] :
( member(W,V)
| ~ member(W,U)
| ~ member(U,pow(V)) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [W: $i,V: $i,U: $i] :
( member(W,V)
| ~ member(W,U)
| ~ member(U,pow(V)) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( member(W,V)
| ~ member(W,U)
| ~ member(U,pow(V)) )
| member(sk2,un(a,b))
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),pow(un(a,b))) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( member(W,V)
| ~ member(W,U)
| ~ member(U,pow(V)) )
| member(sk2,un(a,b))
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),pow(un(a,b))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( member(W,V)
| ~ member(W,U)
| ~ member(U,pow(V)) )
| member(sk2,un(a,b))
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),pow(un(a,b))) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( member(W,V)
| ~ member(W,U)
| ~ member(U,pow(V)) )
| member(sk2,un(a,b))
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),pow(un(a,b))) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),pow(un(a,b))),
inference(unit_resolution,[status(thm)],[30,27,17,14]) ).
tff(32,plain,
^ [A: $i,X: $i] :
refl(
( ( ~ member(X,eptset)
| member(X,A) )
<=> ( ~ member(X,eptset)
| member(X,A) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [A: $i,X: $i] :
( ~ member(X,eptset)
| member(X,A) )
<=> ! [A: $i,X: $i] :
( ~ member(X,eptset)
| member(X,A) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [A: $i,X: $i] :
( ~ member(X,eptset)
| member(X,A) )
<=> ! [A: $i,X: $i] :
( ~ member(X,eptset)
| member(X,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
! [A: $i,X: $i] :
( ~ member(X,eptset)
| member(X,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause135) ).
tff(36,plain,
! [A: $i,X: $i] :
( ~ member(X,eptset)
| member(X,A) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [A: $i,X: $i] :
( ~ member(X,eptset)
| member(X,A) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [A: $i,X: $i] :
( ~ member(X,eptset)
| member(X,A) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ( ~ ! [A: $i,X: $i] :
( ~ member(X,eptset)
| member(X,A) )
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),pow(un(a,b))) )
<=> ( ~ ! [A: $i,X: $i] :
( ~ member(X,eptset)
| member(X,A) )
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),pow(un(a,b))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ~ ! [A: $i,X: $i] :
( ~ member(X,eptset)
| member(X,A) )
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),pow(un(a,b))) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [A: $i,X: $i] :
( ~ member(X,eptset)
| member(X,A) )
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),pow(un(a,b))) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset),
inference(unit_resolution,[status(thm)],[41,38,31]) ).
tff(43,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ~ member(C,A)
| member(C,un(A,B)) )
<=> ( ~ member(C,A)
| member(C,un(A,B)) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,un(A,B)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,un(A,B)) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,un(A,B)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,un(A,B)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,un(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unI1) ).
tff(47,plain,
! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,un(A,B)) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,un(A,B)) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,un(A,B)) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,un(A,B)) )
| ~ member(sk2,a)
| member(sk2,un(a,b)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,un(A,B)) )
| ~ member(sk2,a)
| member(sk2,un(a,b)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,un(A,B)) )
| ~ member(sk2,a)
| member(sk2,un(a,b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,un(A,B)) )
| ~ member(sk2,a)
| member(sk2,un(a,b)) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
~ member(sk2,a),
inference(unit_resolution,[status(thm)],[52,49,17]) ).
tff(54,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) )
<=> ( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
^ [B: $i,A: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( ~ subset(A,B)
| ~ member(C,A) )
<=> ( ~ member(C,A)
| ~ subset(A,B) ) )),
( ( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) )
<=> ( ~ member(C,A)
| ~ subset(A,B)
| member(C,B) ) )),
rewrite(
( ( ~ member(C,A)
| ~ subset(A,B)
| member(C,B) )
<=> ( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) ) )),
( ( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) )
<=> ( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,axiom,
! [B: $i,A: $i,C: $i] :
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetD) ).
tff(60,plain,
! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) ),
inference(modus_ponens,[status(thm)],[62,55]) ).
tff(64,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) )
| member(sk2,a)
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) )
| member(sk2,a)
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ( ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| member(sk2,a)
| ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) )
<=> ( member(sk2,a)
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) )
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| member(sk2,a)
| ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) )
| member(sk2,a)
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) ) ),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) )
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| member(sk2,a)
| ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) )
| member(sk2,a)
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) ) ),
inference(transitivity,[status(thm)],[66,64]) ).
tff(68,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) )
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| member(sk2,a)
| ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) )
| member(sk2,a)
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a),
inference(unit_resolution,[status(thm)],[69,63,14,53]) ).
tff(71,plain,
^ [B: $i,A: $i] :
refl(
( ( ( A != B )
| subset(A,B) )
<=> ( ( A != B )
| subset(A,B) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [B: $i,A: $i] :
( ( A != B )
| subset(A,B) )
<=> ! [B: $i,A: $i] :
( ( A != B )
| subset(A,B) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [B: $i,A: $i] :
( ( A != B )
| subset(A,B) )
<=> ! [B: $i,A: $i] :
( ( A != B )
| subset(A,B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,axiom,
! [B: $i,A: $i] :
( ( A != B )
| subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause149) ).
tff(75,plain,
! [B: $i,A: $i] :
( ( A != B )
| subset(A,B) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [B: $i,A: $i] :
( ( A != B )
| subset(A,B) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [B: $i,A: $i] :
( ( A != B )
| subset(A,B) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
( ( ~ ! [B: $i,A: $i] :
( ( A != B )
| subset(A,B) )
| ( unionE_sk1(sk2,cons(a,cons(b,eptset))) != a )
| subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) )
<=> ( ~ ! [B: $i,A: $i] :
( ( A != B )
| subset(A,B) )
| ( unionE_sk1(sk2,cons(a,cons(b,eptset))) != a )
| subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ~ ! [B: $i,A: $i] :
( ( A != B )
| subset(A,B) )
| ( unionE_sk1(sk2,cons(a,cons(b,eptset))) != a )
| subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
( ~ ! [B: $i,A: $i] :
( ( A != B )
| subset(A,B) )
| ( unionE_sk1(sk2,cons(a,cons(b,eptset))) != a )
| subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
unionE_sk1(sk2,cons(a,cons(b,eptset))) != a,
inference(unit_resolution,[status(thm)],[80,77,70]) ).
tff(82,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ member(U,union(V))
| member(unionE_sk1(U,V),V) )
<=> ( ~ member(U,union(V))
| member(unionE_sk1(U,V),V) ) )),
inference(bind,[status(th)],]) ).
tff(83,plain,
( ! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(unionE_sk1(U,V),V) )
<=> ! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(unionE_sk1(U,V),V) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(unionE_sk1(U,V),V) )
<=> ! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(unionE_sk1(U,V),V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,axiom,
! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(unionE_sk1(U,V),V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).
tff(86,plain,
! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(unionE_sk1(U,V),V) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(unionE_sk1(U,V),V) ),
inference(skolemize,[status(sab)],[86]) ).
tff(88,plain,
! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(unionE_sk1(U,V),V) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(unionE_sk1(U,V),V) )
| ~ member(sk2,union(cons(a,cons(b,eptset))))
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(unionE_sk1(U,V),V) )
| ~ member(sk2,union(cons(a,cons(b,eptset))))
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ~ ! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(unionE_sk1(U,V),V) )
| ~ member(sk2,union(cons(a,cons(b,eptset))))
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
( ~ ! [V: $i,U: $i] :
( ~ member(U,union(V))
| member(unionE_sk1(U,V),V) )
| ~ member(sk2,union(cons(a,cons(b,eptset))))
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))),
inference(unit_resolution,[status(thm)],[91,88,3]) ).
tff(93,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) )
<=> ( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) ) )),
inference(bind,[status(th)],]) ).
tff(94,plain,
( ! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) )
<=> ! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,plain,
( ! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) )
<=> ! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
^ [W: $i,V: $i,U: $i] :
rewrite(
( ( ~ member(U,cons(V,W))
| ( U = V )
| member(U,W) )
<=> ( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) ) )),
inference(bind,[status(th)],]) ).
tff(97,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ member(U,cons(V,W))
| ( U = V )
| member(U,W) )
<=> ! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,axiom,
! [W: $i,V: $i,U: $i] :
( ~ member(U,cons(V,W))
| ( U = V )
| member(U,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause112) ).
tff(99,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) ),
inference(modus_ponens,[status(thm)],[101,94]) ).
tff(103,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) )
| ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a )
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) )
| ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a )
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) )
| ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a )
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))) ),
inference(quant_inst,[status(thm)],]) ).
tff(105,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) )
| ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a )
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
( ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a )
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) ),
inference(unit_resolution,[status(thm)],[105,102,92]) ).
tff(107,plain,
member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)),
inference(unit_resolution,[status(thm)],[106,81]) ).
tff(108,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) )
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
| ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) )
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
| ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
( ( ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b )
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) )
<=> ( member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
| ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) )
| ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b )
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) )
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
| ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b ) ) ),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) )
| ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b )
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) )
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
| ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b ) ) ),
inference(transitivity,[status(thm)],[110,108]) ).
tff(112,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) )
| ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b )
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) ),
inference(quant_inst,[status(thm)],]) ).
tff(113,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| member(U,W)
| ~ member(U,cons(V,W)) )
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
| ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b ) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
unionE_sk1(sk2,cons(a,cons(b,eptset))) = b,
inference(unit_resolution,[status(thm)],[113,102,107,42]) ).
tff(115,plain,
b = unionE_sk1(sk2,cons(a,cons(b,eptset))),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ~ member(C,B)
| member(C,un(A,B)) )
<=> ( ~ member(C,B)
| member(C,un(A,B)) ) )),
inference(bind,[status(th)],]) ).
tff(117,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ member(C,B)
| member(C,un(A,B)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ member(C,B)
| member(C,un(A,B)) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ member(C,B)
| member(C,un(A,B)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ member(C,B)
| member(C,un(A,B)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,axiom,
! [B: $i,A: $i,C: $i] :
( ~ member(C,B)
| member(C,un(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unI2) ).
tff(120,plain,
! [B: $i,A: $i,C: $i] :
( ~ member(C,B)
| member(C,un(A,B)) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
! [B: $i,A: $i,C: $i] :
( ~ member(C,B)
| member(C,un(A,B)) ),
inference(skolemize,[status(sab)],[120]) ).
tff(122,plain,
! [B: $i,A: $i,C: $i] :
( ~ member(C,B)
| member(C,un(A,B)) ),
inference(modus_ponens,[status(thm)],[121,117]) ).
tff(123,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,B)
| member(C,un(A,B)) )
| ~ member(sk2,b)
| member(sk2,un(a,b)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,B)
| member(C,un(A,B)) )
| ~ member(sk2,b)
| member(sk2,un(a,b)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,B)
| member(C,un(A,B)) )
| ~ member(sk2,b)
| member(sk2,un(a,b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,B)
| member(C,un(A,B)) )
| ~ member(sk2,b)
| member(sk2,un(a,b)) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
~ member(sk2,b),
inference(unit_resolution,[status(thm)],[125,122,17]) ).
tff(127,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) )
| member(sk2,b)
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) )
| member(sk2,b)
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(128,plain,
( ( ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| member(sk2,b)
| ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) )
<=> ( member(sk2,b)
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(129,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) )
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| member(sk2,b)
| ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) )
| member(sk2,b)
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) ) ),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) )
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| member(sk2,b)
| ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) )
| member(sk2,b)
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) ) ),
inference(transitivity,[status(thm)],[129,127]) ).
tff(131,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) )
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| member(sk2,b)
| ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) ),
inference(quant_inst,[status(thm)],]) ).
tff(132,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ member(C,A)
| member(C,B)
| ~ subset(A,B) )
| member(sk2,b)
| ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
| ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) ),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b),
inference(unit_resolution,[status(thm)],[132,63,14,126]) ).
tff(134,plain,
^ [B: $i,A: $i] :
refl(
( ( ( A != B )
| subset(B,A) )
<=> ( ( A != B )
| subset(B,A) ) )),
inference(bind,[status(th)],]) ).
tff(135,plain,
( ! [B: $i,A: $i] :
( ( A != B )
| subset(B,A) )
<=> ! [B: $i,A: $i] :
( ( A != B )
| subset(B,A) ) ),
inference(quant_intro,[status(thm)],[134]) ).
tff(136,plain,
( ! [B: $i,A: $i] :
( ( A != B )
| subset(B,A) )
<=> ! [B: $i,A: $i] :
( ( A != B )
| subset(B,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(137,axiom,
! [B: $i,A: $i] :
( ( A != B )
| subset(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause150) ).
tff(138,plain,
! [B: $i,A: $i] :
( ( A != B )
| subset(B,A) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
! [B: $i,A: $i] :
( ( A != B )
| subset(B,A) ),
inference(skolemize,[status(sab)],[138]) ).
tff(140,plain,
! [B: $i,A: $i] :
( ( A != B )
| subset(B,A) ),
inference(modus_ponens,[status(thm)],[139,135]) ).
tff(141,plain,
( ( ~ ! [B: $i,A: $i] :
( ( A != B )
| subset(B,A) )
| ( b != unionE_sk1(sk2,cons(a,cons(b,eptset))) )
| subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) )
<=> ( ~ ! [B: $i,A: $i] :
( ( A != B )
| subset(B,A) )
| ( b != unionE_sk1(sk2,cons(a,cons(b,eptset))) )
| subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(142,plain,
( ~ ! [B: $i,A: $i] :
( ( A != B )
| subset(B,A) )
| ( b != unionE_sk1(sk2,cons(a,cons(b,eptset))) )
| subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
( ~ ! [B: $i,A: $i] :
( ( A != B )
| subset(B,A) )
| ( b != unionE_sk1(sk2,cons(a,cons(b,eptset))) )
| subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
b != unionE_sk1(sk2,cons(a,cons(b,eptset))),
inference(unit_resolution,[status(thm)],[143,140,133]) ).
tff(145,plain,
$false,
inference(unit_resolution,[status(thm)],[144,115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET787-2 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.32 % Computer : n022.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Sat Sep 3 08:00:09 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------