TSTP Solution File: HWV061-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV061-1 : TPTP v8.1.0. Bugfixed v5.5.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 02:15:38 EDT 2022
% Result : Unsatisfiable 27.66s 20.43s
% Output : Proof 29.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 61
% Syntax : Number of formulae : 126 ( 24 unt; 11 typ; 0 def)
% Number of atoms : 750 ( 0 equ)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 1107 ( 538 ~; 494 |; 0 &)
% ( 75 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 66 ( 66 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 8 >; 14 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 4 prp; 0-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 408 ( 366 !; 0 ?; 408 :)
% Comments :
%------------------------------------------------------------------------------
tff(esk27894_3_type,type,
esk27894_3: ( $i * $i * $i ) > $o ).
tff(true_type,type,
true: $i ).
tff(esk16605_3_type,type,
esk16605_3: ( $i * $i * $i ) > $o ).
tff(esk16546_3_type,type,
esk16546_3: ( $i * $i * $i ) > $o ).
tff(esk19872_3_type,type,
esk19872_3: ( $i * $i * $i ) > $o ).
tff(esk17210_3_type,type,
esk17210_3: ( $i * $i * $i ) > $o ).
tff(esk17269_3_type,type,
esk17269_3: ( $i * $i * $i ) > $o ).
tff(esk27959_3_type,type,
esk27959_3: ( $i * $i * $i ) > $o ).
tff(p_type,type,
p: $i > $o ).
tff(esk2_0_type,type,
esk2_0: $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)
| esk27959_3(X1,X2,X3) )
<=> ( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| esk27959_3(X1,X2,X3) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| esk27959_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| esk27959_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)
| esk27959_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| esk27959_3(X1,X2,X3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [X3: $i,X2: $i,X1: $i] :
trans(
monotonicity(
trans(
monotonicity(
iff_true(asserted(esk2_0),
( esk2_0
<=> $true )),
( ~ esk2_0
<=> ~ $true )),
rewrite(
( ~ $true
<=> $false )),
( ~ esk2_0
<=> $false )),
( ( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk27959_3(X1,X2,X3) )
<=> ( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| $false
| esk27959_3(X1,X2,X3) ) )),
rewrite(
( ( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| $false
| esk27959_3(X1,X2,X3) )
<=> ( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| esk27959_3(X1,X2,X3) ) )),
( ( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk27959_3(X1,X2,X3) )
<=> ( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| esk27959_3(X1,X2,X3) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk27959_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| esk27959_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
^ [X3: $i,X2: $i,X1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ esk2_0
| ~ p(X2)
| ~ p(X1) )
<=> ( ~ p(X2)
| ~ p(X1)
| ~ esk2_0 ) )),
( ( ~ esk2_0
| ~ p(X2)
| ~ p(X1)
| esk27959_3(X1,X2,X3) )
<=> ( ~ p(X2)
| ~ p(X1)
| ~ esk2_0
| esk27959_3(X1,X2,X3) ) )),
rewrite(
( ( ~ p(X2)
| ~ p(X1)
| ~ esk2_0
| esk27959_3(X1,X2,X3) )
<=> ( ~ p(X2)
| ~ p(X1)
| ~ esk2_0
| esk27959_3(X1,X2,X3) ) )),
( ( ~ esk2_0
| ~ p(X2)
| ~ p(X1)
| esk27959_3(X1,X2,X3) )
<=> ( ~ p(X2)
| ~ p(X1)
| ~ esk2_0
| esk27959_3(X1,X2,X3) ) )),
( ( ~ esk2_0
| ~ p(X2)
| ~ p(X1)
| esk27959_3(X1,X2,X3)
| ~ p(X3) )
<=> ( ~ p(X2)
| ~ p(X1)
| ~ esk2_0
| esk27959_3(X1,X2,X3)
| ~ p(X3) ) )),
rewrite(
( ( ~ p(X2)
| ~ p(X1)
| ~ esk2_0
| esk27959_3(X1,X2,X3)
| ~ p(X3) )
<=> ( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk27959_3(X1,X2,X3) ) )),
( ( ~ esk2_0
| ~ p(X2)
| ~ p(X1)
| esk27959_3(X1,X2,X3)
| ~ p(X3) )
<=> ( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk27959_3(X1,X2,X3) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ esk2_0
| ~ p(X2)
| ~ p(X1)
| esk27959_3(X1,X2,X3)
| ~ p(X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk27959_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,axiom,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk2_0
| ~ p(X2)
| ~ p(X1)
| esk27959_3(X1,X2,X3)
| ~ p(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_0_4346) ).
tff(12,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk2_0
| esk27959_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| esk27959_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| esk27959_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[13,6]) ).
tff(15,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| esk27959_3(X1,X2,X3) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| esk27959_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[15,5]) ).
tff(17,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| esk27959_3(X1,X2,X3) )
| ~ p(true)
| esk27959_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| esk27959_3(X1,X2,X3) )
| ~ p(true)
| esk27959_3(true,true,true) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ( ~ p(true)
| ~ p(true)
| ~ p(true)
| esk27959_3(true,true,true) )
<=> ( ~ p(true)
| esk27959_3(true,true,true) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| esk27959_3(X1,X2,X3) )
| ~ p(true)
| ~ p(true)
| ~ p(true)
| esk27959_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| esk27959_3(X1,X2,X3) )
| ~ p(true)
| esk27959_3(true,true,true) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| esk27959_3(X1,X2,X3) )
| ~ p(true)
| ~ p(true)
| ~ p(true)
| esk27959_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| esk27959_3(X1,X2,X3) )
| ~ p(true)
| esk27959_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)
| esk27959_3(X1,X2,X3) )
| ~ p(true)
| ~ p(true)
| ~ p(true)
| esk27959_3(true,true,true) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| esk27959_3(X1,X2,X3) )
| ~ p(true)
| esk27959_3(true,true,true) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
esk27959_3(true,true,true),
inference(unit_resolution,[status(thm)],[22,16,3]) ).
tff(24,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(
( ( ~ esk27959_3(X1,X2,X3)
| esk17269_3(X1,X2,X3) )
<=> ( ~ esk27959_3(X1,X2,X3)
| esk17269_3(X1,X2,X3) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ esk27959_3(X1,X2,X3)
| esk17269_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk27959_3(X1,X2,X3)
| esk17269_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ esk27959_3(X1,X2,X3)
| esk17269_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk27959_3(X1,X2,X3)
| esk17269_3(X1,X2,X3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
^ [X3: $i,X2: $i,X1: $i] :
rewrite(
( ( esk17269_3(X1,X2,X3)
| ~ esk27959_3(X1,X2,X3) )
<=> ( ~ esk27959_3(X1,X2,X3)
| esk17269_3(X1,X2,X3) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( esk17269_3(X1,X2,X3)
| ~ esk27959_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk27959_3(X1,X2,X3)
| esk17269_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [X3: $i,X2: $i,X1: $i] :
( esk17269_3(X1,X2,X3)
| ~ esk27959_3(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_0_70759) ).
tff(30,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk27959_3(X1,X2,X3)
| esk17269_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk27959_3(X1,X2,X3)
| esk17269_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk27959_3(X1,X2,X3)
| esk17269_3(X1,X2,X3) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk27959_3(X1,X2,X3)
| esk17269_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk27959_3(X1,X2,X3)
| esk17269_3(X1,X2,X3) )
| ~ esk27959_3(true,true,true)
| esk17269_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk27959_3(X1,X2,X3)
| esk17269_3(X1,X2,X3) )
| ~ esk27959_3(true,true,true)
| esk17269_3(true,true,true) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk27959_3(X1,X2,X3)
| esk17269_3(X1,X2,X3) )
| ~ esk27959_3(true,true,true)
| esk17269_3(true,true,true) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk27959_3(X1,X2,X3)
| esk17269_3(X1,X2,X3) )
| ~ esk27959_3(true,true,true)
| esk17269_3(true,true,true) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
esk17269_3(true,true,true),
inference(unit_resolution,[status(thm)],[36,33,23]) ).
tff(38,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(
( ( ~ esk17269_3(X1,X2,X3)
| esk17210_3(X1,X2,X3) )
<=> ( ~ esk17269_3(X1,X2,X3)
| esk17210_3(X1,X2,X3) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ esk17269_3(X1,X2,X3)
| esk17210_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk17269_3(X1,X2,X3)
| esk17210_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ esk17269_3(X1,X2,X3)
| esk17210_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk17269_3(X1,X2,X3)
| esk17210_3(X1,X2,X3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,axiom,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk17269_3(X1,X2,X3)
| esk17210_3(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_0_48155) ).
tff(42,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk17269_3(X1,X2,X3)
| esk17210_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk17269_3(X1,X2,X3)
| esk17210_3(X1,X2,X3) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk17269_3(X1,X2,X3)
| esk17210_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk17269_3(X1,X2,X3)
| esk17210_3(X1,X2,X3) )
| ~ esk17269_3(true,true,true)
| esk17210_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk17269_3(X1,X2,X3)
| esk17210_3(X1,X2,X3) )
| ~ esk17269_3(true,true,true)
| esk17210_3(true,true,true) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk17269_3(X1,X2,X3)
| esk17210_3(X1,X2,X3) )
| ~ esk17269_3(true,true,true)
| esk17210_3(true,true,true) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk17269_3(X1,X2,X3)
| esk17210_3(X1,X2,X3) )
| ~ esk17269_3(true,true,true)
| esk17210_3(true,true,true) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
esk17210_3(true,true,true),
inference(unit_resolution,[status(thm)],[47,44,37]) ).
tff(49,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(
( ( ~ esk17210_3(X1,X2,X3)
| esk19872_3(X1,X2,X3) )
<=> ( ~ esk17210_3(X1,X2,X3)
| esk19872_3(X1,X2,X3) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ esk17210_3(X1,X2,X3)
| esk19872_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk17210_3(X1,X2,X3)
| esk19872_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ esk17210_3(X1,X2,X3)
| esk19872_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk17210_3(X1,X2,X3)
| esk19872_3(X1,X2,X3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,axiom,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk17210_3(X1,X2,X3)
| esk19872_3(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_0_50171) ).
tff(53,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk17210_3(X1,X2,X3)
| esk19872_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk17210_3(X1,X2,X3)
| esk19872_3(X1,X2,X3) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk17210_3(X1,X2,X3)
| esk19872_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk17210_3(X1,X2,X3)
| esk19872_3(X1,X2,X3) )
| ~ esk17210_3(true,true,true)
| esk19872_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk17210_3(X1,X2,X3)
| esk19872_3(X1,X2,X3) )
| ~ esk17210_3(true,true,true)
| esk19872_3(true,true,true) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk17210_3(X1,X2,X3)
| esk19872_3(X1,X2,X3) )
| ~ esk17210_3(true,true,true)
| esk19872_3(true,true,true) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk17210_3(X1,X2,X3)
| esk19872_3(X1,X2,X3) )
| ~ esk17210_3(true,true,true)
| esk19872_3(true,true,true) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
esk19872_3(true,true,true),
inference(unit_resolution,[status(thm)],[58,55,48]) ).
tff(60,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(
( ( ~ esk19872_3(X1,X2,X3)
| esk16546_3(X1,X2,X3) )
<=> ( ~ esk19872_3(X1,X2,X3)
| esk16546_3(X1,X2,X3) ) )),
inference(bind,[status(th)],]) ).
tff(61,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ esk19872_3(X1,X2,X3)
| esk16546_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk19872_3(X1,X2,X3)
| esk16546_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ esk19872_3(X1,X2,X3)
| esk16546_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk19872_3(X1,X2,X3)
| esk16546_3(X1,X2,X3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,axiom,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk19872_3(X1,X2,X3)
| esk16546_3(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_0_40292) ).
tff(64,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk19872_3(X1,X2,X3)
| esk16546_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk19872_3(X1,X2,X3)
| esk16546_3(X1,X2,X3) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk19872_3(X1,X2,X3)
| esk16546_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk19872_3(X1,X2,X3)
| esk16546_3(X1,X2,X3) )
| ~ esk19872_3(true,true,true)
| esk16546_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk19872_3(X1,X2,X3)
| esk16546_3(X1,X2,X3) )
| ~ esk19872_3(true,true,true)
| esk16546_3(true,true,true) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk19872_3(X1,X2,X3)
| esk16546_3(X1,X2,X3) )
| ~ esk19872_3(true,true,true)
| esk16546_3(true,true,true) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk19872_3(X1,X2,X3)
| esk16546_3(X1,X2,X3) )
| ~ esk19872_3(true,true,true)
| esk16546_3(true,true,true) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
esk16546_3(true,true,true),
inference(unit_resolution,[status(thm)],[69,66,59]) ).
tff(71,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(
( ( ~ esk16546_3(X1,X2,X3)
| esk16605_3(X1,X2,X3) )
<=> ( ~ esk16546_3(X1,X2,X3)
| esk16605_3(X1,X2,X3) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16546_3(X1,X2,X3)
| esk16605_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16546_3(X1,X2,X3)
| esk16605_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16546_3(X1,X2,X3)
| esk16605_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16546_3(X1,X2,X3)
| esk16605_3(X1,X2,X3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
^ [X3: $i,X2: $i,X1: $i] :
rewrite(
( ( esk16605_3(X1,X2,X3)
| ~ esk16546_3(X1,X2,X3) )
<=> ( ~ esk16546_3(X1,X2,X3)
| esk16605_3(X1,X2,X3) ) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( esk16605_3(X1,X2,X3)
| ~ esk16546_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16546_3(X1,X2,X3)
| esk16605_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,axiom,
! [X3: $i,X2: $i,X1: $i] :
( esk16605_3(X1,X2,X3)
| ~ esk16546_3(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_0_21546) ).
tff(77,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk16546_3(X1,X2,X3)
| esk16605_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk16546_3(X1,X2,X3)
| esk16605_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk16546_3(X1,X2,X3)
| esk16605_3(X1,X2,X3) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk16546_3(X1,X2,X3)
| esk16605_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[79,72]) ).
tff(81,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16546_3(X1,X2,X3)
| esk16605_3(X1,X2,X3) )
| ~ esk16546_3(true,true,true)
| esk16605_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16546_3(X1,X2,X3)
| esk16605_3(X1,X2,X3) )
| ~ esk16546_3(true,true,true)
| esk16605_3(true,true,true) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16546_3(X1,X2,X3)
| esk16605_3(X1,X2,X3) )
| ~ esk16546_3(true,true,true)
| esk16605_3(true,true,true) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16546_3(X1,X2,X3)
| esk16605_3(X1,X2,X3) )
| ~ esk16546_3(true,true,true)
| esk16605_3(true,true,true) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
esk16605_3(true,true,true),
inference(unit_resolution,[status(thm)],[83,80,70]) ).
tff(85,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(
( ( ~ esk16605_3(X1,X2,X3)
| esk27894_3(X1,X2,X3) )
<=> ( ~ esk16605_3(X1,X2,X3)
| esk27894_3(X1,X2,X3) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16605_3(X1,X2,X3)
| esk27894_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16605_3(X1,X2,X3)
| esk27894_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16605_3(X1,X2,X3)
| esk27894_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16605_3(X1,X2,X3)
| esk27894_3(X1,X2,X3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,axiom,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk16605_3(X1,X2,X3)
| esk27894_3(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_0_24888) ).
tff(89,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk16605_3(X1,X2,X3)
| esk27894_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk16605_3(X1,X2,X3)
| esk27894_3(X1,X2,X3) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ esk16605_3(X1,X2,X3)
| esk27894_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16605_3(X1,X2,X3)
| esk27894_3(X1,X2,X3) )
| ~ esk16605_3(true,true,true)
| esk27894_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16605_3(X1,X2,X3)
| esk27894_3(X1,X2,X3) )
| ~ esk16605_3(true,true,true)
| esk27894_3(true,true,true) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16605_3(X1,X2,X3)
| esk27894_3(X1,X2,X3) )
| ~ esk16605_3(true,true,true)
| esk27894_3(true,true,true) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ esk16605_3(X1,X2,X3)
| esk27894_3(X1,X2,X3) )
| ~ esk16605_3(true,true,true)
| esk27894_3(true,true,true) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
esk27894_3(true,true,true),
inference(unit_resolution,[status(thm)],[94,91,84]) ).
tff(96,plain,
^ [X3: $i,X2: $i,X1: $i] :
refl(
( ( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) )
<=> ( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) ) )),
inference(bind,[status(th)],]) ).
tff(97,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
^ [X3: $i,X2: $i,X1: $i] :
trans(
monotonicity(
iff_false(asserted(~ esk1_0),
( esk1_0
<=> $false )),
( ( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) )
<=> ( $false
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) ) )),
rewrite(
( ( $false
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) )
<=> ( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) ) )),
( ( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) )
<=> ( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) ) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,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)
| ~ p(X2) )
<=> ( ~ p(X1)
| ~ p(X3)
| ~ p(X2) ) )),
rewrite(
( ( ~ p(X1)
| ~ p(X3)
| ~ p(X2) )
<=> ( ~ p(X2)
| ~ p(X1)
| ~ p(X3) ) )),
( ( ~ p(X3)
| ~ p(X1)
| ~ p(X2) )
<=> ( ~ p(X2)
| ~ p(X1)
| ~ p(X3) ) )),
( ( ~ p(X3)
| ~ p(X1)
| ~ p(X2)
| esk1_0 )
<=> ( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| esk1_0 ) )),
rewrite(
( ( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| esk1_0 )
<=> ( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3) ) )),
( ( ~ p(X3)
| ~ p(X1)
| ~ p(X2)
| esk1_0 )
<=> ( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3) ) )),
( ( ~ p(X3)
| ~ p(X1)
| ~ p(X2)
| esk1_0
| ~ esk27894_3(X1,X2,X3) )
<=> ( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) ) )),
rewrite(
( ( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) )
<=> ( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) ) )),
( ( ~ p(X3)
| ~ p(X1)
| ~ p(X2)
| esk1_0
| ~ esk27894_3(X1,X2,X3) )
<=> ( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) ) )),
inference(bind,[status(th)],]) ).
tff(102,plain,
( ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ p(X2)
| esk1_0
| ~ esk27894_3(X1,X2,X3) )
<=> ! [X3: $i,X2: $i,X1: $i] :
( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,axiom,
! [X3: $i,X2: $i,X1: $i] :
( ~ p(X3)
| ~ p(X1)
| ~ p(X2)
| esk1_0
| ~ esk27894_3(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_0_44121) ).
tff(104,plain,
! [X3: $i,X2: $i,X1: $i] :
( esk1_0
| ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[105,98]) ).
tff(107,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) ),
inference(skolemize,[status(sab)],[106]) ).
tff(108,plain,
! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) ),
inference(modus_ponens,[status(thm)],[107,97]) ).
tff(109,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) )
| ~ p(true)
| ~ esk27894_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) )
| ~ p(true)
| ~ esk27894_3(true,true,true) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( ( ~ p(true)
| ~ p(true)
| ~ p(true)
| ~ esk27894_3(true,true,true) )
<=> ( ~ p(true)
| ~ esk27894_3(true,true,true) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) )
| ~ p(true)
| ~ p(true)
| ~ p(true)
| ~ esk27894_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) )
| ~ p(true)
| ~ esk27894_3(true,true,true) ) ),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
( ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) )
| ~ p(true)
| ~ p(true)
| ~ p(true)
| ~ esk27894_3(true,true,true) )
<=> ( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) )
| ~ p(true)
| ~ esk27894_3(true,true,true) ) ),
inference(transitivity,[status(thm)],[111,109]) ).
tff(113,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) )
| ~ p(true)
| ~ p(true)
| ~ p(true)
| ~ esk27894_3(true,true,true) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
( ~ ! [X3: $i,X2: $i,X1: $i] :
( ~ p(X2)
| ~ p(X1)
| ~ p(X3)
| ~ esk27894_3(X1,X2,X3) )
| ~ p(true)
| ~ esk27894_3(true,true,true) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
$false,
inference(unit_resolution,[status(thm)],[114,108,3,95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HWV061-1 : TPTP v8.1.0. Bugfixed v5.5.1.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n020.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 : Wed Aug 31 23:32:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 27.66/20.43 % SZS status Unsatisfiable
% 27.66/20.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------