TSTP Solution File: KRS013-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS013-1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 Sep 17 17:44:22 EDT 2022
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 98
% Syntax : Number of formulae : 197 ( 38 unt; 18 typ; 0 def)
% Number of atoms : 863 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1140 ( 500 ~; 558 |; 0 &)
% ( 82 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 44 ( 44 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 17 >; 4 *; 0 +; 0 <<)
% Number of predicates : 17 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 308 ( 276 !; 0 ?; 308 :)
% Comments :
%------------------------------------------------------------------------------
tff(equalish_type,type,
equalish: ( $i * $i ) > $o ).
tff(u1r1_type,type,
u1r1: $i > $i ).
tff(u6r1_type,type,
u6r1: $i > $i ).
tff(exist_type,type,
exist: $i ).
tff(u1r2_type,type,
u1r2: $i > $i ).
tff(t2least_type,type,
t2least: $i > $o ).
tff(c_type,type,
c: $i > $o ).
tff(s2least_type,type,
s2least: $i > $o ).
tff(s_type,type,
s: ( $i * $i ) > $o ).
tff(u7r1_type,type,
u7r1: $i > $i ).
tff(s1most_type,type,
s1most: $i > $o ).
tff(f_type,type,
f: $i > $o ).
tff(u7r2_type,type,
u7r2: $i > $i ).
tff(r_type,type,
r: ( $i * $i ) > $o ).
tff(e_type,type,
e: $i > $o ).
tff(t_type,type,
t: ( $i * $i ) > $o ).
tff(t1most_type,type,
t1most: $i > $o ).
tff(d_type,type,
d: $i > $o ).
tff(1,plain,
^ [X1: $i] :
refl(
( ( f(X1)
| ~ s1most(u6r1(X1)) )
<=> ( f(X1)
| ~ s1most(u6r1(X1)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X1: $i] :
( f(X1)
| ~ s1most(u6r1(X1)) )
<=> ! [X1: $i] :
( f(X1)
| ~ s1most(u6r1(X1)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X1: $i] :
( f(X1)
| ~ s1most(u6r1(X1)) )
<=> ! [X1: $i] :
( f(X1)
| ~ s1most(u6r1(X1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X1: $i] :
( f(X1)
| ~ s1most(u6r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_28) ).
tff(5,plain,
! [X1: $i] :
( f(X1)
| ~ s1most(u6r1(X1)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X1: $i] :
( f(X1)
| ~ s1most(u6r1(X1)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X1: $i] :
( f(X1)
| ~ s1most(u6r1(X1)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ f(exist)
<=> ~ f(exist) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
~ f(exist),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
tff(10,plain,
~ f(exist),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [X1: $i] :
( f(X1)
| ~ s1most(u6r1(X1)) )
| f(exist)
| ~ s1most(u6r1(exist)) )
<=> ( ~ ! [X1: $i] :
( f(X1)
| ~ s1most(u6r1(X1)) )
| f(exist)
| ~ s1most(u6r1(exist)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [X1: $i] :
( f(X1)
| ~ s1most(u6r1(X1)) )
| f(exist)
| ~ s1most(u6r1(exist)) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [X1: $i] :
( f(X1)
| ~ s1most(u6r1(X1)) )
| f(exist)
| ~ s1most(u6r1(exist)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ s1most(u6r1(exist)),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
^ [X1: $i] :
refl(
( ( s1most(X1)
| s(X1,u7r1(X1)) )
<=> ( s1most(X1)
| s(X1,u7r1(X1)) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [X1: $i] :
( s1most(X1)
| s(X1,u7r1(X1)) )
<=> ! [X1: $i] :
( s1most(X1)
| s(X1,u7r1(X1)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [X1: $i] :
( s1most(X1)
| s(X1,u7r1(X1)) )
<=> ! [X1: $i] :
( s1most(X1)
| s(X1,u7r1(X1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
! [X1: $i] :
( s1most(X1)
| s(X1,u7r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_32) ).
tff(19,plain,
! [X1: $i] :
( s1most(X1)
| s(X1,u7r1(X1)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [X1: $i] :
( s1most(X1)
| s(X1,u7r1(X1)) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [X1: $i] :
( s1most(X1)
| s(X1,u7r1(X1)) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [X1: $i] :
( s1most(X1)
| s(X1,u7r1(X1)) )
| s1most(u6r1(exist))
| s(u6r1(exist),u7r1(u6r1(exist))) )
<=> ( ~ ! [X1: $i] :
( s1most(X1)
| s(X1,u7r1(X1)) )
| s1most(u6r1(exist))
| s(u6r1(exist),u7r1(u6r1(exist))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ~ ! [X1: $i] :
( s1most(X1)
| s(X1,u7r1(X1)) )
| s1most(u6r1(exist))
| s(u6r1(exist),u7r1(u6r1(exist))) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
( ~ ! [X1: $i] :
( s1most(X1)
| s(X1,u7r1(X1)) )
| s1most(u6r1(exist))
| s(u6r1(exist),u7r1(u6r1(exist))) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
s(u6r1(exist),u7r1(u6r1(exist))),
inference(unit_resolution,[status(thm)],[24,21,14]) ).
tff(26,plain,
^ [X1: $i] :
refl(
( ( s1most(X1)
| ~ equalish(u7r2(X1),u7r1(X1)) )
<=> ( s1most(X1)
| ~ equalish(u7r2(X1),u7r1(X1)) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [X1: $i] :
( s1most(X1)
| ~ equalish(u7r2(X1),u7r1(X1)) )
<=> ! [X1: $i] :
( s1most(X1)
| ~ equalish(u7r2(X1),u7r1(X1)) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [X1: $i] :
( s1most(X1)
| ~ equalish(u7r2(X1),u7r1(X1)) )
<=> ! [X1: $i] :
( s1most(X1)
| ~ equalish(u7r2(X1),u7r1(X1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
! [X1: $i] :
( s1most(X1)
| ~ equalish(u7r2(X1),u7r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_31) ).
tff(30,plain,
! [X1: $i] :
( s1most(X1)
| ~ equalish(u7r2(X1),u7r1(X1)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [X1: $i] :
( s1most(X1)
| ~ equalish(u7r2(X1),u7r1(X1)) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [X1: $i] :
( s1most(X1)
| ~ equalish(u7r2(X1),u7r1(X1)) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ( ~ ! [X1: $i] :
( s1most(X1)
| ~ equalish(u7r2(X1),u7r1(X1)) )
| s1most(u6r1(exist))
| ~ equalish(u7r2(u6r1(exist)),u7r1(u6r1(exist))) )
<=> ( ~ ! [X1: $i] :
( s1most(X1)
| ~ equalish(u7r2(X1),u7r1(X1)) )
| s1most(u6r1(exist))
| ~ equalish(u7r2(u6r1(exist)),u7r1(u6r1(exist))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ~ ! [X1: $i] :
( s1most(X1)
| ~ equalish(u7r2(X1),u7r1(X1)) )
| s1most(u6r1(exist))
| ~ equalish(u7r2(u6r1(exist)),u7r1(u6r1(exist))) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
( ~ ! [X1: $i] :
( s1most(X1)
| ~ equalish(u7r2(X1),u7r1(X1)) )
| s1most(u6r1(exist))
| ~ equalish(u7r2(u6r1(exist)),u7r1(u6r1(exist))) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
~ equalish(u7r2(u6r1(exist)),u7r1(u6r1(exist))),
inference(unit_resolution,[status(thm)],[35,32,14]) ).
tff(37,plain,
^ [X1: $i] :
refl(
( ( s1most(X1)
| s(X1,u7r2(X1)) )
<=> ( s1most(X1)
| s(X1,u7r2(X1)) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [X1: $i] :
( s1most(X1)
| s(X1,u7r2(X1)) )
<=> ! [X1: $i] :
( s1most(X1)
| s(X1,u7r2(X1)) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [X1: $i] :
( s1most(X1)
| s(X1,u7r2(X1)) )
<=> ! [X1: $i] :
( s1most(X1)
| s(X1,u7r2(X1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
! [X1: $i] :
( s1most(X1)
| s(X1,u7r2(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_33) ).
tff(41,plain,
! [X1: $i] :
( s1most(X1)
| s(X1,u7r2(X1)) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [X1: $i] :
( s1most(X1)
| s(X1,u7r2(X1)) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [X1: $i] :
( s1most(X1)
| s(X1,u7r2(X1)) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ( ~ ! [X1: $i] :
( s1most(X1)
| s(X1,u7r2(X1)) )
| s1most(u6r1(exist))
| s(u6r1(exist),u7r2(u6r1(exist))) )
<=> ( ~ ! [X1: $i] :
( s1most(X1)
| s(X1,u7r2(X1)) )
| s1most(u6r1(exist))
| s(u6r1(exist),u7r2(u6r1(exist))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ~ ! [X1: $i] :
( s1most(X1)
| s(X1,u7r2(X1)) )
| s1most(u6r1(exist))
| s(u6r1(exist),u7r2(u6r1(exist))) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
( ~ ! [X1: $i] :
( s1most(X1)
| s(X1,u7r2(X1)) )
| s1most(u6r1(exist))
| s(u6r1(exist),u7r2(u6r1(exist))) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
s(u6r1(exist),u7r2(u6r1(exist))),
inference(unit_resolution,[status(thm)],[46,43,14]) ).
tff(48,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(
( ( equalish(X3,X2)
| s2least(X1)
| ~ s(X1,X2)
| ~ s(X1,X3) )
<=> ( equalish(X3,X2)
| s2least(X1)
| ~ s(X1,X2)
| ~ s(X1,X3) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( equalish(X3,X2)
| s2least(X1)
| ~ s(X1,X2)
| ~ s(X1,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( equalish(X3,X2)
| s2least(X1)
| ~ s(X1,X2)
| ~ s(X1,X3) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( equalish(X3,X2)
| s2least(X1)
| ~ s(X1,X2)
| ~ s(X1,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( equalish(X3,X2)
| s2least(X1)
| ~ s(X1,X2)
| ~ s(X1,X3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
^ [X3: $i,X2: $i,X1: $i] :
trans(
monotonicity(
rewrite(
( ( s2least(X1)
| equalish(X3,X2)
| ~ s(X1,X3) )
<=> ( equalish(X3,X2)
| s2least(X1)
| ~ s(X1,X3) ) )),
( ( s2least(X1)
| equalish(X3,X2)
| ~ s(X1,X3)
| ~ s(X1,X2) )
<=> ( equalish(X3,X2)
| s2least(X1)
| ~ s(X1,X3)
| ~ s(X1,X2) ) )),
rewrite(
( ( equalish(X3,X2)
| s2least(X1)
| ~ s(X1,X3)
| ~ s(X1,X2) )
<=> ( equalish(X3,X2)
| s2least(X1)
| ~ s(X1,X2)
| ~ s(X1,X3) ) )),
( ( s2least(X1)
| equalish(X3,X2)
| ~ s(X1,X3)
| ~ s(X1,X2) )
<=> ( equalish(X3,X2)
| s2least(X1)
| ~ s(X1,X2)
| ~ s(X1,X3) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( s2least(X1)
| equalish(X3,X2)
| ~ s(X1,X3)
| ~ s(X1,X2) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( equalish(X3,X2)
| s2least(X1)
| ~ s(X1,X2)
| ~ s(X1,X3) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,axiom,
! [X3: $i,X2: $i,X1: $i] :
( s2least(X1)
| equalish(X3,X2)
| ~ s(X1,X3)
| ~ s(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_26) ).
tff(54,plain,
! [X3: $i,X2: $i,X1: $i] :
( equalish(X3,X2)
| s2least(X1)
| ~ s(X1,X2)
| ~ s(X1,X3) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [X3: $i,X2: $i,X1: $i] :
( equalish(X3,X2)
| s2least(X1)
| ~ s(X1,X2)
| ~ s(X1,X3) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
! [X3: $i,X2: $i,X1: $i] :
( equalish(X3,X2)
| s2least(X1)
| ~ s(X1,X2)
| ~ s(X1,X3) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [X3: $i,X2: $i,X1: $i] :
( equalish(X3,X2)
| s2least(X1)
| ~ s(X1,X2)
| ~ s(X1,X3) ),
inference(modus_ponens,[status(thm)],[56,49]) ).
tff(58,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( equalish(X3,X2)
| s2least(X1)
| ~ s(X1,X2)
| ~ s(X1,X3) )
| equalish(u7r2(u6r1(exist)),u7r1(u6r1(exist)))
| s2least(u6r1(exist))
| ~ s(u6r1(exist),u7r1(u6r1(exist)))
| ~ s(u6r1(exist),u7r2(u6r1(exist))) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( equalish(X3,X2)
| s2least(X1)
| ~ s(X1,X2)
| ~ s(X1,X3) )
| equalish(u7r2(u6r1(exist)),u7r1(u6r1(exist)))
| s2least(u6r1(exist))
| ~ s(u6r1(exist),u7r1(u6r1(exist)))
| ~ s(u6r1(exist),u7r2(u6r1(exist))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( equalish(X3,X2)
| s2least(X1)
| ~ s(X1,X2)
| ~ s(X1,X3) )
| equalish(u7r2(u6r1(exist)),u7r1(u6r1(exist)))
| s2least(u6r1(exist))
| ~ s(u6r1(exist),u7r1(u6r1(exist)))
| ~ s(u6r1(exist),u7r2(u6r1(exist))) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( equalish(X3,X2)
| s2least(X1)
| ~ s(X1,X2)
| ~ s(X1,X3) )
| equalish(u7r2(u6r1(exist)),u7r1(u6r1(exist)))
| s2least(u6r1(exist))
| ~ s(u6r1(exist),u7r1(u6r1(exist)))
| ~ s(u6r1(exist),u7r2(u6r1(exist))) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
s2least(u6r1(exist)),
inference(unit_resolution,[status(thm)],[60,57,47,36,25]) ).
tff(62,plain,
^ [X1: $i] :
refl(
( ( f(X1)
| r(X1,u6r1(X1)) )
<=> ( f(X1)
| r(X1,u6r1(X1)) ) )),
inference(bind,[status(th)],]) ).
tff(63,plain,
( ! [X1: $i] :
( f(X1)
| r(X1,u6r1(X1)) )
<=> ! [X1: $i] :
( f(X1)
| r(X1,u6r1(X1)) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [X1: $i] :
( f(X1)
| r(X1,u6r1(X1)) )
<=> ! [X1: $i] :
( f(X1)
| r(X1,u6r1(X1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,axiom,
! [X1: $i] :
( f(X1)
| r(X1,u6r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_29) ).
tff(66,plain,
! [X1: $i] :
( f(X1)
| r(X1,u6r1(X1)) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [X1: $i] :
( f(X1)
| r(X1,u6r1(X1)) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [X1: $i] :
( f(X1)
| r(X1,u6r1(X1)) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
( ( ~ ! [X1: $i] :
( f(X1)
| r(X1,u6r1(X1)) )
| f(exist)
| r(exist,u6r1(exist)) )
<=> ( ~ ! [X1: $i] :
( f(X1)
| r(X1,u6r1(X1)) )
| f(exist)
| r(exist,u6r1(exist)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ~ ! [X1: $i] :
( f(X1)
| r(X1,u6r1(X1)) )
| f(exist)
| r(exist,u6r1(exist)) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
( ~ ! [X1: $i] :
( f(X1)
| r(X1,u6r1(X1)) )
| f(exist)
| r(exist,u6r1(exist)) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
r(exist,u6r1(exist)),
inference(unit_resolution,[status(thm)],[71,10,68]) ).
tff(73,plain,
^ [X2: $i,X1: $i] :
refl(
( ( ~ r(X1,X2)
| ~ e(X1)
| ~ s2least(X2)
| c(X2) )
<=> ( ~ r(X1,X2)
| ~ e(X1)
| ~ s2least(X2)
| c(X2) ) )),
inference(bind,[status(th)],]) ).
tff(74,plain,
( ! [X2: $i,X1: $i] :
( ~ r(X1,X2)
| ~ e(X1)
| ~ s2least(X2)
| c(X2) )
<=> ! [X2: $i,X1: $i] :
( ~ r(X1,X2)
| ~ e(X1)
| ~ s2least(X2)
| c(X2) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
( ! [X2: $i,X1: $i] :
( ~ r(X1,X2)
| ~ e(X1)
| ~ s2least(X2)
| c(X2) )
<=> ! [X2: $i,X1: $i] :
( ~ r(X1,X2)
| ~ e(X1)
| ~ s2least(X2)
| c(X2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
^ [X2: $i,X1: $i] :
trans(
monotonicity(
rewrite(
( ( c(X2)
| ~ e(X1)
| ~ r(X1,X2) )
<=> ( ~ r(X1,X2)
| ~ e(X1)
| c(X2) ) )),
( ( c(X2)
| ~ e(X1)
| ~ r(X1,X2)
| ~ s2least(X2) )
<=> ( ~ r(X1,X2)
| ~ e(X1)
| c(X2)
| ~ s2least(X2) ) )),
rewrite(
( ( ~ r(X1,X2)
| ~ e(X1)
| c(X2)
| ~ s2least(X2) )
<=> ( ~ r(X1,X2)
| ~ e(X1)
| ~ s2least(X2)
| c(X2) ) )),
( ( c(X2)
| ~ e(X1)
| ~ r(X1,X2)
| ~ s2least(X2) )
<=> ( ~ r(X1,X2)
| ~ e(X1)
| ~ s2least(X2)
| c(X2) ) )),
inference(bind,[status(th)],]) ).
tff(77,plain,
( ! [X2: $i,X1: $i] :
( c(X2)
| ~ e(X1)
| ~ r(X1,X2)
| ~ s2least(X2) )
<=> ! [X2: $i,X1: $i] :
( ~ r(X1,X2)
| ~ e(X1)
| ~ s2least(X2)
| c(X2) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,axiom,
! [X2: $i,X1: $i] :
( c(X2)
| ~ e(X1)
| ~ r(X1,X2)
| ~ s2least(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_16) ).
tff(79,plain,
! [X2: $i,X1: $i] :
( ~ r(X1,X2)
| ~ e(X1)
| ~ s2least(X2)
| c(X2) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [X2: $i,X1: $i] :
( ~ r(X1,X2)
| ~ e(X1)
| ~ s2least(X2)
| c(X2) ),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
! [X2: $i,X1: $i] :
( ~ r(X1,X2)
| ~ e(X1)
| ~ s2least(X2)
| c(X2) ),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [X2: $i,X1: $i] :
( ~ r(X1,X2)
| ~ e(X1)
| ~ s2least(X2)
| c(X2) ),
inference(modus_ponens,[status(thm)],[81,74]) ).
tff(83,plain,
( e(exist)
<=> e(exist) ),
inference(rewrite,[status(thm)],]) ).
tff(84,axiom,
e(exist),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
tff(85,plain,
e(exist),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
( ( ~ ! [X2: $i,X1: $i] :
( ~ r(X1,X2)
| ~ e(X1)
| ~ s2least(X2)
| c(X2) )
| ~ r(exist,u6r1(exist))
| ~ e(exist)
| ~ s2least(u6r1(exist))
| c(u6r1(exist)) )
<=> ( ~ ! [X2: $i,X1: $i] :
( ~ r(X1,X2)
| ~ e(X1)
| ~ s2least(X2)
| c(X2) )
| ~ r(exist,u6r1(exist))
| ~ e(exist)
| ~ s2least(u6r1(exist))
| c(u6r1(exist)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ~ ! [X2: $i,X1: $i] :
( ~ r(X1,X2)
| ~ e(X1)
| ~ s2least(X2)
| c(X2) )
| ~ r(exist,u6r1(exist))
| ~ e(exist)
| ~ s2least(u6r1(exist))
| c(u6r1(exist)) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
( ~ ! [X2: $i,X1: $i] :
( ~ r(X1,X2)
| ~ e(X1)
| ~ s2least(X2)
| c(X2) )
| ~ r(exist,u6r1(exist))
| ~ e(exist)
| ~ s2least(u6r1(exist))
| c(u6r1(exist)) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
( ~ s2least(u6r1(exist))
| c(u6r1(exist)) ),
inference(unit_resolution,[status(thm)],[88,85,82,72]) ).
tff(90,plain,
c(u6r1(exist)),
inference(unit_resolution,[status(thm)],[89,61]) ).
tff(91,plain,
^ [X1: $i] :
refl(
( ( t2least(X1)
| ~ c(X1) )
<=> ( t2least(X1)
| ~ c(X1) ) )),
inference(bind,[status(th)],]) ).
tff(92,plain,
( ! [X1: $i] :
( t2least(X1)
| ~ c(X1) )
<=> ! [X1: $i] :
( t2least(X1)
| ~ c(X1) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,plain,
( ! [X1: $i] :
( t2least(X1)
| ~ c(X1) )
<=> ! [X1: $i] :
( t2least(X1)
| ~ c(X1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,axiom,
! [X1: $i] :
( t2least(X1)
| ~ c(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
tff(95,plain,
! [X1: $i] :
( t2least(X1)
| ~ c(X1) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [X1: $i] :
( t2least(X1)
| ~ c(X1) ),
inference(skolemize,[status(sab)],[95]) ).
tff(97,plain,
! [X1: $i] :
( t2least(X1)
| ~ c(X1) ),
inference(modus_ponens,[status(thm)],[96,92]) ).
tff(98,plain,
( ( ~ ! [X1: $i] :
( t2least(X1)
| ~ c(X1) )
| t2least(u6r1(exist))
| ~ c(u6r1(exist)) )
<=> ( ~ ! [X1: $i] :
( t2least(X1)
| ~ c(X1) )
| t2least(u6r1(exist))
| ~ c(u6r1(exist)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
( ~ ! [X1: $i] :
( t2least(X1)
| ~ c(X1) )
| t2least(u6r1(exist))
| ~ c(u6r1(exist)) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
( ~ ! [X1: $i] :
( t2least(X1)
| ~ c(X1) )
| t2least(u6r1(exist))
| ~ c(u6r1(exist)) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
t2least(u6r1(exist)),
inference(unit_resolution,[status(thm)],[100,97,90]) ).
tff(102,plain,
^ [X1: $i] :
refl(
( ( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
<=> ( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ) )),
inference(bind,[status(th)],]) ).
tff(103,plain,
( ! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
<=> ! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,plain,
( ! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
<=> ! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,axiom,
! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
tff(106,plain,
! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ),
inference(skolemize,[status(sab)],[106]) ).
tff(108,plain,
! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
( ( ~ ! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
| ~ t2least(u6r1(exist))
| ~ equalish(u1r2(u6r1(exist)),u1r1(u6r1(exist))) )
<=> ( ~ ! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
| ~ t2least(u6r1(exist))
| ~ equalish(u1r2(u6r1(exist)),u1r1(u6r1(exist))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( ~ ! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
| ~ t2least(u6r1(exist))
| ~ equalish(u1r2(u6r1(exist)),u1r1(u6r1(exist))) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
( ~ ! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
| ~ t2least(u6r1(exist))
| ~ equalish(u1r2(u6r1(exist)),u1r1(u6r1(exist))) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
~ equalish(u1r2(u6r1(exist)),u1r1(u6r1(exist))),
inference(unit_resolution,[status(thm)],[111,108,101]) ).
tff(113,plain,
^ [X1: $i] :
refl(
( ( ~ t2least(X1)
| t(X1,u1r1(X1)) )
<=> ( ~ t2least(X1)
| t(X1,u1r1(X1)) ) )),
inference(bind,[status(th)],]) ).
tff(114,plain,
( ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) )
<=> ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) )
<=> ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(116,plain,
^ [X1: $i] :
rewrite(
( ( t(X1,u1r1(X1))
| ~ t2least(X1) )
<=> ( ~ t2least(X1)
| t(X1,u1r1(X1)) ) )),
inference(bind,[status(th)],]) ).
tff(117,plain,
( ! [X1: $i] :
( t(X1,u1r1(X1))
| ~ t2least(X1) )
<=> ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,axiom,
! [X1: $i] :
( t(X1,u1r1(X1))
| ~ t2least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
tff(119,plain,
! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) ),
inference(modus_ponens,[status(thm)],[119,115]) ).
tff(121,plain,
! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) ),
inference(skolemize,[status(sab)],[120]) ).
tff(122,plain,
! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) ),
inference(modus_ponens,[status(thm)],[121,114]) ).
tff(123,plain,
( ( ~ ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) )
| ~ t2least(u6r1(exist))
| t(u6r1(exist),u1r1(u6r1(exist))) )
<=> ( ~ ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) )
| ~ t2least(u6r1(exist))
| t(u6r1(exist),u1r1(u6r1(exist))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ~ ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) )
| ~ t2least(u6r1(exist))
| t(u6r1(exist),u1r1(u6r1(exist))) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
( ~ ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) )
| ~ t2least(u6r1(exist))
| t(u6r1(exist),u1r1(u6r1(exist))) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
t(u6r1(exist),u1r1(u6r1(exist))),
inference(unit_resolution,[status(thm)],[125,122,101]) ).
tff(127,plain,
^ [X1: $i] :
refl(
( ( ~ t2least(X1)
| t(X1,u1r2(X1)) )
<=> ( ~ t2least(X1)
| t(X1,u1r2(X1)) ) )),
inference(bind,[status(th)],]) ).
tff(128,plain,
( ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) )
<=> ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,plain,
( ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) )
<=> ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(130,plain,
^ [X1: $i] :
rewrite(
( ( t(X1,u1r2(X1))
| ~ t2least(X1) )
<=> ( ~ t2least(X1)
| t(X1,u1r2(X1)) ) )),
inference(bind,[status(th)],]) ).
tff(131,plain,
( ! [X1: $i] :
( t(X1,u1r2(X1))
| ~ t2least(X1) )
<=> ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,axiom,
! [X1: $i] :
( t(X1,u1r2(X1))
| ~ t2least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
tff(133,plain,
! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) ),
inference(modus_ponens,[status(thm)],[133,129]) ).
tff(135,plain,
! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) ),
inference(skolemize,[status(sab)],[134]) ).
tff(136,plain,
! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) ),
inference(modus_ponens,[status(thm)],[135,128]) ).
tff(137,plain,
( ( ~ ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) )
| ~ t2least(u6r1(exist))
| t(u6r1(exist),u1r2(u6r1(exist))) )
<=> ( ~ ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) )
| ~ t2least(u6r1(exist))
| t(u6r1(exist),u1r2(u6r1(exist))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(138,plain,
( ~ ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) )
| ~ t2least(u6r1(exist))
| t(u6r1(exist),u1r2(u6r1(exist))) ),
inference(quant_inst,[status(thm)],]) ).
tff(139,plain,
( ~ ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) )
| ~ t2least(u6r1(exist))
| t(u6r1(exist),u1r2(u6r1(exist))) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
t(u6r1(exist),u1r2(u6r1(exist))),
inference(unit_resolution,[status(thm)],[139,136,101]) ).
tff(141,plain,
^ [X3: $i,X1: $i] :
refl(
( ( ~ r(X1,X3)
| ~ e(X1)
| d(X3) )
<=> ( ~ r(X1,X3)
| ~ e(X1)
| d(X3) ) )),
inference(bind,[status(th)],]) ).
tff(142,plain,
( ! [X3: $i,X1: $i] :
( ~ r(X1,X3)
| ~ e(X1)
| d(X3) )
<=> ! [X3: $i,X1: $i] :
( ~ r(X1,X3)
| ~ e(X1)
| d(X3) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,plain,
( ! [X3: $i,X1: $i] :
( ~ r(X1,X3)
| ~ e(X1)
| d(X3) )
<=> ! [X3: $i,X1: $i] :
( ~ r(X1,X3)
| ~ e(X1)
| d(X3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(144,plain,
^ [X3: $i,X1: $i] :
rewrite(
( ( d(X3)
| ~ e(X1)
| ~ r(X1,X3) )
<=> ( ~ r(X1,X3)
| ~ e(X1)
| d(X3) ) )),
inference(bind,[status(th)],]) ).
tff(145,plain,
( ! [X3: $i,X1: $i] :
( d(X3)
| ~ e(X1)
| ~ r(X1,X3) )
<=> ! [X3: $i,X1: $i] :
( ~ r(X1,X3)
| ~ e(X1)
| d(X3) ) ),
inference(quant_intro,[status(thm)],[144]) ).
tff(146,axiom,
! [X3: $i,X1: $i] :
( d(X3)
| ~ e(X1)
| ~ r(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15) ).
tff(147,plain,
! [X3: $i,X1: $i] :
( ~ r(X1,X3)
| ~ e(X1)
| d(X3) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
! [X3: $i,X1: $i] :
( ~ r(X1,X3)
| ~ e(X1)
| d(X3) ),
inference(modus_ponens,[status(thm)],[147,143]) ).
tff(149,plain,
! [X3: $i,X1: $i] :
( ~ r(X1,X3)
| ~ e(X1)
| d(X3) ),
inference(skolemize,[status(sab)],[148]) ).
tff(150,plain,
! [X3: $i,X1: $i] :
( ~ r(X1,X3)
| ~ e(X1)
| d(X3) ),
inference(modus_ponens,[status(thm)],[149,142]) ).
tff(151,plain,
( ( ~ ! [X3: $i,X1: $i] :
( ~ r(X1,X3)
| ~ e(X1)
| d(X3) )
| ~ r(exist,u6r1(exist))
| ~ e(exist)
| d(u6r1(exist)) )
<=> ( ~ ! [X3: $i,X1: $i] :
( ~ r(X1,X3)
| ~ e(X1)
| d(X3) )
| ~ r(exist,u6r1(exist))
| ~ e(exist)
| d(u6r1(exist)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(152,plain,
( ~ ! [X3: $i,X1: $i] :
( ~ r(X1,X3)
| ~ e(X1)
| d(X3) )
| ~ r(exist,u6r1(exist))
| ~ e(exist)
| d(u6r1(exist)) ),
inference(quant_inst,[status(thm)],]) ).
tff(153,plain,
( ~ ! [X3: $i,X1: $i] :
( ~ r(X1,X3)
| ~ e(X1)
| d(X3) )
| ~ r(exist,u6r1(exist))
| ~ e(exist)
| d(u6r1(exist)) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
d(u6r1(exist)),
inference(unit_resolution,[status(thm)],[153,85,150,72]) ).
tff(155,plain,
^ [X1: $i] :
refl(
( ( t1most(X1)
| ~ d(X1) )
<=> ( t1most(X1)
| ~ d(X1) ) )),
inference(bind,[status(th)],]) ).
tff(156,plain,
( ! [X1: $i] :
( t1most(X1)
| ~ d(X1) )
<=> ! [X1: $i] :
( t1most(X1)
| ~ d(X1) ) ),
inference(quant_intro,[status(thm)],[155]) ).
tff(157,plain,
( ! [X1: $i] :
( t1most(X1)
| ~ d(X1) )
<=> ! [X1: $i] :
( t1most(X1)
| ~ d(X1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(158,axiom,
! [X1: $i] :
( t1most(X1)
| ~ d(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
tff(159,plain,
! [X1: $i] :
( t1most(X1)
| ~ d(X1) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
! [X1: $i] :
( t1most(X1)
| ~ d(X1) ),
inference(skolemize,[status(sab)],[159]) ).
tff(161,plain,
! [X1: $i] :
( t1most(X1)
| ~ d(X1) ),
inference(modus_ponens,[status(thm)],[160,156]) ).
tff(162,plain,
( ( ~ ! [X1: $i] :
( t1most(X1)
| ~ d(X1) )
| t1most(u6r1(exist))
| ~ d(u6r1(exist)) )
<=> ( ~ ! [X1: $i] :
( t1most(X1)
| ~ d(X1) )
| t1most(u6r1(exist))
| ~ d(u6r1(exist)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(163,plain,
( ~ ! [X1: $i] :
( t1most(X1)
| ~ d(X1) )
| t1most(u6r1(exist))
| ~ d(u6r1(exist)) ),
inference(quant_inst,[status(thm)],]) ).
tff(164,plain,
( ~ ! [X1: $i] :
( t1most(X1)
| ~ d(X1) )
| t1most(u6r1(exist))
| ~ d(u6r1(exist)) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
t1most(u6r1(exist)),
inference(unit_resolution,[status(thm)],[164,161,154]) ).
tff(166,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(
( ( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) )
<=> ( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) ) )),
inference(bind,[status(th)],]) ).
tff(167,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) ) ),
inference(quant_intro,[status(thm)],[166]) ).
tff(168,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(169,plain,
^ [X3: $i,X2: $i,X1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( equalish(X3,X2)
| ~ t1most(X1) )
<=> ( ~ t1most(X1)
| equalish(X3,X2) ) )),
( ( equalish(X3,X2)
| ~ t1most(X1)
| ~ t(X1,X3) )
<=> ( ~ t1most(X1)
| equalish(X3,X2)
| ~ t(X1,X3) ) )),
rewrite(
( ( ~ t1most(X1)
| equalish(X3,X2)
| ~ t(X1,X3) )
<=> ( ~ t1most(X1)
| ~ t(X1,X3)
| equalish(X3,X2) ) )),
( ( equalish(X3,X2)
| ~ t1most(X1)
| ~ t(X1,X3) )
<=> ( ~ t1most(X1)
| ~ t(X1,X3)
| equalish(X3,X2) ) )),
( ( equalish(X3,X2)
| ~ t1most(X1)
| ~ t(X1,X3)
| ~ t(X1,X2) )
<=> ( ~ t1most(X1)
| ~ t(X1,X3)
| equalish(X3,X2)
| ~ t(X1,X2) ) )),
rewrite(
( ( ~ t1most(X1)
| ~ t(X1,X3)
| equalish(X3,X2)
| ~ t(X1,X2) )
<=> ( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) ) )),
( ( equalish(X3,X2)
| ~ t1most(X1)
| ~ t(X1,X3)
| ~ t(X1,X2) )
<=> ( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) ) )),
inference(bind,[status(th)],]) ).
tff(170,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( equalish(X3,X2)
| ~ t1most(X1)
| ~ t(X1,X3)
| ~ t(X1,X2) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) ) ),
inference(quant_intro,[status(thm)],[169]) ).
tff(171,axiom,
! [X3: $i,X2: $i,X1: $i] :
( equalish(X3,X2)
| ~ t1most(X1)
| ~ t(X1,X3)
| ~ t(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).
tff(172,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) ),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) ),
inference(modus_ponens,[status(thm)],[172,168]) ).
tff(174,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) ),
inference(skolemize,[status(sab)],[173]) ).
tff(175,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) ),
inference(modus_ponens,[status(thm)],[174,167]) ).
tff(176,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) )
| ~ t1most(u6r1(exist))
| ~ t(u6r1(exist),u1r1(u6r1(exist)))
| ~ t(u6r1(exist),u1r2(u6r1(exist)))
| equalish(u1r2(u6r1(exist)),u1r1(u6r1(exist))) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) )
| ~ t1most(u6r1(exist))
| ~ t(u6r1(exist),u1r1(u6r1(exist)))
| ~ t(u6r1(exist),u1r2(u6r1(exist)))
| equalish(u1r2(u6r1(exist)),u1r1(u6r1(exist))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(177,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) )
| ~ t1most(u6r1(exist))
| ~ t(u6r1(exist),u1r1(u6r1(exist)))
| ~ t(u6r1(exist),u1r2(u6r1(exist)))
| equalish(u1r2(u6r1(exist)),u1r1(u6r1(exist))) ),
inference(quant_inst,[status(thm)],]) ).
tff(178,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) )
| ~ t1most(u6r1(exist))
| ~ t(u6r1(exist),u1r1(u6r1(exist)))
| ~ t(u6r1(exist),u1r2(u6r1(exist)))
| equalish(u1r2(u6r1(exist)),u1r1(u6r1(exist))) ),
inference(modus_ponens,[status(thm)],[177,176]) ).
tff(179,plain,
$false,
inference(unit_resolution,[status(thm)],[178,175,165,140,126,112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS013-1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n027.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 Sep 1 09:31:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------