%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV061-1 : TPTP v9.0.0. Bugfixed v5.5.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:10:37 AM UTC 2025
% Result : Unsatisfiable 24.62s 24.76s
% Output : Proof 27.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 51
% Syntax : Number of formulae : 112 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 694 ( 0 equ)
% Maximal formula atoms : 18 ( 6 avg)
% Number of connectives : 1036 ( 495 ~; 479 |; 0 &)
% ( 62 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 41 ( 41 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 3 prp; 0-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 372 ( 339 !; 0 ?; 372 :)
% Comments :
%------------------------------------------------------------------------------
tff(esk17873_3_type,type,
esk17873_3: ( $i * $i * $i ) > $o ).
tff(true_type,type,
true: $i ).
tff(esk17931_3_type,type,
esk17931_3: ( $i * $i * $i ) > $o ).
tff(esk28023_3_type,type,
esk28023_3: ( $i * $i * $i ) > $o ).
tff(p_type,type,
p: $i > $o ).
tff(esk2_0_type,type,
esk2_0: $o ).
tff(esk19870_3_type,type,
esk19870_3: ( $i * $i * $i ) > $o ).
tff(esk16545_3_type,type,
esk16545_3: ( $i * $i * $i ) > $o ).
tff(esk16603_3_type,type,
esk16603_3: ( $i * $i * $i ) > $o ).
tff(esk27893_3_type,type,
esk27893_3: ( $i * $i * $i ) > $o ).
tff(esk1_0_type,type,
esk1_0: $o ).
tff(1,plain,
( p(true)
<=> p(true) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
p(true),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_true) ).
tff(3,plain,
p(true),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(( ( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) )
<=> ( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [X3: $i,X2: $i,X1: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ p(X3)
| ~ p(X1) )
<=> ( ~ p(X1)
| ~ p(X3) ) )),
( ( ~ p(X3)
| ~ p(X1)
| ~ esk2_0 )
<=> ( ~ p(X1)
| ~ p(X3)
| ~ esk2_0 ) )),
rewrite(( ( ~ p(X1)
| ~ p(X3)
| ~ esk2_0 )
<=> ( ~ p(X1)
| ~ p(X3)
| ~ esk2_0 ) )),
( ( ~ p(X3)
| ~ p(X1)
| ~ esk2_0 )
<=> ( ~ p(X1)
| ~ p(X3)
| ~ esk2_0 ) )),
( ( ~ p(X3)
| ~ p(X1)
| ~ esk2_0
| esk28023_3(X1,X2,X3) )
<=> ( ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) ) )),
rewrite(( ( ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) )
<=> ( ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) ) )),
( ( ~ p(X3)
| ~ p(X1)
| ~ esk2_0
| esk28023_3(X1,X2,X3) )
<=> ( ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) ) )),
( ( ~ p(X3)
| ~ p(X1)
| ~ esk2_0
| esk28023_3(X1,X2,X3)
| ~ p(X2) )
<=> ( ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3)
| ~ p(X2) ) )),
rewrite(( ( ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3)
| ~ p(X2) )
<=> ( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) ) )),
( ( ~ p(X3)
| ~ p(X1)
| ~ esk2_0
| esk28023_3(X1,X2,X3)
| ~ p(X2) )
<=> ( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ esk2_0
| esk28023_3(X1,X2,X3)
| ~ p(X2) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ esk2_0
| esk28023_3(X1,X2,X3)
| ~ p(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_0_60042) ).
tff(10,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( esk2_0
<=> esk2_0 ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
esk2_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_0_21820) ).
tff(16,plain,
esk2_0,
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) )
| ~ esk2_0
| ~ p(true)
| esk28023_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) )
| ~ esk2_0
| ~ p(true)
| esk28023_3(true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( ~ p(true)
| ~ p(true)
| ~ p(true)
| ~ esk2_0
| esk28023_3(true,true,true) )
<=> ( ~ esk2_0
| ~ p(true)
| esk28023_3(true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) )
| ~ p(true)
| ~ p(true)
| ~ p(true)
| ~ esk2_0
| esk28023_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) )
| ~ esk2_0
| ~ p(true)
| esk28023_3(true,true,true) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) )
| ~ p(true)
| ~ p(true)
| ~ p(true)
| ~ esk2_0
| esk28023_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) )
| ~ esk2_0
| ~ p(true)
| esk28023_3(true,true,true) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) )
| ~ p(true)
| ~ p(true)
| ~ p(true)
| ~ esk2_0
| esk28023_3(true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk28023_3(X1,X2,X3) )
| ~ esk2_0
| ~ p(true)
| esk28023_3(true,true,true) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
esk28023_3(true,true,true),
inference(unit_resolution,[status(thm)],[22,16,13,3]) ).
tff(24,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(( ( ~ esk28023_3(X1,X2,X3)
| esk17931_3(X1,X2,X3) )
<=> ( ~ esk28023_3(X1,X2,X3)
| esk17931_3(X1,X2,X3) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ esk28023_3(X1,X2,X3)
| esk17931_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk28023_3(X1,X2,X3)
| esk17931_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ esk28023_3(X1,X2,X3)
| esk17931_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk28023_3(X1,X2,X3)
| esk17931_3(X1,X2,X3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk28023_3(X1,X2,X3)
| esk17931_3(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_0_18185) ).
tff(28,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk28023_3(X1,X2,X3)
| esk17931_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk28023_3(X1,X2,X3)
| esk17931_3(X1,X2,X3) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk28023_3(X1,X2,X3)
| esk17931_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk28023_3(X1,X2,X3)
| esk17931_3(X1,X2,X3) )
| ~ esk28023_3(true,true,true)
| esk17931_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk28023_3(X1,X2,X3)
| esk17931_3(X1,X2,X3) )
| ~ esk28023_3(true,true,true)
| esk17931_3(true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk28023_3(X1,X2,X3)
| esk17931_3(X1,X2,X3) )
| ~ esk28023_3(true,true,true)
| esk17931_3(true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk28023_3(X1,X2,X3)
| esk17931_3(X1,X2,X3) )
| ~ esk28023_3(true,true,true)
| esk17931_3(true,true,true) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
esk17931_3(true,true,true),
inference(unit_resolution,[status(thm)],[33,30,23]) ).
tff(35,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(( ( esk17873_3(X1,X2,X3)
| ~ esk17931_3(X1,X2,X3) )
<=> ( esk17873_3(X1,X2,X3)
| ~ esk17931_3(X1,X2,X3) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( esk17873_3(X1,X2,X3)
| ~ esk17931_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( esk17873_3(X1,X2,X3)
| ~ esk17931_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( esk17873_3(X1,X2,X3)
| ~ esk17931_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( esk17873_3(X1,X2,X3)
| ~ esk17931_3(X1,X2,X3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
! [X3: $i,X2: $i,X1: $i] :
( esk17873_3(X1,X2,X3)
| ~ esk17931_3(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_0_7284) ).
tff(39,plain,
! [X3: $i,X2: $i,X1: $i] :
( esk17873_3(X1,X2,X3)
| ~ esk17931_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [X3: $i,X2: $i,X1: $i] :
( esk17873_3(X1,X2,X3)
| ~ esk17931_3(X1,X2,X3) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [X3: $i,X2: $i,X1: $i] :
( esk17873_3(X1,X2,X3)
| ~ esk17931_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( esk17873_3(X1,X2,X3)
| ~ esk17931_3(X1,X2,X3) )
| esk17873_3(true,true,true)
| ~ esk17931_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( esk17873_3(X1,X2,X3)
| ~ esk17931_3(X1,X2,X3) )
| esk17873_3(true,true,true)
| ~ esk17931_3(true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( esk17873_3(X1,X2,X3)
| ~ esk17931_3(X1,X2,X3) )
| esk17873_3(true,true,true)
| ~ esk17931_3(true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( esk17873_3(X1,X2,X3)
| ~ esk17931_3(X1,X2,X3) )
| esk17873_3(true,true,true)
| ~ esk17931_3(true,true,true) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
esk17873_3(true,true,true),
inference(unit_resolution,[status(thm)],[44,41,34]) ).
tff(46,plain,
( ~ esk1_0
<=> ~ esk1_0 ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
~ esk1_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_0_49597) ).
tff(48,plain,
~ esk1_0,
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(( ( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) )
<=> ( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
^ [X3: $i,X2: $i,X1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ p(X1)
| ~ p(X2)
| esk1_0 )
<=> ( esk1_0
| ~ p(X2)
| ~ p(X1) ) )),
( ( ~ p(X1)
| ~ p(X2)
| esk1_0
| ~ p(X3) )
<=> ( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3) ) )),
rewrite(( ( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3) )
<=> ( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3) ) )),
( ( ~ p(X1)
| ~ p(X2)
| esk1_0
| ~ p(X3) )
<=> ( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3) ) )),
( ( ~ p(X1)
| ~ p(X2)
| esk1_0
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) )
<=> ( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) ) )),
rewrite(( ( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) )
<=> ( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) ) )),
( ( ~ p(X1)
| ~ p(X2)
| esk1_0
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) )
<=> ( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X1)
| ~ p(X2)
| esk1_0
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,axiom,
! [X3: $i,X2: $i,X1: $i] :
( ~ p(X1)
| ~ p(X2)
| esk1_0
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_0_46668) ).
tff(55,plain,
! [X3: $i,X2: $i,X1: $i] :
( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [X3: $i,X2: $i,X1: $i] :
( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
! [X3: $i,X2: $i,X1: $i] :
( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [X3: $i,X2: $i,X1: $i] :
( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[57,50]) ).
tff(59,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) )
| esk1_0
| ~ p(true)
| ~ esk27893_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) )
| esk1_0
| ~ p(true)
| ~ esk27893_3(true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
( ( esk1_0
| ~ p(true)
| ~ p(true)
| ~ p(true)
| ~ esk27893_3(true,true,true) )
<=> ( esk1_0
| ~ p(true)
| ~ esk27893_3(true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) )
| esk1_0
| ~ p(true)
| ~ p(true)
| ~ p(true)
| ~ esk27893_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) )
| esk1_0
| ~ p(true)
| ~ esk27893_3(true,true,true) ) ),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) )
| esk1_0
| ~ p(true)
| ~ p(true)
| ~ p(true)
| ~ esk27893_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) )
| esk1_0
| ~ p(true)
| ~ esk27893_3(true,true,true) ) ),
inference(transitivity,[status(thm)],[61,59]) ).
tff(63,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) )
| esk1_0
| ~ p(true)
| ~ p(true)
| ~ p(true)
| ~ esk27893_3(true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27893_3(X1,X2,X3) )
| esk1_0
| ~ p(true)
| ~ esk27893_3(true,true,true) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
~ esk27893_3(true,true,true),
inference(unit_resolution,[status(thm)],[64,58,48,3]) ).
tff(66,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(( ( ~ esk16603_3(X1,X2,X3)
| esk27893_3(X1,X2,X3) )
<=> ( ~ esk16603_3(X1,X2,X3)
| esk27893_3(X1,X2,X3) ) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16603_3(X1,X2,X3)
| esk27893_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16603_3(X1,X2,X3)
| esk27893_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16603_3(X1,X2,X3)
| esk27893_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16603_3(X1,X2,X3)
| esk27893_3(X1,X2,X3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,axiom,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk16603_3(X1,X2,X3)
| esk27893_3(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_0_83646) ).
tff(70,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk16603_3(X1,X2,X3)
| esk27893_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk16603_3(X1,X2,X3)
| esk27893_3(X1,X2,X3) ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk16603_3(X1,X2,X3)
| esk27893_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16603_3(X1,X2,X3)
| esk27893_3(X1,X2,X3) )
| ~ esk16603_3(true,true,true)
| esk27893_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16603_3(X1,X2,X3)
| esk27893_3(X1,X2,X3) )
| ~ esk16603_3(true,true,true)
| esk27893_3(true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16603_3(X1,X2,X3)
| esk27893_3(X1,X2,X3) )
| ~ esk16603_3(true,true,true)
| esk27893_3(true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16603_3(X1,X2,X3)
| esk27893_3(X1,X2,X3) )
| ~ esk16603_3(true,true,true)
| esk27893_3(true,true,true) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
~ esk16603_3(true,true,true),
inference(unit_resolution,[status(thm)],[75,72,65]) ).
tff(77,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(( ( esk16603_3(X1,X2,X3)
| ~ esk16545_3(X1,X2,X3) )
<=> ( esk16603_3(X1,X2,X3)
| ~ esk16545_3(X1,X2,X3) ) )),
inference(bind,[status(th)],[]) ).
tff(78,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( esk16603_3(X1,X2,X3)
| ~ esk16545_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( esk16603_3(X1,X2,X3)
| ~ esk16545_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( esk16603_3(X1,X2,X3)
| ~ esk16545_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( esk16603_3(X1,X2,X3)
| ~ esk16545_3(X1,X2,X3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,axiom,
! [X3: $i,X2: $i,X1: $i] :
( esk16603_3(X1,X2,X3)
| ~ esk16545_3(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_0_23187) ).
tff(81,plain,
! [X3: $i,X2: $i,X1: $i] :
( esk16603_3(X1,X2,X3)
| ~ esk16545_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [X3: $i,X2: $i,X1: $i] :
( esk16603_3(X1,X2,X3)
| ~ esk16545_3(X1,X2,X3) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [X3: $i,X2: $i,X1: $i] :
( esk16603_3(X1,X2,X3)
| ~ esk16545_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( esk16603_3(X1,X2,X3)
| ~ esk16545_3(X1,X2,X3) )
| esk16603_3(true,true,true)
| ~ esk16545_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( esk16603_3(X1,X2,X3)
| ~ esk16545_3(X1,X2,X3) )
| esk16603_3(true,true,true)
| ~ esk16545_3(true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( esk16603_3(X1,X2,X3)
| ~ esk16545_3(X1,X2,X3) )
| esk16603_3(true,true,true)
| ~ esk16545_3(true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( esk16603_3(X1,X2,X3)
| ~ esk16545_3(X1,X2,X3) )
| esk16603_3(true,true,true)
| ~ esk16545_3(true,true,true) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
~ esk16545_3(true,true,true),
inference(unit_resolution,[status(thm)],[86,83,76]) ).
tff(88,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(( ( ~ esk19870_3(X1,X2,X3)
| esk16545_3(X1,X2,X3) )
<=> ( ~ esk19870_3(X1,X2,X3)
| esk16545_3(X1,X2,X3) ) )),
inference(bind,[status(th)],[]) ).
tff(89,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ esk19870_3(X1,X2,X3)
| esk16545_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk19870_3(X1,X2,X3)
| esk16545_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ esk19870_3(X1,X2,X3)
| esk16545_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk19870_3(X1,X2,X3)
| esk16545_3(X1,X2,X3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
^ [X3: $i,X2: $i,X1: $i] :
rewrite(( ( esk16545_3(X1,X2,X3)
| ~ esk19870_3(X1,X2,X3) )
<=> ( ~ esk19870_3(X1,X2,X3)
| esk16545_3(X1,X2,X3) ) )),
inference(bind,[status(th)],[]) ).
tff(92,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( esk16545_3(X1,X2,X3)
| ~ esk19870_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk19870_3(X1,X2,X3)
| esk16545_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,axiom,
! [X3: $i,X2: $i,X1: $i] :
( esk16545_3(X1,X2,X3)
| ~ esk19870_3(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_0_57758) ).
tff(94,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk19870_3(X1,X2,X3)
| esk16545_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk19870_3(X1,X2,X3)
| esk16545_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk19870_3(X1,X2,X3)
| esk16545_3(X1,X2,X3) ),
inference(skolemize,[status(sab)],[95]) ).
tff(97,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk19870_3(X1,X2,X3)
| esk16545_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[96,89]) ).
tff(98,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk19870_3(X1,X2,X3)
| esk16545_3(X1,X2,X3) )
| ~ esk19870_3(true,true,true)
| esk16545_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk19870_3(X1,X2,X3)
| esk16545_3(X1,X2,X3) )
| ~ esk19870_3(true,true,true)
| esk16545_3(true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk19870_3(X1,X2,X3)
| esk16545_3(X1,X2,X3) )
| ~ esk19870_3(true,true,true)
| esk16545_3(true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk19870_3(X1,X2,X3)
| esk16545_3(X1,X2,X3) )
| ~ esk19870_3(true,true,true)
| esk16545_3(true,true,true) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
~ esk19870_3(true,true,true),
inference(unit_resolution,[status(thm)],[100,97,87]) ).
tff(102,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(( ( esk19870_3(X1,X2,X3)
| ~ esk17873_3(X1,X2,X3) )
<=> ( esk19870_3(X1,X2,X3)
| ~ esk17873_3(X1,X2,X3) ) )),
inference(bind,[status(th)],[]) ).
tff(103,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( esk19870_3(X1,X2,X3)
| ~ esk17873_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( esk19870_3(X1,X2,X3)
| ~ esk17873_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( esk19870_3(X1,X2,X3)
| ~ esk17873_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( esk19870_3(X1,X2,X3)
| ~ esk17873_3(X1,X2,X3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,axiom,
! [X3: $i,X2: $i,X1: $i] :
( esk19870_3(X1,X2,X3)
| ~ esk17873_3(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_0_64270) ).
tff(106,plain,
! [X3: $i,X2: $i,X1: $i] :
( esk19870_3(X1,X2,X3)
| ~ esk17873_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
! [X3: $i,X2: $i,X1: $i] :
( esk19870_3(X1,X2,X3)
| ~ esk17873_3(X1,X2,X3) ),
inference(skolemize,[status(sab)],[106]) ).
tff(108,plain,
! [X3: $i,X2: $i,X1: $i] :
( esk19870_3(X1,X2,X3)
| ~ esk17873_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( esk19870_3(X1,X2,X3)
| ~ esk17873_3(X1,X2,X3) )
| esk19870_3(true,true,true)
| ~ esk17873_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( esk19870_3(X1,X2,X3)
| ~ esk17873_3(X1,X2,X3) )
| esk19870_3(true,true,true)
| ~ esk17873_3(true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( esk19870_3(X1,X2,X3)
| ~ esk17873_3(X1,X2,X3) )
| esk19870_3(true,true,true)
| ~ esk17873_3(true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( esk19870_3(X1,X2,X3)
| ~ esk17873_3(X1,X2,X3) )
| esk19870_3(true,true,true)
| ~ esk17873_3(true,true,true) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
$false,
inference(unit_resolution,[status(thm)],[111,108,101,45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : HWV061-1 : TPTP v9.0.0. Bugfixed v5.5.1.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 17:33:05 EDT 2025
% 0.11/0.32 % CPUTime :
% 24.62/24.76 % SZS status Unsatisfiable
% 24.62/24.76 % SZS output start Proof
% See solution above
% 27.09/27.28 % E exiting
%------------------------------------------------------------------------------