%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV069-1 : TPTP v9.0.0. Bugfixed v5.5.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:10:38 AM UTC 2025
% Result : Unsatisfiable 7.23s 7.41s
% Output : Proof 8.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 84
% Syntax : Number of formulae : 190 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 1374 ( 0 equ)
% Maximal formula atoms : 21 ( 7 avg)
% Number of connectives : 2052 ( 960 ~; 977 |; 0 &)
% ( 115 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 92 ( 92 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 21 ( 20 usr; 3 prp; 0-4 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 860 ( 780 !; 0 ?; 860 :)
% Comments :
%------------------------------------------------------------------------------
tff(esk9168_4_type,type,
esk9168_4: ( $i * $i * $i * $i ) > $o ).
tff(true_type,type,
true: $i ).
tff(esk8752_4_type,type,
esk8752_4: ( $i * $i * $i * $i ) > $o ).
tff(esk7951_4_type,type,
esk7951_4: ( $i * $i * $i * $i ) > $o ).
tff(esk7953_4_type,type,
esk7953_4: ( $i * $i * $i * $i ) > $o ).
tff(esk7824_4_type,type,
esk7824_4: ( $i * $i * $i * $i ) > $o ).
tff(esk7825_4_type,type,
esk7825_4: ( $i * $i * $i * $i ) > $o ).
tff(esk8761_4_type,type,
esk8761_4: ( $i * $i * $i * $i ) > $o ).
tff(esk8120_4_type,type,
esk8120_4: ( $i * $i * $i * $i ) > $o ).
tff(esk7826_4_type,type,
esk7826_4: ( $i * $i * $i * $i ) > $o ).
tff(esk8751_4_type,type,
esk8751_4: ( $i * $i * $i * $i ) > $o ).
tff(p_type,type,
p: $i > $o ).
tff(esk2_0_type,type,
esk2_0: $o ).
tff(esk7952_4_type,type,
esk7952_4: ( $i * $i * $i * $i ) > $o ).
tff(esk9108_4_type,type,
esk9108_4: ( $i * $i * $i * $i ) > $o ).
tff(esk7937_4_type,type,
esk7937_4: ( $i * $i * $i * $i ) > $o ).
tff(esk1_0_type,type,
esk1_0: $o ).
tff(1,plain,
^ [X4: $i,X3: $i,X2: $i,X1: $i] :
refl(( ~ esk8120_4(X1,X2,X3,X4)
<=> ~ esk8120_4(X1,X2,X3,X4) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] : ~ esk8120_4(X1,X2,X3,X4)
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] : ~ esk8120_4(X1,X2,X3,X4) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] : ~ esk8120_4(X1,X2,X3,X4)
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] : ~ esk8120_4(X1,X2,X3,X4) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X4: $i,X3: $i,X2: $i,X1: $i] : ~ esk8120_4(X1,X2,X3,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_0_18461) ).
tff(5,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] : ~ esk8120_4(X1,X2,X3,X4),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] : ~ esk8120_4(X1,X2,X3,X4),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] : ~ esk8120_4(X1,X2,X3,X4),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] : ~ esk8120_4(X1,X2,X3,X4)
| ~ esk8120_4(true,true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
~ esk8120_4(true,true,true,true),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X4: $i,X3: $i,X2: $i,X1: $i] :
refl(( ( ~ esk8761_4(X1,X2,X3,X4)
| esk8120_4(X1,X2,X3,X4) )
<=> ( ~ esk8761_4(X1,X2,X3,X4)
| esk8120_4(X1,X2,X3,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8761_4(X1,X2,X3,X4)
| esk8120_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8761_4(X1,X2,X3,X4)
| esk8120_4(X1,X2,X3,X4) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8761_4(X1,X2,X3,X4)
| esk8120_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8761_4(X1,X2,X3,X4)
| esk8120_4(X1,X2,X3,X4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8761_4(X1,X2,X3,X4)
| esk8120_4(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_0_27269) ).
tff(14,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8761_4(X1,X2,X3,X4)
| esk8120_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8761_4(X1,X2,X3,X4)
| esk8120_4(X1,X2,X3,X4) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8761_4(X1,X2,X3,X4)
| esk8120_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8761_4(X1,X2,X3,X4)
| esk8120_4(X1,X2,X3,X4) )
| ~ esk8761_4(true,true,true,true)
| esk8120_4(true,true,true,true) )
<=> ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8761_4(X1,X2,X3,X4)
| esk8120_4(X1,X2,X3,X4) )
| ~ esk8761_4(true,true,true,true)
| esk8120_4(true,true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8761_4(X1,X2,X3,X4)
| esk8120_4(X1,X2,X3,X4) )
| ~ esk8761_4(true,true,true,true)
| esk8120_4(true,true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8761_4(X1,X2,X3,X4)
| esk8120_4(X1,X2,X3,X4) )
| ~ esk8761_4(true,true,true,true)
| esk8120_4(true,true,true,true) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ esk8761_4(true,true,true,true),
inference(unit_resolution,[status(thm)],[19,16,9]) ).
tff(21,plain,
^ [X4: $i,X3: $i,X2: $i,X1: $i] :
refl(( ( ~ esk7825_4(X1,X2,X3,X4)
| esk8761_4(X1,X2,X3,X4) )
<=> ( ~ esk7825_4(X1,X2,X3,X4)
| esk8761_4(X1,X2,X3,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7825_4(X1,X2,X3,X4)
| esk8761_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7825_4(X1,X2,X3,X4)
| esk8761_4(X1,X2,X3,X4) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7825_4(X1,X2,X3,X4)
| esk8761_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7825_4(X1,X2,X3,X4)
| esk8761_4(X1,X2,X3,X4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7825_4(X1,X2,X3,X4)
| esk8761_4(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_0_17201) ).
tff(25,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7825_4(X1,X2,X3,X4)
| esk8761_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7825_4(X1,X2,X3,X4)
| esk8761_4(X1,X2,X3,X4) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7825_4(X1,X2,X3,X4)
| esk8761_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7825_4(X1,X2,X3,X4)
| esk8761_4(X1,X2,X3,X4) )
| ~ esk7825_4(true,true,true,true)
| esk8761_4(true,true,true,true) )
<=> ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7825_4(X1,X2,X3,X4)
| esk8761_4(X1,X2,X3,X4) )
| ~ esk7825_4(true,true,true,true)
| esk8761_4(true,true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7825_4(X1,X2,X3,X4)
| esk8761_4(X1,X2,X3,X4) )
| ~ esk7825_4(true,true,true,true)
| esk8761_4(true,true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7825_4(X1,X2,X3,X4)
| esk8761_4(X1,X2,X3,X4) )
| ~ esk7825_4(true,true,true,true)
| esk8761_4(true,true,true,true) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
~ esk7825_4(true,true,true,true),
inference(unit_resolution,[status(thm)],[30,27,20]) ).
tff(32,plain,
( p(true)
<=> p(true) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
p(true),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_true) ).
tff(34,plain,
p(true),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( esk2_0
<=> esk2_0 ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
esk2_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_0_25550) ).
tff(37,plain,
esk2_0,
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
^ [X4: $i,X3: $i,X2: $i,X1: $i] :
refl(( ( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 )
<=> ( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
^ [X4: $i,X3: $i,X2: $i,X1: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ p(X1)
| ~ p(X4)
| ~ p(X2) )
<=> ( ~ p(X1)
| ~ p(X4)
| ~ p(X2) ) )),
( ( ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| ~ esk2_0 )
<=> ( ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| ~ esk2_0 ) )),
rewrite(( ( ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| ~ esk2_0 )
<=> ( ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| ~ esk2_0 ) )),
( ( ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| ~ esk2_0 )
<=> ( ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| ~ esk2_0 ) )),
( ( ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| ~ esk2_0
| ~ p(X3) )
<=> ( ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| ~ esk2_0
| ~ p(X3) ) )),
rewrite(( ( ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| ~ esk2_0
| ~ p(X3) )
<=> ( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| ~ esk2_0 ) )),
( ( ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| ~ esk2_0
| ~ p(X3) )
<=> ( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| ~ esk2_0 ) )),
( ( ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| ~ esk2_0
| ~ p(X3)
| esk8751_4(X1,X2,X3,X4) )
<=> ( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| ~ esk2_0
| esk8751_4(X1,X2,X3,X4) ) )),
rewrite(( ( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| ~ esk2_0
| esk8751_4(X1,X2,X3,X4) )
<=> ( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 ) )),
( ( ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| ~ esk2_0
| ~ p(X3)
| esk8751_4(X1,X2,X3,X4) )
<=> ( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| ~ esk2_0
| ~ p(X3)
| esk8751_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| ~ esk2_0
| ~ p(X3)
| esk8751_4(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_0_14639) ).
tff(44,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 )
| ~ esk2_0
| ~ p(true)
| esk8751_4(true,true,true,true) )
<=> ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 )
| ~ esk2_0
| ~ p(true)
| esk8751_4(true,true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ( ~ p(true)
| ~ p(true)
| ~ p(true)
| ~ p(true)
| esk8751_4(true,true,true,true)
| ~ esk2_0 )
<=> ( ~ esk2_0
| ~ p(true)
| esk8751_4(true,true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 )
| ~ p(true)
| ~ p(true)
| ~ p(true)
| ~ p(true)
| esk8751_4(true,true,true,true)
| ~ esk2_0 )
<=> ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 )
| ~ esk2_0
| ~ p(true)
| esk8751_4(true,true,true,true) ) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 )
| ~ p(true)
| ~ p(true)
| ~ p(true)
| ~ p(true)
| esk8751_4(true,true,true,true)
| ~ esk2_0 )
<=> ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 )
| ~ esk2_0
| ~ p(true)
| esk8751_4(true,true,true,true) ) ),
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 )
| ~ p(true)
| ~ p(true)
| ~ p(true)
| ~ p(true)
| esk8751_4(true,true,true,true)
| ~ esk2_0 ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ p(X4)
| ~ p(X2)
| esk8751_4(X1,X2,X3,X4)
| ~ esk2_0 )
| ~ esk2_0
| ~ p(true)
| esk8751_4(true,true,true,true) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
esk8751_4(true,true,true,true),
inference(unit_resolution,[status(thm)],[53,47,37,34]) ).
tff(55,plain,
^ [X4: $i,X3: $i,X2: $i,X1: $i] :
refl(( ( ~ esk8751_4(X1,X2,X3,X4)
| esk7826_4(X1,X2,X3,X4) )
<=> ( ~ esk8751_4(X1,X2,X3,X4)
| esk7826_4(X1,X2,X3,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8751_4(X1,X2,X3,X4)
| esk7826_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8751_4(X1,X2,X3,X4)
| esk7826_4(X1,X2,X3,X4) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8751_4(X1,X2,X3,X4)
| esk7826_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8751_4(X1,X2,X3,X4)
| esk7826_4(X1,X2,X3,X4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8751_4(X1,X2,X3,X4)
| esk7826_4(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_0_1548) ).
tff(59,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8751_4(X1,X2,X3,X4)
| esk7826_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8751_4(X1,X2,X3,X4)
| esk7826_4(X1,X2,X3,X4) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8751_4(X1,X2,X3,X4)
| esk7826_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8751_4(X1,X2,X3,X4)
| esk7826_4(X1,X2,X3,X4) )
| ~ esk8751_4(true,true,true,true)
| esk7826_4(true,true,true,true) )
<=> ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8751_4(X1,X2,X3,X4)
| esk7826_4(X1,X2,X3,X4) )
| ~ esk8751_4(true,true,true,true)
| esk7826_4(true,true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8751_4(X1,X2,X3,X4)
| esk7826_4(X1,X2,X3,X4) )
| ~ esk8751_4(true,true,true,true)
| esk7826_4(true,true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8751_4(X1,X2,X3,X4)
| esk7826_4(X1,X2,X3,X4) )
| ~ esk8751_4(true,true,true,true)
| esk7826_4(true,true,true,true) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
esk7826_4(true,true,true,true),
inference(unit_resolution,[status(thm)],[64,61,54]) ).
tff(66,plain,
^ [X4: $i,X3: $i,X2: $i,X1: $i] :
refl(( ( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) )
<=> ( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
^ [X4: $i,X3: $i,X2: $i,X1: $i] :
trans(monotonicity(rewrite(( ( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4) )
<=> ( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4) ) )),
( ( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) )
<=> ( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) ) )),
rewrite(( ( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) )
<=> ( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) ) )),
( ( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) )
<=> ( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,axiom,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_0_3978) ).
tff(72,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[74,67]) ).
tff(76,plain,
( ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) )
| esk7825_4(true,true,true,true)
| esk7824_4(true,true,true,true)
| ~ esk7826_4(true,true,true,true) )
<=> ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) )
| esk7825_4(true,true,true,true)
| esk7824_4(true,true,true,true)
| ~ esk7826_4(true,true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) )
| esk7825_4(true,true,true,true)
| esk7824_4(true,true,true,true)
| ~ esk7826_4(true,true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7825_4(X1,X2,X3,X4)
| esk7824_4(X1,X2,X3,X4)
| ~ esk7826_4(X1,X2,X3,X4) )
| esk7825_4(true,true,true,true)
| esk7824_4(true,true,true,true)
| ~ esk7826_4(true,true,true,true) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
( esk7825_4(true,true,true,true)
| esk7824_4(true,true,true,true) ),
inference(unit_resolution,[status(thm)],[78,75,65]) ).
tff(80,plain,
esk7824_4(true,true,true,true),
inference(unit_resolution,[status(thm)],[79,31]) ).
tff(81,plain,
^ [X4: $i,X3: $i,X2: $i,X1: $i] :
refl(( ( ~ esk7824_4(X1,X2,X3,X4)
| esk7953_4(X1,X2,X3,X4) )
<=> ( ~ esk7824_4(X1,X2,X3,X4)
| esk7953_4(X1,X2,X3,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(82,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7824_4(X1,X2,X3,X4)
| esk7953_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7824_4(X1,X2,X3,X4)
| esk7953_4(X1,X2,X3,X4) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7824_4(X1,X2,X3,X4)
| esk7953_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7824_4(X1,X2,X3,X4)
| esk7953_4(X1,X2,X3,X4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
^ [X4: $i,X3: $i,X2: $i,X1: $i] :
rewrite(( ( esk7953_4(X1,X2,X3,X4)
| ~ esk7824_4(X1,X2,X3,X4) )
<=> ( ~ esk7824_4(X1,X2,X3,X4)
| esk7953_4(X1,X2,X3,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7953_4(X1,X2,X3,X4)
| ~ esk7824_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7824_4(X1,X2,X3,X4)
| esk7953_4(X1,X2,X3,X4) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,axiom,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7953_4(X1,X2,X3,X4)
| ~ esk7824_4(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_0_8559) ).
tff(87,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7824_4(X1,X2,X3,X4)
| esk7953_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7824_4(X1,X2,X3,X4)
| esk7953_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7824_4(X1,X2,X3,X4)
| esk7953_4(X1,X2,X3,X4) ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7824_4(X1,X2,X3,X4)
| esk7953_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[89,82]) ).
tff(91,plain,
( ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7824_4(X1,X2,X3,X4)
| esk7953_4(X1,X2,X3,X4) )
| ~ esk7824_4(true,true,true,true)
| esk7953_4(true,true,true,true) )
<=> ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7824_4(X1,X2,X3,X4)
| esk7953_4(X1,X2,X3,X4) )
| ~ esk7824_4(true,true,true,true)
| esk7953_4(true,true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7824_4(X1,X2,X3,X4)
| esk7953_4(X1,X2,X3,X4) )
| ~ esk7824_4(true,true,true,true)
| esk7953_4(true,true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7824_4(X1,X2,X3,X4)
| esk7953_4(X1,X2,X3,X4) )
| ~ esk7824_4(true,true,true,true)
| esk7953_4(true,true,true,true) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
esk7953_4(true,true,true,true),
inference(unit_resolution,[status(thm)],[93,90,80]) ).
tff(95,plain,
( ~ esk1_0
<=> ~ esk1_0 ),
inference(rewrite,[status(thm)],[]) ).
tff(96,axiom,
~ esk1_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_0_15881) ).
tff(97,plain,
~ esk1_0,
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
^ [X4: $i,X3: $i,X2: $i,X1: $i] :
refl(( ( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) )
<=> ( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(99,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
^ [X4: $i,X3: $i,X2: $i,X1: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ p(X4)
| esk1_0 )
<=> ( esk1_0
| ~ p(X4) ) )),
( ( ~ p(X4)
| esk1_0
| ~ p(X3) )
<=> ( esk1_0
| ~ p(X4)
| ~ p(X3) ) )),
rewrite(( ( esk1_0
| ~ p(X4)
| ~ p(X3) )
<=> ( ~ p(X3)
| esk1_0
| ~ p(X4) ) )),
( ( ~ p(X4)
| esk1_0
| ~ p(X3) )
<=> ( ~ p(X3)
| esk1_0
| ~ p(X4) ) )),
( ( ~ p(X4)
| esk1_0
| ~ p(X3)
| ~ esk7937_4(X1,X2,X3,X4) )
<=> ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ esk7937_4(X1,X2,X3,X4) ) )),
rewrite(( ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ esk7937_4(X1,X2,X3,X4) )
<=> ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ esk7937_4(X1,X2,X3,X4) ) )),
( ( ~ p(X4)
| esk1_0
| ~ p(X3)
| ~ esk7937_4(X1,X2,X3,X4) )
<=> ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ esk7937_4(X1,X2,X3,X4) ) )),
( ( ~ p(X4)
| esk1_0
| ~ p(X3)
| ~ esk7937_4(X1,X2,X3,X4)
| ~ p(X2) )
<=> ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ esk7937_4(X1,X2,X3,X4)
| ~ p(X2) ) )),
rewrite(( ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ esk7937_4(X1,X2,X3,X4)
| ~ p(X2) )
<=> ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) ) )),
( ( ~ p(X4)
| esk1_0
| ~ p(X3)
| ~ esk7937_4(X1,X2,X3,X4)
| ~ p(X2) )
<=> ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) ) )),
( ( ~ p(X4)
| esk1_0
| ~ p(X3)
| ~ esk7937_4(X1,X2,X3,X4)
| ~ p(X2)
| ~ p(X1) )
<=> ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4)
| ~ p(X1) ) )),
rewrite(( ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4)
| ~ p(X1) )
<=> ( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) ) )),
( ( ~ p(X4)
| esk1_0
| ~ p(X3)
| ~ esk7937_4(X1,X2,X3,X4)
| ~ p(X2)
| ~ p(X1) )
<=> ( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(102,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X4)
| esk1_0
| ~ p(X3)
| ~ esk7937_4(X1,X2,X3,X4)
| ~ p(X2)
| ~ p(X1) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,axiom,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X4)
| esk1_0
| ~ p(X3)
| ~ esk7937_4(X1,X2,X3,X4)
| ~ p(X2)
| ~ p(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_0_902) ).
tff(104,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) ),
inference(skolemize,[status(sab)],[105]) ).
tff(107,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[106,99]) ).
tff(108,plain,
( ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) )
| esk1_0
| ~ p(true)
| ~ esk7937_4(true,true,true,true) )
<=> ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) )
| esk1_0
| ~ p(true)
| ~ esk7937_4(true,true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
( ( ~ p(true)
| ~ p(true)
| esk1_0
| ~ p(true)
| ~ p(true)
| ~ esk7937_4(true,true,true,true) )
<=> ( esk1_0
| ~ p(true)
| ~ esk7937_4(true,true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) )
| ~ p(true)
| ~ p(true)
| esk1_0
| ~ p(true)
| ~ p(true)
| ~ esk7937_4(true,true,true,true) )
<=> ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) )
| esk1_0
| ~ p(true)
| ~ esk7937_4(true,true,true,true) ) ),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
( ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) )
| ~ p(true)
| ~ p(true)
| esk1_0
| ~ p(true)
| ~ p(true)
| ~ esk7937_4(true,true,true,true) )
<=> ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) )
| esk1_0
| ~ p(true)
| ~ esk7937_4(true,true,true,true) ) ),
inference(transitivity,[status(thm)],[110,108]) ).
tff(112,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) )
| ~ p(true)
| ~ p(true)
| esk1_0
| ~ p(true)
| ~ p(true)
| ~ esk7937_4(true,true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk7937_4(X1,X2,X3,X4) )
| esk1_0
| ~ p(true)
| ~ esk7937_4(true,true,true,true) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
~ esk7937_4(true,true,true,true),
inference(unit_resolution,[status(thm)],[113,107,97,34]) ).
tff(115,plain,
^ [X4: $i,X3: $i,X2: $i,X1: $i] :
refl(( ( esk7937_4(X1,X2,X3,X4)
| ~ esk9108_4(X1,X2,X3,X4) )
<=> ( esk7937_4(X1,X2,X3,X4)
| ~ esk9108_4(X1,X2,X3,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(116,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7937_4(X1,X2,X3,X4)
| ~ esk9108_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7937_4(X1,X2,X3,X4)
| ~ esk9108_4(X1,X2,X3,X4) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7937_4(X1,X2,X3,X4)
| ~ esk9108_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7937_4(X1,X2,X3,X4)
| ~ esk9108_4(X1,X2,X3,X4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,axiom,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7937_4(X1,X2,X3,X4)
| ~ esk9108_4(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_0_18074) ).
tff(119,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7937_4(X1,X2,X3,X4)
| ~ esk9108_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7937_4(X1,X2,X3,X4)
| ~ esk9108_4(X1,X2,X3,X4) ),
inference(skolemize,[status(sab)],[119]) ).
tff(121,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7937_4(X1,X2,X3,X4)
| ~ esk9108_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[120,116]) ).
tff(122,plain,
( ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7937_4(X1,X2,X3,X4)
| ~ esk9108_4(X1,X2,X3,X4) )
| esk7937_4(true,true,true,true)
| ~ esk9108_4(true,true,true,true) )
<=> ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7937_4(X1,X2,X3,X4)
| ~ esk9108_4(X1,X2,X3,X4) )
| esk7937_4(true,true,true,true)
| ~ esk9108_4(true,true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7937_4(X1,X2,X3,X4)
| ~ esk9108_4(X1,X2,X3,X4) )
| esk7937_4(true,true,true,true)
| ~ esk9108_4(true,true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7937_4(X1,X2,X3,X4)
| ~ esk9108_4(X1,X2,X3,X4) )
| esk7937_4(true,true,true,true)
| ~ esk9108_4(true,true,true,true) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
~ esk9108_4(true,true,true,true),
inference(unit_resolution,[status(thm)],[124,121,114]) ).
tff(126,plain,
^ [X4: $i,X3: $i,X2: $i,X1: $i] :
refl(( ( esk9108_4(X1,X2,X3,X4)
| ~ esk7952_4(X1,X2,X3,X4) )
<=> ( esk9108_4(X1,X2,X3,X4)
| ~ esk7952_4(X1,X2,X3,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(127,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk9108_4(X1,X2,X3,X4)
| ~ esk7952_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk9108_4(X1,X2,X3,X4)
| ~ esk7952_4(X1,X2,X3,X4) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk9108_4(X1,X2,X3,X4)
| ~ esk7952_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk9108_4(X1,X2,X3,X4)
| ~ esk7952_4(X1,X2,X3,X4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,axiom,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk9108_4(X1,X2,X3,X4)
| ~ esk7952_4(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_0_26419) ).
tff(130,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk9108_4(X1,X2,X3,X4)
| ~ esk7952_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk9108_4(X1,X2,X3,X4)
| ~ esk7952_4(X1,X2,X3,X4) ),
inference(skolemize,[status(sab)],[130]) ).
tff(132,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk9108_4(X1,X2,X3,X4)
| ~ esk7952_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[131,127]) ).
tff(133,plain,
( ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk9108_4(X1,X2,X3,X4)
| ~ esk7952_4(X1,X2,X3,X4) )
| esk9108_4(true,true,true,true)
| ~ esk7952_4(true,true,true,true) )
<=> ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk9108_4(X1,X2,X3,X4)
| ~ esk7952_4(X1,X2,X3,X4) )
| esk9108_4(true,true,true,true)
| ~ esk7952_4(true,true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk9108_4(X1,X2,X3,X4)
| ~ esk7952_4(X1,X2,X3,X4) )
| esk9108_4(true,true,true,true)
| ~ esk7952_4(true,true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(135,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk9108_4(X1,X2,X3,X4)
| ~ esk7952_4(X1,X2,X3,X4) )
| esk9108_4(true,true,true,true)
| ~ esk7952_4(true,true,true,true) ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
~ esk7952_4(true,true,true,true),
inference(unit_resolution,[status(thm)],[135,132,125]) ).
tff(137,plain,
^ [X4: $i,X3: $i,X2: $i,X1: $i] :
refl(( ( esk7952_4(X1,X2,X3,X4)
| esk7951_4(X1,X2,X3,X4)
| ~ esk7953_4(X1,X2,X3,X4) )
<=> ( esk7952_4(X1,X2,X3,X4)
| esk7951_4(X1,X2,X3,X4)
| ~ esk7953_4(X1,X2,X3,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(138,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7952_4(X1,X2,X3,X4)
| esk7951_4(X1,X2,X3,X4)
| ~ esk7953_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7952_4(X1,X2,X3,X4)
| esk7951_4(X1,X2,X3,X4)
| ~ esk7953_4(X1,X2,X3,X4) ) ),
inference(quant_intro,[status(thm)],[137]) ).
tff(139,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7952_4(X1,X2,X3,X4)
| esk7951_4(X1,X2,X3,X4)
| ~ esk7953_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7952_4(X1,X2,X3,X4)
| esk7951_4(X1,X2,X3,X4)
| ~ esk7953_4(X1,X2,X3,X4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(140,plain,
^ [X4: $i,X3: $i,X2: $i,X1: $i] :
rewrite(( ( ~ esk7953_4(X1,X2,X3,X4)
| esk7952_4(X1,X2,X3,X4)
| esk7951_4(X1,X2,X3,X4) )
<=> ( esk7952_4(X1,X2,X3,X4)
| esk7951_4(X1,X2,X3,X4)
| ~ esk7953_4(X1,X2,X3,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(141,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7953_4(X1,X2,X3,X4)
| esk7952_4(X1,X2,X3,X4)
| esk7951_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7952_4(X1,X2,X3,X4)
| esk7951_4(X1,X2,X3,X4)
| ~ esk7953_4(X1,X2,X3,X4) ) ),
inference(quant_intro,[status(thm)],[140]) ).
tff(142,axiom,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk7953_4(X1,X2,X3,X4)
| esk7952_4(X1,X2,X3,X4)
| esk7951_4(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_0_3018) ).
tff(143,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7952_4(X1,X2,X3,X4)
| esk7951_4(X1,X2,X3,X4)
| ~ esk7953_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7952_4(X1,X2,X3,X4)
| esk7951_4(X1,X2,X3,X4)
| ~ esk7953_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[143,139]) ).
tff(145,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7952_4(X1,X2,X3,X4)
| esk7951_4(X1,X2,X3,X4)
| ~ esk7953_4(X1,X2,X3,X4) ),
inference(skolemize,[status(sab)],[144]) ).
tff(146,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7952_4(X1,X2,X3,X4)
| esk7951_4(X1,X2,X3,X4)
| ~ esk7953_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[145,138]) ).
tff(147,plain,
( ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7952_4(X1,X2,X3,X4)
| esk7951_4(X1,X2,X3,X4)
| ~ esk7953_4(X1,X2,X3,X4) )
| esk7952_4(true,true,true,true)
| esk7951_4(true,true,true,true)
| ~ esk7953_4(true,true,true,true) )
<=> ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7952_4(X1,X2,X3,X4)
| esk7951_4(X1,X2,X3,X4)
| ~ esk7953_4(X1,X2,X3,X4) )
| esk7952_4(true,true,true,true)
| esk7951_4(true,true,true,true)
| ~ esk7953_4(true,true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7952_4(X1,X2,X3,X4)
| esk7951_4(X1,X2,X3,X4)
| ~ esk7953_4(X1,X2,X3,X4) )
| esk7952_4(true,true,true,true)
| esk7951_4(true,true,true,true)
| ~ esk7953_4(true,true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(149,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk7952_4(X1,X2,X3,X4)
| esk7951_4(X1,X2,X3,X4)
| ~ esk7953_4(X1,X2,X3,X4) )
| esk7952_4(true,true,true,true)
| esk7951_4(true,true,true,true)
| ~ esk7953_4(true,true,true,true) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
( esk7951_4(true,true,true,true)
| ~ esk7953_4(true,true,true,true) ),
inference(unit_resolution,[status(thm)],[149,146,136]) ).
tff(151,plain,
esk7951_4(true,true,true,true),
inference(unit_resolution,[status(thm)],[150,94]) ).
tff(152,plain,
^ [X4: $i,X3: $i,X2: $i,X1: $i] :
refl(( ( esk8752_4(X1,X2,X3,X4)
| ~ esk7951_4(X1,X2,X3,X4) )
<=> ( esk8752_4(X1,X2,X3,X4)
| ~ esk7951_4(X1,X2,X3,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(153,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk8752_4(X1,X2,X3,X4)
| ~ esk7951_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk8752_4(X1,X2,X3,X4)
| ~ esk7951_4(X1,X2,X3,X4) ) ),
inference(quant_intro,[status(thm)],[152]) ).
tff(154,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk8752_4(X1,X2,X3,X4)
| ~ esk7951_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk8752_4(X1,X2,X3,X4)
| ~ esk7951_4(X1,X2,X3,X4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(155,axiom,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk8752_4(X1,X2,X3,X4)
| ~ esk7951_4(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_0_15706) ).
tff(156,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk8752_4(X1,X2,X3,X4)
| ~ esk7951_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk8752_4(X1,X2,X3,X4)
| ~ esk7951_4(X1,X2,X3,X4) ),
inference(skolemize,[status(sab)],[156]) ).
tff(158,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk8752_4(X1,X2,X3,X4)
| ~ esk7951_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[157,153]) ).
tff(159,plain,
( ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk8752_4(X1,X2,X3,X4)
| ~ esk7951_4(X1,X2,X3,X4) )
| esk8752_4(true,true,true,true)
| ~ esk7951_4(true,true,true,true) )
<=> ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk8752_4(X1,X2,X3,X4)
| ~ esk7951_4(X1,X2,X3,X4) )
| esk8752_4(true,true,true,true)
| ~ esk7951_4(true,true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(160,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk8752_4(X1,X2,X3,X4)
| ~ esk7951_4(X1,X2,X3,X4) )
| esk8752_4(true,true,true,true)
| ~ esk7951_4(true,true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(161,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( esk8752_4(X1,X2,X3,X4)
| ~ esk7951_4(X1,X2,X3,X4) )
| esk8752_4(true,true,true,true)
| ~ esk7951_4(true,true,true,true) ),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
esk8752_4(true,true,true,true),
inference(unit_resolution,[status(thm)],[161,158,151]) ).
tff(163,plain,
^ [X4: $i,X3: $i,X2: $i,X1: $i] :
refl(( ( ~ esk8752_4(X1,X2,X3,X4)
| esk9168_4(X1,X2,X3,X4) )
<=> ( ~ esk8752_4(X1,X2,X3,X4)
| esk9168_4(X1,X2,X3,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(164,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8752_4(X1,X2,X3,X4)
| esk9168_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8752_4(X1,X2,X3,X4)
| esk9168_4(X1,X2,X3,X4) ) ),
inference(quant_intro,[status(thm)],[163]) ).
tff(165,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8752_4(X1,X2,X3,X4)
| esk9168_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8752_4(X1,X2,X3,X4)
| esk9168_4(X1,X2,X3,X4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(166,axiom,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8752_4(X1,X2,X3,X4)
| esk9168_4(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_0_6826) ).
tff(167,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8752_4(X1,X2,X3,X4)
| esk9168_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8752_4(X1,X2,X3,X4)
| esk9168_4(X1,X2,X3,X4) ),
inference(skolemize,[status(sab)],[167]) ).
tff(169,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8752_4(X1,X2,X3,X4)
| esk9168_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[168,164]) ).
tff(170,plain,
( ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8752_4(X1,X2,X3,X4)
| esk9168_4(X1,X2,X3,X4) )
| ~ esk8752_4(true,true,true,true)
| esk9168_4(true,true,true,true) )
<=> ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8752_4(X1,X2,X3,X4)
| esk9168_4(X1,X2,X3,X4) )
| ~ esk8752_4(true,true,true,true)
| esk9168_4(true,true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8752_4(X1,X2,X3,X4)
| esk9168_4(X1,X2,X3,X4) )
| ~ esk8752_4(true,true,true,true)
| esk9168_4(true,true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ esk8752_4(X1,X2,X3,X4)
| esk9168_4(X1,X2,X3,X4) )
| ~ esk8752_4(true,true,true,true)
| esk9168_4(true,true,true,true) ),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
esk9168_4(true,true,true,true),
inference(unit_resolution,[status(thm)],[172,169,162]) ).
tff(174,plain,
^ [X4: $i,X3: $i,X2: $i,X1: $i] :
refl(( ( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) )
<=> ( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(175,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) ) ),
inference(quant_intro,[status(thm)],[174]) ).
tff(176,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(177,plain,
^ [X4: $i,X3: $i,X2: $i,X1: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ p(X3)
| esk1_0 )
<=> ( ~ p(X3)
| esk1_0 ) )),
( ( ~ p(X3)
| esk1_0
| ~ p(X4) )
<=> ( ~ p(X3)
| esk1_0
| ~ p(X4) ) )),
rewrite(( ( ~ p(X3)
| esk1_0
| ~ p(X4) )
<=> ( ~ p(X3)
| esk1_0
| ~ p(X4) ) )),
( ( ~ p(X3)
| esk1_0
| ~ p(X4) )
<=> ( ~ p(X3)
| esk1_0
| ~ p(X4) ) )),
( ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2) )
<=> ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2) ) )),
rewrite(( ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2) )
<=> ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2) ) )),
( ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2) )
<=> ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2) ) )),
( ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) )
<=> ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) ) )),
rewrite(( ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) )
<=> ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) ) )),
( ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) )
<=> ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) ) )),
( ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4)
| ~ p(X1) )
<=> ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4)
| ~ p(X1) ) )),
rewrite(( ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4)
| ~ p(X1) )
<=> ( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) ) )),
( ( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4)
| ~ p(X1) )
<=> ( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(178,plain,
( ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4)
| ~ p(X1) )
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) ) ),
inference(quant_intro,[status(thm)],[177]) ).
tff(179,axiom,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4)
| ~ p(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_0_16826) ).
tff(180,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[179,178]) ).
tff(181,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[180,176]) ).
tff(182,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) ),
inference(skolemize,[status(sab)],[181]) ).
tff(183,plain,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[182,175]) ).
tff(184,plain,
( ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) )
| esk1_0
| ~ p(true)
| ~ esk9168_4(true,true,true,true) )
<=> ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) )
| esk1_0
| ~ p(true)
| ~ esk9168_4(true,true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(185,plain,
( ( ~ p(true)
| ~ p(true)
| esk1_0
| ~ p(true)
| ~ p(true)
| ~ esk9168_4(true,true,true,true) )
<=> ( esk1_0
| ~ p(true)
| ~ esk9168_4(true,true,true,true) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(186,plain,
( ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) )
| ~ p(true)
| ~ p(true)
| esk1_0
| ~ p(true)
| ~ p(true)
| ~ esk9168_4(true,true,true,true) )
<=> ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) )
| esk1_0
| ~ p(true)
| ~ esk9168_4(true,true,true,true) ) ),
inference(monotonicity,[status(thm)],[185]) ).
tff(187,plain,
( ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) )
| ~ p(true)
| ~ p(true)
| esk1_0
| ~ p(true)
| ~ p(true)
| ~ esk9168_4(true,true,true,true) )
<=> ( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) )
| esk1_0
| ~ p(true)
| ~ esk9168_4(true,true,true,true) ) ),
inference(transitivity,[status(thm)],[186,184]) ).
tff(188,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) )
| ~ p(true)
| ~ p(true)
| esk1_0
| ~ p(true)
| ~ p(true)
| ~ esk9168_4(true,true,true,true) ),
inference(quant_inst,[status(thm)],[]) ).
tff(189,plain,
( ~ ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| esk1_0
| ~ p(X4)
| ~ p(X2)
| ~ esk9168_4(X1,X2,X3,X4) )
| esk1_0
| ~ p(true)
| ~ esk9168_4(true,true,true,true) ),
inference(modus_ponens,[status(thm)],[188,187]) ).
tff(190,plain,
$false,
inference(unit_resolution,[status(thm)],[189,97,183,34,173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : HWV069-1 : TPTP v9.0.0. Bugfixed v5.5.1.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 17:34:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 7.23/7.41 % SZS status Unsatisfiable
% 7.23/7.41 % SZS output start Proof
% See solution above
% 8.07/8.26 % E exiting
%------------------------------------------------------------------------------