%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS015-1 : TPTP v9.0.0. Released v2.0.0.
% 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 05:13:12 AM UTC 2025
% Result : Unsatisfiable 0.14s 0.39s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 59
% Syntax : Number of formulae : 134 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 639 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 895 ( 425 ~; 406 |; 0 &)
% ( 64 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 35 ( 35 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 243 ( 216 !; 0 ?; 243 :)
% Comments :
%------------------------------------------------------------------------------
tff(t1most_type,type,
t1most: $i > $o ).
tff(u4r4_type,type,
u4r4: $i > $i ).
tff(exist_type,type,
exist: $i ).
tff(d_type,type,
d: $i > $o ).
tff(s_type,type,
s: ( $i * $i ) > $o ).
tff(r_type,type,
r: ( $i * $i ) > $o ).
tff(e_type,type,
e: $i > $o ).
tff(equalish_type,type,
equalish: ( $i * $i ) > $o ).
tff(u1r1_type,type,
u1r1: $i > $i ).
tff(u1r2_type,type,
u1r2: $i > $i ).
tff(t2least_type,type,
t2least: $i > $o ).
tff(c_type,type,
c: $i > $o ).
tff(t_type,type,
t: ( $i * $i ) > $o ).
tff(1,plain,
^ [X1: $i] :
refl(( ( ~ e(X1)
| r(X1,u4r4(X1)) )
<=> ( ~ e(X1)
| r(X1,u4r4(X1)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X1: $i] :
( ~ e(X1)
| r(X1,u4r4(X1)) )
<=> ! [X1: $i] :
( ~ e(X1)
| r(X1,u4r4(X1)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X1: $i] :
( ~ e(X1)
| r(X1,u4r4(X1)) )
<=> ! [X1: $i] :
( ~ e(X1)
| r(X1,u4r4(X1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [X1: $i] :
rewrite(( ( r(X1,u4r4(X1))
| ~ e(X1) )
<=> ( ~ e(X1)
| r(X1,u4r4(X1)) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X1: $i] :
( r(X1,u4r4(X1))
| ~ e(X1) )
<=> ! [X1: $i] :
( ~ e(X1)
| r(X1,u4r4(X1)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [X1: $i] :
( r(X1,u4r4(X1))
| ~ e(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_14) ).
tff(7,plain,
! [X1: $i] :
( ~ e(X1)
| r(X1,u4r4(X1)) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X1: $i] :
( ~ e(X1)
| r(X1,u4r4(X1)) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [X1: $i] :
( ~ e(X1)
| r(X1,u4r4(X1)) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X1: $i] :
( ~ e(X1)
| r(X1,u4r4(X1)) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( e(exist)
<=> e(exist) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
e(exist),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
tff(13,plain,
e(exist),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [X1: $i] :
( ~ e(X1)
| r(X1,u4r4(X1)) )
| ~ e(exist)
| r(exist,u4r4(exist)) )
<=> ( ~ ! [X1: $i] :
( ~ e(X1)
| r(X1,u4r4(X1)) )
| ~ e(exist)
| r(exist,u4r4(exist)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [X1: $i] :
( ~ e(X1)
| r(X1,u4r4(X1)) )
| ~ e(exist)
| r(exist,u4r4(exist)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [X1: $i] :
( ~ e(X1)
| r(X1,u4r4(X1)) )
| ~ e(exist)
| r(exist,u4r4(exist)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
r(exist,u4r4(exist)),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [X4: $i,X1: $i] :
refl(( ( ~ e(X1)
| ~ r(X1,X4)
| s(X1,X4) )
<=> ( ~ e(X1)
| ~ r(X1,X4)
| s(X1,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [X4: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X4)
| s(X1,X4) )
<=> ! [X4: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X4)
| s(X1,X4) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [X4: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X4)
| s(X1,X4) )
<=> ! [X4: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X4)
| s(X1,X4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [X4: $i,X1: $i] :
trans(monotonicity(rewrite(( ( s(X1,X4)
| ~ e(X1) )
<=> ( ~ e(X1)
| s(X1,X4) ) )),
( ( s(X1,X4)
| ~ e(X1)
| ~ r(X1,X4) )
<=> ( ~ e(X1)
| s(X1,X4)
| ~ r(X1,X4) ) )),
rewrite(( ( ~ e(X1)
| s(X1,X4)
| ~ r(X1,X4) )
<=> ( ~ e(X1)
| ~ r(X1,X4)
| s(X1,X4) ) )),
( ( s(X1,X4)
| ~ e(X1)
| ~ r(X1,X4) )
<=> ( ~ e(X1)
| ~ r(X1,X4)
| s(X1,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [X4: $i,X1: $i] :
( s(X1,X4)
| ~ e(X1)
| ~ r(X1,X4) )
<=> ! [X4: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X4)
| s(X1,X4) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [X4: $i,X1: $i] :
( s(X1,X4)
| ~ e(X1)
| ~ r(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15) ).
tff(24,plain,
! [X4: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X4)
| s(X1,X4) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [X4: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X4)
| s(X1,X4) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [X4: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X4)
| s(X1,X4) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X4: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X4)
| s(X1,X4) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [X4: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X4)
| s(X1,X4) )
| ~ e(exist)
| ~ r(exist,u4r4(exist))
| s(exist,u4r4(exist)) )
<=> ( ~ ! [X4: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X4)
| s(X1,X4) )
| ~ e(exist)
| ~ r(exist,u4r4(exist))
| s(exist,u4r4(exist)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [X4: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X4)
| s(X1,X4) )
| ~ e(exist)
| ~ r(exist,u4r4(exist))
| s(exist,u4r4(exist)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [X4: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X4)
| s(X1,X4) )
| ~ e(exist)
| ~ r(exist,u4r4(exist))
| s(exist,u4r4(exist)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
s(exist,u4r4(exist)),
inference(unit_resolution,[status(thm)],[30,13,27,17]) ).
tff(32,plain,
^ [X3: $i,X1: $i] :
refl(( ( ~ e(X1)
| ~ s(X1,X3)
| d(X3) )
<=> ( ~ e(X1)
| ~ s(X1,X3)
| d(X3) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [X3: $i,X1: $i] :
( ~ e(X1)
| ~ s(X1,X3)
| d(X3) )
<=> ! [X3: $i,X1: $i] :
( ~ e(X1)
| ~ s(X1,X3)
| d(X3) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X3: $i,X1: $i] :
( ~ e(X1)
| ~ s(X1,X3)
| d(X3) )
<=> ! [X3: $i,X1: $i] :
( ~ e(X1)
| ~ s(X1,X3)
| d(X3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [X3: $i,X1: $i] :
rewrite(( ( d(X3)
| ~ e(X1)
| ~ s(X1,X3) )
<=> ( ~ e(X1)
| ~ s(X1,X3)
| d(X3) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [X3: $i,X1: $i] :
( d(X3)
| ~ e(X1)
| ~ s(X1,X3) )
<=> ! [X3: $i,X1: $i] :
( ~ e(X1)
| ~ s(X1,X3)
| d(X3) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [X3: $i,X1: $i] :
( d(X3)
| ~ e(X1)
| ~ s(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_17) ).
tff(38,plain,
! [X3: $i,X1: $i] :
( ~ e(X1)
| ~ s(X1,X3)
| d(X3) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [X3: $i,X1: $i] :
( ~ e(X1)
| ~ s(X1,X3)
| d(X3) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [X3: $i,X1: $i] :
( ~ e(X1)
| ~ s(X1,X3)
| d(X3) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [X3: $i,X1: $i] :
( ~ e(X1)
| ~ s(X1,X3)
| d(X3) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [X3: $i,X1: $i] :
( ~ e(X1)
| ~ s(X1,X3)
| d(X3) )
| ~ e(exist)
| ~ s(exist,u4r4(exist))
| d(u4r4(exist)) )
<=> ( ~ ! [X3: $i,X1: $i] :
( ~ e(X1)
| ~ s(X1,X3)
| d(X3) )
| ~ e(exist)
| ~ s(exist,u4r4(exist))
| d(u4r4(exist)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [X3: $i,X1: $i] :
( ~ e(X1)
| ~ s(X1,X3)
| d(X3) )
| ~ e(exist)
| ~ s(exist,u4r4(exist))
| d(u4r4(exist)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [X3: $i,X1: $i] :
( ~ e(X1)
| ~ s(X1,X3)
| d(X3) )
| ~ e(exist)
| ~ s(exist,u4r4(exist))
| d(u4r4(exist)) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
d(u4r4(exist)),
inference(unit_resolution,[status(thm)],[44,13,41,31]) ).
tff(46,plain,
^ [X1: $i] :
refl(( ( t1most(X1)
| ~ d(X1) )
<=> ( t1most(X1)
| ~ d(X1) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [X1: $i] :
( t1most(X1)
| ~ d(X1) )
<=> ! [X1: $i] :
( t1most(X1)
| ~ d(X1) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [X1: $i] :
( t1most(X1)
| ~ d(X1) )
<=> ! [X1: $i] :
( t1most(X1)
| ~ d(X1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
! [X1: $i] :
( t1most(X1)
| ~ d(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
tff(50,plain,
! [X1: $i] :
( t1most(X1)
| ~ d(X1) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [X1: $i] :
( t1most(X1)
| ~ d(X1) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [X1: $i] :
( t1most(X1)
| ~ d(X1) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ( ~ ! [X1: $i] :
( t1most(X1)
| ~ d(X1) )
| t1most(u4r4(exist))
| ~ d(u4r4(exist)) )
<=> ( ~ ! [X1: $i] :
( t1most(X1)
| ~ d(X1) )
| t1most(u4r4(exist))
| ~ d(u4r4(exist)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [X1: $i] :
( t1most(X1)
| ~ d(X1) )
| t1most(u4r4(exist))
| ~ d(u4r4(exist)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [X1: $i] :
( t1most(X1)
| ~ d(X1) )
| t1most(u4r4(exist))
| ~ d(u4r4(exist)) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
t1most(u4r4(exist)),
inference(unit_resolution,[status(thm)],[55,52,45]) ).
tff(57,plain,
^ [X2: $i,X1: $i] :
refl(( ( ~ e(X1)
| ~ r(X1,X2)
| c(X2) )
<=> ( ~ e(X1)
| ~ r(X1,X2)
| c(X2) ) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X2)
| c(X2) )
<=> ! [X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X2)
| c(X2) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X2)
| c(X2) )
<=> ! [X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X2)
| c(X2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
^ [X2: $i,X1: $i] :
rewrite(( ( c(X2)
| ~ e(X1)
| ~ r(X1,X2) )
<=> ( ~ e(X1)
| ~ r(X1,X2)
| c(X2) ) )),
inference(bind,[status(th)],[]) ).
tff(61,plain,
( ! [X2: $i,X1: $i] :
( c(X2)
| ~ e(X1)
| ~ r(X1,X2) )
<=> ! [X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X2)
| c(X2) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,axiom,
! [X2: $i,X1: $i] :
( c(X2)
| ~ e(X1)
| ~ r(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_18) ).
tff(63,plain,
! [X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X2)
| c(X2) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X2)
| c(X2) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
! [X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X2)
| c(X2) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X2)
| c(X2) ),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
( ( ~ ! [X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X2)
| c(X2) )
| ~ e(exist)
| ~ r(exist,u4r4(exist))
| c(u4r4(exist)) )
<=> ( ~ ! [X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X2)
| c(X2) )
| ~ e(exist)
| ~ r(exist,u4r4(exist))
| c(u4r4(exist)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X2)
| c(X2) )
| ~ e(exist)
| ~ r(exist,u4r4(exist))
| c(u4r4(exist)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [X2: $i,X1: $i] :
( ~ e(X1)
| ~ r(X1,X2)
| c(X2) )
| ~ e(exist)
| ~ r(exist,u4r4(exist))
| c(u4r4(exist)) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
c(u4r4(exist)),
inference(unit_resolution,[status(thm)],[69,13,66,17]) ).
tff(71,plain,
^ [X1: $i] :
refl(( ( t2least(X1)
| ~ c(X1) )
<=> ( t2least(X1)
| ~ c(X1) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [X1: $i] :
( t2least(X1)
| ~ c(X1) )
<=> ! [X1: $i] :
( t2least(X1)
| ~ c(X1) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [X1: $i] :
( t2least(X1)
| ~ c(X1) )
<=> ! [X1: $i] :
( t2least(X1)
| ~ c(X1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,axiom,
! [X1: $i] :
( t2least(X1)
| ~ c(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
tff(75,plain,
! [X1: $i] :
( t2least(X1)
| ~ c(X1) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [X1: $i] :
( t2least(X1)
| ~ c(X1) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [X1: $i] :
( t2least(X1)
| ~ c(X1) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
( ( ~ ! [X1: $i] :
( t2least(X1)
| ~ c(X1) )
| t2least(u4r4(exist))
| ~ c(u4r4(exist)) )
<=> ( ~ ! [X1: $i] :
( t2least(X1)
| ~ c(X1) )
| t2least(u4r4(exist))
| ~ c(u4r4(exist)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
( ~ ! [X1: $i] :
( t2least(X1)
| ~ c(X1) )
| t2least(u4r4(exist))
| ~ c(u4r4(exist)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
( ~ ! [X1: $i] :
( t2least(X1)
| ~ c(X1) )
| t2least(u4r4(exist))
| ~ c(u4r4(exist)) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
t2least(u4r4(exist)),
inference(unit_resolution,[status(thm)],[80,77,70]) ).
tff(82,plain,
^ [X1: $i] :
refl(( ( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
<=> ( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ) )),
inference(bind,[status(th)],[]) ).
tff(83,plain,
( ! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
<=> ! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
<=> ! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,axiom,
! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
tff(86,plain,
! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ),
inference(skolemize,[status(sab)],[86]) ).
tff(88,plain,
! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
( ( ~ ! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
| ~ t2least(u4r4(exist))
| ~ equalish(u1r2(u4r4(exist)),u1r1(u4r4(exist))) )
<=> ( ~ ! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
| ~ t2least(u4r4(exist))
| ~ equalish(u1r2(u4r4(exist)),u1r1(u4r4(exist))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,plain,
( ~ ! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
| ~ t2least(u4r4(exist))
| ~ equalish(u1r2(u4r4(exist)),u1r1(u4r4(exist))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
( ~ ! [X1: $i] :
( ~ t2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) )
| ~ t2least(u4r4(exist))
| ~ equalish(u1r2(u4r4(exist)),u1r1(u4r4(exist))) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
~ equalish(u1r2(u4r4(exist)),u1r1(u4r4(exist))),
inference(unit_resolution,[status(thm)],[91,88,81]) ).
tff(93,plain,
^ [X1: $i] :
refl(( ( ~ t2least(X1)
| t(X1,u1r1(X1)) )
<=> ( ~ t2least(X1)
| t(X1,u1r1(X1)) ) )),
inference(bind,[status(th)],[]) ).
tff(94,plain,
( ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) )
<=> ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,plain,
( ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) )
<=> ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
^ [X1: $i] :
rewrite(( ( t(X1,u1r1(X1))
| ~ t2least(X1) )
<=> ( ~ t2least(X1)
| t(X1,u1r1(X1)) ) )),
inference(bind,[status(th)],[]) ).
tff(97,plain,
( ! [X1: $i] :
( t(X1,u1r1(X1))
| ~ t2least(X1) )
<=> ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,axiom,
! [X1: $i] :
( t(X1,u1r1(X1))
| ~ t2least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
tff(99,plain,
! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) ),
inference(modus_ponens,[status(thm)],[101,94]) ).
tff(103,plain,
( ( ~ ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) )
| ~ t2least(u4r4(exist))
| t(u4r4(exist),u1r1(u4r4(exist))) )
<=> ( ~ ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) )
| ~ t2least(u4r4(exist))
| t(u4r4(exist),u1r1(u4r4(exist))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
( ~ ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) )
| ~ t2least(u4r4(exist))
| t(u4r4(exist),u1r1(u4r4(exist))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
( ~ ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) )
| ~ t2least(u4r4(exist))
| t(u4r4(exist),u1r1(u4r4(exist))) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
t(u4r4(exist),u1r1(u4r4(exist))),
inference(unit_resolution,[status(thm)],[105,102,81]) ).
tff(107,plain,
^ [X1: $i] :
refl(( ( ~ t2least(X1)
| t(X1,u1r2(X1)) )
<=> ( ~ t2least(X1)
| t(X1,u1r2(X1)) ) )),
inference(bind,[status(th)],[]) ).
tff(108,plain,
( ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) )
<=> ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) ) ),
inference(quant_intro,[status(thm)],[107]) ).
tff(109,plain,
( ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) )
<=> ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
^ [X1: $i] :
rewrite(( ( t(X1,u1r2(X1))
| ~ t2least(X1) )
<=> ( ~ t2least(X1)
| t(X1,u1r2(X1)) ) )),
inference(bind,[status(th)],[]) ).
tff(111,plain,
( ! [X1: $i] :
( t(X1,u1r2(X1))
| ~ t2least(X1) )
<=> ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) ) ),
inference(quant_intro,[status(thm)],[110]) ).
tff(112,axiom,
! [X1: $i] :
( t(X1,u1r2(X1))
| ~ t2least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
tff(113,plain,
! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) ),
inference(modus_ponens,[status(thm)],[113,109]) ).
tff(115,plain,
! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) ),
inference(skolemize,[status(sab)],[114]) ).
tff(116,plain,
! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) ),
inference(modus_ponens,[status(thm)],[115,108]) ).
tff(117,plain,
( ( ~ ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) )
| ~ t2least(u4r4(exist))
| t(u4r4(exist),u1r2(u4r4(exist))) )
<=> ( ~ ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) )
| ~ t2least(u4r4(exist))
| t(u4r4(exist),u1r2(u4r4(exist))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,plain,
( ~ ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) )
| ~ t2least(u4r4(exist))
| t(u4r4(exist),u1r2(u4r4(exist))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(119,plain,
( ~ ! [X1: $i] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) )
| ~ t2least(u4r4(exist))
| t(u4r4(exist),u1r2(u4r4(exist))) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
t(u4r4(exist),u1r2(u4r4(exist))),
inference(unit_resolution,[status(thm)],[119,116,81]) ).
tff(121,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(122,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)],[121]) ).
tff(123,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(124,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(125,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)],[124]) ).
tff(126,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_10) ).
tff(127,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) ),
inference(modus_ponens,[status(thm)],[127,123]) ).
tff(129,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) ),
inference(skolemize,[status(sab)],[128]) ).
tff(130,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) ),
inference(modus_ponens,[status(thm)],[129,122]) ).
tff(131,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) )
| ~ t1most(u4r4(exist))
| ~ t(u4r4(exist),u1r1(u4r4(exist)))
| ~ t(u4r4(exist),u1r2(u4r4(exist)))
| equalish(u1r2(u4r4(exist)),u1r1(u4r4(exist))) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) )
| ~ t1most(u4r4(exist))
| ~ t(u4r4(exist),u1r1(u4r4(exist)))
| ~ t(u4r4(exist),u1r2(u4r4(exist)))
| equalish(u1r2(u4r4(exist)),u1r1(u4r4(exist))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(132,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) )
| ~ t1most(u4r4(exist))
| ~ t(u4r4(exist),u1r1(u4r4(exist)))
| ~ t(u4r4(exist),u1r2(u4r4(exist)))
| equalish(u1r2(u4r4(exist)),u1r1(u4r4(exist))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(133,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ t1most(X1)
| ~ t(X1,X2)
| ~ t(X1,X3)
| equalish(X3,X2) )
| ~ t1most(u4r4(exist))
| ~ t(u4r4(exist),u1r1(u4r4(exist)))
| ~ t(u4r4(exist),u1r2(u4r4(exist)))
| equalish(u1r2(u4r4(exist)),u1r1(u4r4(exist))) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
$false,
inference(unit_resolution,[status(thm)],[133,130,120,106,92,56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KRS015-1 : TPTP v9.0.0. Released v2.0.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Jun 19 19:11:16 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.39 % SZS status Unsatisfiable
% 0.14/0.39 % SZS output start Proof
% See solution above
% 0.22/0.41 % E exiting
%------------------------------------------------------------------------------