TSTP Solution File: SYN100-1.005 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN100-1.005 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 : Thu Sep 29 23:53:45 EDT 2022
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 123
% Syntax : Number of formulae : 258 ( 53 unt; 19 typ; 0 def)
% Number of atoms : 1220 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 1812 ( 862 ~; 844 |; 0 &)
% ( 106 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 31 ( 31 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of predicates : 21 ( 20 usr; 1 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 280 ( 249 !; 0 ?; 280 :)
% Comments :
%------------------------------------------------------------------------------
tff(p_0_type,type,
p_0: $i > $o ).
tff(a_type,type,
a: $i ).
tff(q_1_type,type,
q_1: $i > $o ).
tff(p_2_type,type,
p_2: $i > $o ).
tff(q_3_type,type,
q_3: $i > $o ).
tff(p_4_type,type,
p_4: $i > $o ).
tff(q_5_type,type,
q_5: $i > $o ).
tff(p_6_type,type,
p_6: $i > $o ).
tff(q_7_type,type,
q_7: $i > $o ).
tff(q_9_type,type,
q_9: $i > $o ).
tff(p_8_type,type,
p_8: $i > $o ).
tff(q_8_type,type,
q_8: $i > $o ).
tff(q_6_type,type,
q_6: $i > $o ).
tff(q_4_type,type,
q_4: $i > $o ).
tff(p_5_type,type,
p_5: $i > $o ).
tff(q_2_type,type,
q_2: $i > $o ).
tff(p_3_type,type,
p_3: $i > $o ).
tff(q_0_type,type,
q_0: $i > $o ).
tff(p_1_type,type,
p_1: $i > $o ).
tff(1,plain,
( q_9(a)
<=> q_9(a) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
q_9(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_t3_4) ).
tff(3,plain,
q_9(a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( p_8(a)
<=> p_8(a) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
p_8(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_t3_1) ).
tff(6,plain,
p_8(a),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [X: $i] :
refl(
( ( q_7(X)
| ~ p_8(X)
| ~ q_9(X) )
<=> ( q_7(X)
| ~ p_8(X)
| ~ q_9(X) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [X: $i] :
( q_7(X)
| ~ p_8(X)
| ~ q_9(X) )
<=> ! [X: $i] :
( q_7(X)
| ~ p_8(X)
| ~ q_9(X) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [X: $i] :
( q_7(X)
| ~ p_8(X)
| ~ q_9(X) )
<=> ! [X: $i] :
( q_7(X)
| ~ p_8(X)
| ~ q_9(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
^ [X: $i] :
rewrite(
( ( q_7(X)
| ~ p_8(X)
| ~ q_9(X) )
<=> ( q_7(X)
| ~ p_8(X)
| ~ q_9(X) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] :
( q_7(X)
| ~ p_8(X)
| ~ q_9(X) )
<=> ! [X: $i] :
( q_7(X)
| ~ p_8(X)
| ~ q_9(X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [X: $i] :
( q_7(X)
| ~ p_8(X)
| ~ q_9(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type12_15) ).
tff(13,plain,
! [X: $i] :
( q_7(X)
| ~ p_8(X)
| ~ q_9(X) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [X: $i] :
( q_7(X)
| ~ p_8(X)
| ~ q_9(X) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [X: $i] :
( q_7(X)
| ~ p_8(X)
| ~ q_9(X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] :
( q_7(X)
| ~ p_8(X)
| ~ q_9(X) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [X: $i] :
( q_7(X)
| ~ p_8(X)
| ~ q_9(X) )
| q_7(a)
| ~ p_8(a)
| ~ q_9(a) )
<=> ( ~ ! [X: $i] :
( q_7(X)
| ~ p_8(X)
| ~ q_9(X) )
| q_7(a)
| ~ p_8(a)
| ~ q_9(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [X: $i] :
( q_7(X)
| ~ p_8(X)
| ~ q_9(X) )
| q_7(a)
| ~ p_8(a)
| ~ q_9(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [X: $i] :
( q_7(X)
| ~ p_8(X)
| ~ q_9(X) )
| q_7(a)
| ~ p_8(a)
| ~ q_9(a) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
q_7(a),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
( q_8(a)
<=> q_8(a) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
q_8(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_t3_3) ).
tff(23,plain,
q_8(a),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [X: $i] :
refl(
( ( p_6(X)
| ~ q_7(X)
| ~ q_8(X) )
<=> ( p_6(X)
| ~ q_7(X)
| ~ q_8(X) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [X: $i] :
( p_6(X)
| ~ q_7(X)
| ~ q_8(X) )
<=> ! [X: $i] :
( p_6(X)
| ~ q_7(X)
| ~ q_8(X) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [X: $i] :
( p_6(X)
| ~ q_7(X)
| ~ q_8(X) )
<=> ! [X: $i] :
( p_6(X)
| ~ q_7(X)
| ~ q_8(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
^ [X: $i] :
rewrite(
( ( p_6(X)
| ~ q_7(X)
| ~ q_8(X) )
<=> ( p_6(X)
| ~ q_7(X)
| ~ q_8(X) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [X: $i] :
( p_6(X)
| ~ q_7(X)
| ~ q_8(X) )
<=> ! [X: $i] :
( p_6(X)
| ~ q_7(X)
| ~ q_8(X) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [X: $i] :
( p_6(X)
| ~ q_7(X)
| ~ q_8(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type11_14) ).
tff(30,plain,
! [X: $i] :
( p_6(X)
| ~ q_7(X)
| ~ q_8(X) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [X: $i] :
( p_6(X)
| ~ q_7(X)
| ~ q_8(X) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [X: $i] :
( p_6(X)
| ~ q_7(X)
| ~ q_8(X) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [X: $i] :
( p_6(X)
| ~ q_7(X)
| ~ q_8(X) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [X: $i] :
( p_6(X)
| ~ q_7(X)
| ~ q_8(X) )
| p_6(a)
| ~ q_7(a)
| ~ q_8(a) )
<=> ( ~ ! [X: $i] :
( p_6(X)
| ~ q_7(X)
| ~ q_8(X) )
| p_6(a)
| ~ q_7(a)
| ~ q_8(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ~ ! [X: $i] :
( p_6(X)
| ~ q_7(X)
| ~ q_8(X) )
| p_6(a)
| ~ q_7(a)
| ~ q_8(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ~ ! [X: $i] :
( p_6(X)
| ~ q_7(X)
| ~ q_8(X) )
| p_6(a)
| ~ q_7(a)
| ~ q_8(a) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
p_6(a),
inference(unit_resolution,[status(thm)],[36,33,23,20]) ).
tff(38,plain,
^ [X: $i] :
refl(
( ( q_5(X)
| ~ p_6(X)
| ~ q_7(X) )
<=> ( q_5(X)
| ~ p_6(X)
| ~ q_7(X) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [X: $i] :
( q_5(X)
| ~ p_6(X)
| ~ q_7(X) )
<=> ! [X: $i] :
( q_5(X)
| ~ p_6(X)
| ~ q_7(X) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [X: $i] :
( q_5(X)
| ~ p_6(X)
| ~ q_7(X) )
<=> ! [X: $i] :
( q_5(X)
| ~ p_6(X)
| ~ q_7(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
^ [X: $i] :
rewrite(
( ( q_5(X)
| ~ p_6(X)
| ~ q_7(X) )
<=> ( q_5(X)
| ~ p_6(X)
| ~ q_7(X) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [X: $i] :
( q_5(X)
| ~ p_6(X)
| ~ q_7(X) )
<=> ! [X: $i] :
( q_5(X)
| ~ p_6(X)
| ~ q_7(X) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [X: $i] :
( q_5(X)
| ~ p_6(X)
| ~ q_7(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type12_11) ).
tff(44,plain,
! [X: $i] :
( q_5(X)
| ~ p_6(X)
| ~ q_7(X) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [X: $i] :
( q_5(X)
| ~ p_6(X)
| ~ q_7(X) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [X: $i] :
( q_5(X)
| ~ p_6(X)
| ~ q_7(X) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [X: $i] :
( q_5(X)
| ~ p_6(X)
| ~ q_7(X) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ( ~ ! [X: $i] :
( q_5(X)
| ~ p_6(X)
| ~ q_7(X) )
| q_5(a)
| ~ p_6(a)
| ~ q_7(a) )
<=> ( ~ ! [X: $i] :
( q_5(X)
| ~ p_6(X)
| ~ q_7(X) )
| q_5(a)
| ~ p_6(a)
| ~ q_7(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ~ ! [X: $i] :
( q_5(X)
| ~ p_6(X)
| ~ q_7(X) )
| q_5(a)
| ~ p_6(a)
| ~ q_7(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
( ~ ! [X: $i] :
( q_5(X)
| ~ p_6(X)
| ~ q_7(X) )
| q_5(a)
| ~ p_6(a)
| ~ q_7(a) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
q_5(a),
inference(unit_resolution,[status(thm)],[50,47,20,37]) ).
tff(52,plain,
^ [X: $i] :
refl(
( ( q_6(X)
| ~ q_7(X)
| ~ p_8(X) )
<=> ( q_6(X)
| ~ q_7(X)
| ~ p_8(X) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [X: $i] :
( q_6(X)
| ~ q_7(X)
| ~ p_8(X) )
<=> ! [X: $i] :
( q_6(X)
| ~ q_7(X)
| ~ p_8(X) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [X: $i] :
( q_6(X)
| ~ q_7(X)
| ~ p_8(X) )
<=> ! [X: $i] :
( q_6(X)
| ~ q_7(X)
| ~ p_8(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
^ [X: $i] :
rewrite(
( ( q_6(X)
| ~ q_7(X)
| ~ p_8(X) )
<=> ( q_6(X)
| ~ q_7(X)
| ~ p_8(X) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [X: $i] :
( q_6(X)
| ~ q_7(X)
| ~ p_8(X) )
<=> ! [X: $i] :
( q_6(X)
| ~ q_7(X)
| ~ p_8(X) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,axiom,
! [X: $i] :
( q_6(X)
| ~ q_7(X)
| ~ p_8(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type12_14) ).
tff(58,plain,
! [X: $i] :
( q_6(X)
| ~ q_7(X)
| ~ p_8(X) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [X: $i] :
( q_6(X)
| ~ q_7(X)
| ~ p_8(X) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
! [X: $i] :
( q_6(X)
| ~ q_7(X)
| ~ p_8(X) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [X: $i] :
( q_6(X)
| ~ q_7(X)
| ~ p_8(X) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
( ( ~ ! [X: $i] :
( q_6(X)
| ~ q_7(X)
| ~ p_8(X) )
| ~ p_8(a)
| q_6(a)
| ~ q_7(a) )
<=> ( ~ ! [X: $i] :
( q_6(X)
| ~ q_7(X)
| ~ p_8(X) )
| ~ p_8(a)
| q_6(a)
| ~ q_7(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ( q_6(a)
| ~ q_7(a)
| ~ p_8(a) )
<=> ( ~ p_8(a)
| q_6(a)
| ~ q_7(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
( ( ~ ! [X: $i] :
( q_6(X)
| ~ q_7(X)
| ~ p_8(X) )
| q_6(a)
| ~ q_7(a)
| ~ p_8(a) )
<=> ( ~ ! [X: $i] :
( q_6(X)
| ~ q_7(X)
| ~ p_8(X) )
| ~ p_8(a)
| q_6(a)
| ~ q_7(a) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( ~ ! [X: $i] :
( q_6(X)
| ~ q_7(X)
| ~ p_8(X) )
| q_6(a)
| ~ q_7(a)
| ~ p_8(a) )
<=> ( ~ ! [X: $i] :
( q_6(X)
| ~ q_7(X)
| ~ p_8(X) )
| ~ p_8(a)
| q_6(a)
| ~ q_7(a) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
( ~ ! [X: $i] :
( q_6(X)
| ~ q_7(X)
| ~ p_8(X) )
| q_6(a)
| ~ q_7(a)
| ~ p_8(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
( ~ ! [X: $i] :
( q_6(X)
| ~ q_7(X)
| ~ p_8(X) )
| ~ p_8(a)
| q_6(a)
| ~ q_7(a) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
q_6(a),
inference(unit_resolution,[status(thm)],[67,61,6,20]) ).
tff(69,plain,
^ [X: $i] :
refl(
( ( p_4(X)
| ~ q_5(X)
| ~ q_6(X) )
<=> ( p_4(X)
| ~ q_5(X)
| ~ q_6(X) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [X: $i] :
( p_4(X)
| ~ q_5(X)
| ~ q_6(X) )
<=> ! [X: $i] :
( p_4(X)
| ~ q_5(X)
| ~ q_6(X) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [X: $i] :
( p_4(X)
| ~ q_5(X)
| ~ q_6(X) )
<=> ! [X: $i] :
( p_4(X)
| ~ q_5(X)
| ~ q_6(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
^ [X: $i] :
rewrite(
( ( p_4(X)
| ~ q_5(X)
| ~ q_6(X) )
<=> ( p_4(X)
| ~ q_5(X)
| ~ q_6(X) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [X: $i] :
( p_4(X)
| ~ q_5(X)
| ~ q_6(X) )
<=> ! [X: $i] :
( p_4(X)
| ~ q_5(X)
| ~ q_6(X) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,axiom,
! [X: $i] :
( p_4(X)
| ~ q_5(X)
| ~ q_6(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type11_10) ).
tff(75,plain,
! [X: $i] :
( p_4(X)
| ~ q_5(X)
| ~ q_6(X) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [X: $i] :
( p_4(X)
| ~ q_5(X)
| ~ q_6(X) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
! [X: $i] :
( p_4(X)
| ~ q_5(X)
| ~ q_6(X) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [X: $i] :
( p_4(X)
| ~ q_5(X)
| ~ q_6(X) ),
inference(modus_ponens,[status(thm)],[77,70]) ).
tff(79,plain,
( ( ~ ! [X: $i] :
( p_4(X)
| ~ q_5(X)
| ~ q_6(X) )
| p_4(a)
| ~ q_5(a)
| ~ q_6(a) )
<=> ( ~ ! [X: $i] :
( p_4(X)
| ~ q_5(X)
| ~ q_6(X) )
| p_4(a)
| ~ q_5(a)
| ~ q_6(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ~ ! [X: $i] :
( p_4(X)
| ~ q_5(X)
| ~ q_6(X) )
| p_4(a)
| ~ q_5(a)
| ~ q_6(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
( ~ ! [X: $i] :
( p_4(X)
| ~ q_5(X)
| ~ q_6(X) )
| p_4(a)
| ~ q_5(a)
| ~ q_6(a) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
p_4(a),
inference(unit_resolution,[status(thm)],[81,78,68,51]) ).
tff(83,plain,
^ [X: $i] :
refl(
( ( q_3(X)
| ~ p_4(X)
| ~ q_5(X) )
<=> ( q_3(X)
| ~ p_4(X)
| ~ q_5(X) ) )),
inference(bind,[status(th)],]) ).
tff(84,plain,
( ! [X: $i] :
( q_3(X)
| ~ p_4(X)
| ~ q_5(X) )
<=> ! [X: $i] :
( q_3(X)
| ~ p_4(X)
| ~ q_5(X) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [X: $i] :
( q_3(X)
| ~ p_4(X)
| ~ q_5(X) )
<=> ! [X: $i] :
( q_3(X)
| ~ p_4(X)
| ~ q_5(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
^ [X: $i] :
rewrite(
( ( q_3(X)
| ~ p_4(X)
| ~ q_5(X) )
<=> ( q_3(X)
| ~ p_4(X)
| ~ q_5(X) ) )),
inference(bind,[status(th)],]) ).
tff(87,plain,
( ! [X: $i] :
( q_3(X)
| ~ p_4(X)
| ~ q_5(X) )
<=> ! [X: $i] :
( q_3(X)
| ~ p_4(X)
| ~ q_5(X) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,axiom,
! [X: $i] :
( q_3(X)
| ~ p_4(X)
| ~ q_5(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type12_7) ).
tff(89,plain,
! [X: $i] :
( q_3(X)
| ~ p_4(X)
| ~ q_5(X) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [X: $i] :
( q_3(X)
| ~ p_4(X)
| ~ q_5(X) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
! [X: $i] :
( q_3(X)
| ~ p_4(X)
| ~ q_5(X) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [X: $i] :
( q_3(X)
| ~ p_4(X)
| ~ q_5(X) ),
inference(modus_ponens,[status(thm)],[91,84]) ).
tff(93,plain,
( ( ~ ! [X: $i] :
( q_3(X)
| ~ p_4(X)
| ~ q_5(X) )
| q_3(a)
| ~ p_4(a)
| ~ q_5(a) )
<=> ( ~ ! [X: $i] :
( q_3(X)
| ~ p_4(X)
| ~ q_5(X) )
| q_3(a)
| ~ p_4(a)
| ~ q_5(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ~ ! [X: $i] :
( q_3(X)
| ~ p_4(X)
| ~ q_5(X) )
| q_3(a)
| ~ p_4(a)
| ~ q_5(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
( ~ ! [X: $i] :
( q_3(X)
| ~ p_4(X)
| ~ q_5(X) )
| q_3(a)
| ~ p_4(a)
| ~ q_5(a) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
q_3(a),
inference(unit_resolution,[status(thm)],[95,92,51,82]) ).
tff(97,plain,
^ [X: $i] :
refl(
( ( p_5(X)
| ~ q_6(X)
| ~ q_7(X) )
<=> ( p_5(X)
| ~ q_6(X)
| ~ q_7(X) ) )),
inference(bind,[status(th)],]) ).
tff(98,plain,
( ! [X: $i] :
( p_5(X)
| ~ q_6(X)
| ~ q_7(X) )
<=> ! [X: $i] :
( p_5(X)
| ~ q_6(X)
| ~ q_7(X) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
( ! [X: $i] :
( p_5(X)
| ~ q_6(X)
| ~ q_7(X) )
<=> ! [X: $i] :
( p_5(X)
| ~ q_6(X)
| ~ q_7(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
^ [X: $i] :
rewrite(
( ( p_5(X)
| ~ q_6(X)
| ~ q_7(X) )
<=> ( p_5(X)
| ~ q_6(X)
| ~ q_7(X) ) )),
inference(bind,[status(th)],]) ).
tff(101,plain,
( ! [X: $i] :
( p_5(X)
| ~ q_6(X)
| ~ q_7(X) )
<=> ! [X: $i] :
( p_5(X)
| ~ q_6(X)
| ~ q_7(X) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,axiom,
! [X: $i] :
( p_5(X)
| ~ q_6(X)
| ~ q_7(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type11_12) ).
tff(103,plain,
! [X: $i] :
( p_5(X)
| ~ q_6(X)
| ~ q_7(X) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
! [X: $i] :
( p_5(X)
| ~ q_6(X)
| ~ q_7(X) ),
inference(modus_ponens,[status(thm)],[103,99]) ).
tff(105,plain,
! [X: $i] :
( p_5(X)
| ~ q_6(X)
| ~ q_7(X) ),
inference(skolemize,[status(sab)],[104]) ).
tff(106,plain,
! [X: $i] :
( p_5(X)
| ~ q_6(X)
| ~ q_7(X) ),
inference(modus_ponens,[status(thm)],[105,98]) ).
tff(107,plain,
( ( ~ ! [X: $i] :
( p_5(X)
| ~ q_6(X)
| ~ q_7(X) )
| p_5(a)
| ~ q_6(a)
| ~ q_7(a) )
<=> ( ~ ! [X: $i] :
( p_5(X)
| ~ q_6(X)
| ~ q_7(X) )
| p_5(a)
| ~ q_6(a)
| ~ q_7(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
( ~ ! [X: $i] :
( p_5(X)
| ~ q_6(X)
| ~ q_7(X) )
| p_5(a)
| ~ q_6(a)
| ~ q_7(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(109,plain,
( ~ ! [X: $i] :
( p_5(X)
| ~ q_6(X)
| ~ q_7(X) )
| p_5(a)
| ~ q_6(a)
| ~ q_7(a) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
p_5(a),
inference(unit_resolution,[status(thm)],[109,106,20,68]) ).
tff(111,plain,
^ [X: $i] :
refl(
( ( q_4(X)
| ~ p_5(X)
| ~ q_6(X) )
<=> ( q_4(X)
| ~ p_5(X)
| ~ q_6(X) ) )),
inference(bind,[status(th)],]) ).
tff(112,plain,
( ! [X: $i] :
( q_4(X)
| ~ p_5(X)
| ~ q_6(X) )
<=> ! [X: $i] :
( q_4(X)
| ~ p_5(X)
| ~ q_6(X) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,plain,
( ! [X: $i] :
( q_4(X)
| ~ p_5(X)
| ~ q_6(X) )
<=> ! [X: $i] :
( q_4(X)
| ~ p_5(X)
| ~ q_6(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
^ [X: $i] :
rewrite(
( ( q_4(X)
| ~ p_5(X)
| ~ q_6(X) )
<=> ( q_4(X)
| ~ p_5(X)
| ~ q_6(X) ) )),
inference(bind,[status(th)],]) ).
tff(115,plain,
( ! [X: $i] :
( q_4(X)
| ~ p_5(X)
| ~ q_6(X) )
<=> ! [X: $i] :
( q_4(X)
| ~ p_5(X)
| ~ q_6(X) ) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,axiom,
! [X: $i] :
( q_4(X)
| ~ p_5(X)
| ~ q_6(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type12_9) ).
tff(117,plain,
! [X: $i] :
( q_4(X)
| ~ p_5(X)
| ~ q_6(X) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
! [X: $i] :
( q_4(X)
| ~ p_5(X)
| ~ q_6(X) ),
inference(modus_ponens,[status(thm)],[117,113]) ).
tff(119,plain,
! [X: $i] :
( q_4(X)
| ~ p_5(X)
| ~ q_6(X) ),
inference(skolemize,[status(sab)],[118]) ).
tff(120,plain,
! [X: $i] :
( q_4(X)
| ~ p_5(X)
| ~ q_6(X) ),
inference(modus_ponens,[status(thm)],[119,112]) ).
tff(121,plain,
( ( ~ ! [X: $i] :
( q_4(X)
| ~ p_5(X)
| ~ q_6(X) )
| q_4(a)
| ~ p_5(a)
| ~ q_6(a) )
<=> ( ~ ! [X: $i] :
( q_4(X)
| ~ p_5(X)
| ~ q_6(X) )
| q_4(a)
| ~ p_5(a)
| ~ q_6(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(122,plain,
( ~ ! [X: $i] :
( q_4(X)
| ~ p_5(X)
| ~ q_6(X) )
| q_4(a)
| ~ p_5(a)
| ~ q_6(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(123,plain,
( ~ ! [X: $i] :
( q_4(X)
| ~ p_5(X)
| ~ q_6(X) )
| q_4(a)
| ~ p_5(a)
| ~ q_6(a) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
q_4(a),
inference(unit_resolution,[status(thm)],[123,120,68,110]) ).
tff(125,plain,
^ [X: $i] :
refl(
( ( p_2(X)
| ~ q_3(X)
| ~ q_4(X) )
<=> ( p_2(X)
| ~ q_3(X)
| ~ q_4(X) ) )),
inference(bind,[status(th)],]) ).
tff(126,plain,
( ! [X: $i] :
( p_2(X)
| ~ q_3(X)
| ~ q_4(X) )
<=> ! [X: $i] :
( p_2(X)
| ~ q_3(X)
| ~ q_4(X) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,plain,
( ! [X: $i] :
( p_2(X)
| ~ q_3(X)
| ~ q_4(X) )
<=> ! [X: $i] :
( p_2(X)
| ~ q_3(X)
| ~ q_4(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(128,plain,
^ [X: $i] :
rewrite(
( ( p_2(X)
| ~ q_3(X)
| ~ q_4(X) )
<=> ( p_2(X)
| ~ q_3(X)
| ~ q_4(X) ) )),
inference(bind,[status(th)],]) ).
tff(129,plain,
( ! [X: $i] :
( p_2(X)
| ~ q_3(X)
| ~ q_4(X) )
<=> ! [X: $i] :
( p_2(X)
| ~ q_3(X)
| ~ q_4(X) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,axiom,
! [X: $i] :
( p_2(X)
| ~ q_3(X)
| ~ q_4(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type11_6) ).
tff(131,plain,
! [X: $i] :
( p_2(X)
| ~ q_3(X)
| ~ q_4(X) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
! [X: $i] :
( p_2(X)
| ~ q_3(X)
| ~ q_4(X) ),
inference(modus_ponens,[status(thm)],[131,127]) ).
tff(133,plain,
! [X: $i] :
( p_2(X)
| ~ q_3(X)
| ~ q_4(X) ),
inference(skolemize,[status(sab)],[132]) ).
tff(134,plain,
! [X: $i] :
( p_2(X)
| ~ q_3(X)
| ~ q_4(X) ),
inference(modus_ponens,[status(thm)],[133,126]) ).
tff(135,plain,
( ( ~ ! [X: $i] :
( p_2(X)
| ~ q_3(X)
| ~ q_4(X) )
| p_2(a)
| ~ q_3(a)
| ~ q_4(a) )
<=> ( ~ ! [X: $i] :
( p_2(X)
| ~ q_3(X)
| ~ q_4(X) )
| p_2(a)
| ~ q_3(a)
| ~ q_4(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(136,plain,
( ~ ! [X: $i] :
( p_2(X)
| ~ q_3(X)
| ~ q_4(X) )
| p_2(a)
| ~ q_3(a)
| ~ q_4(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(137,plain,
( ~ ! [X: $i] :
( p_2(X)
| ~ q_3(X)
| ~ q_4(X) )
| p_2(a)
| ~ q_3(a)
| ~ q_4(a) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
p_2(a),
inference(unit_resolution,[status(thm)],[137,134,124,96]) ).
tff(139,plain,
^ [X: $i] :
refl(
( ( ~ p_2(X)
| q_1(X)
| ~ q_3(X) )
<=> ( ~ p_2(X)
| q_1(X)
| ~ q_3(X) ) )),
inference(bind,[status(th)],]) ).
tff(140,plain,
( ! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) )
<=> ! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) ) ),
inference(quant_intro,[status(thm)],[139]) ).
tff(141,plain,
( ! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) )
<=> ! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(142,plain,
^ [X: $i] :
rewrite(
( ( q_1(X)
| ~ p_2(X)
| ~ q_3(X) )
<=> ( ~ p_2(X)
| q_1(X)
| ~ q_3(X) ) )),
inference(bind,[status(th)],]) ).
tff(143,plain,
( ! [X: $i] :
( q_1(X)
| ~ p_2(X)
| ~ q_3(X) )
<=> ! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) ) ),
inference(quant_intro,[status(thm)],[142]) ).
tff(144,axiom,
! [X: $i] :
( q_1(X)
| ~ p_2(X)
| ~ q_3(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type12_3) ).
tff(145,plain,
! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) ),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) ),
inference(modus_ponens,[status(thm)],[145,141]) ).
tff(147,plain,
! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) ),
inference(skolemize,[status(sab)],[146]) ).
tff(148,plain,
! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) ),
inference(modus_ponens,[status(thm)],[147,140]) ).
tff(149,plain,
( ( ~ ! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) )
| ~ q_3(a)
| ~ p_2(a)
| q_1(a) )
<=> ( ~ ! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) )
| ~ q_3(a)
| ~ p_2(a)
| q_1(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(150,plain,
( ( ~ p_2(a)
| q_1(a)
| ~ q_3(a) )
<=> ( ~ q_3(a)
| ~ p_2(a)
| q_1(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(151,plain,
( ( ~ ! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) )
| ~ p_2(a)
| q_1(a)
| ~ q_3(a) )
<=> ( ~ ! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) )
| ~ q_3(a)
| ~ p_2(a)
| q_1(a) ) ),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
( ( ~ ! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) )
| ~ p_2(a)
| q_1(a)
| ~ q_3(a) )
<=> ( ~ ! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) )
| ~ q_3(a)
| ~ p_2(a)
| q_1(a) ) ),
inference(transitivity,[status(thm)],[151,149]) ).
tff(153,plain,
( ~ ! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) )
| ~ p_2(a)
| q_1(a)
| ~ q_3(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(154,plain,
( ~ ! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) )
| ~ q_3(a)
| ~ p_2(a)
| q_1(a) ),
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
q_1(a),
inference(unit_resolution,[status(thm)],[154,148,96,138]) ).
tff(156,plain,
^ [X: $i] :
refl(
( ( p_3(X)
| ~ q_4(X)
| ~ q_5(X) )
<=> ( p_3(X)
| ~ q_4(X)
| ~ q_5(X) ) )),
inference(bind,[status(th)],]) ).
tff(157,plain,
( ! [X: $i] :
( p_3(X)
| ~ q_4(X)
| ~ q_5(X) )
<=> ! [X: $i] :
( p_3(X)
| ~ q_4(X)
| ~ q_5(X) ) ),
inference(quant_intro,[status(thm)],[156]) ).
tff(158,plain,
( ! [X: $i] :
( p_3(X)
| ~ q_4(X)
| ~ q_5(X) )
<=> ! [X: $i] :
( p_3(X)
| ~ q_4(X)
| ~ q_5(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(159,plain,
^ [X: $i] :
rewrite(
( ( p_3(X)
| ~ q_4(X)
| ~ q_5(X) )
<=> ( p_3(X)
| ~ q_4(X)
| ~ q_5(X) ) )),
inference(bind,[status(th)],]) ).
tff(160,plain,
( ! [X: $i] :
( p_3(X)
| ~ q_4(X)
| ~ q_5(X) )
<=> ! [X: $i] :
( p_3(X)
| ~ q_4(X)
| ~ q_5(X) ) ),
inference(quant_intro,[status(thm)],[159]) ).
tff(161,axiom,
! [X: $i] :
( p_3(X)
| ~ q_4(X)
| ~ q_5(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type11_8) ).
tff(162,plain,
! [X: $i] :
( p_3(X)
| ~ q_4(X)
| ~ q_5(X) ),
inference(modus_ponens,[status(thm)],[161,160]) ).
tff(163,plain,
! [X: $i] :
( p_3(X)
| ~ q_4(X)
| ~ q_5(X) ),
inference(modus_ponens,[status(thm)],[162,158]) ).
tff(164,plain,
! [X: $i] :
( p_3(X)
| ~ q_4(X)
| ~ q_5(X) ),
inference(skolemize,[status(sab)],[163]) ).
tff(165,plain,
! [X: $i] :
( p_3(X)
| ~ q_4(X)
| ~ q_5(X) ),
inference(modus_ponens,[status(thm)],[164,157]) ).
tff(166,plain,
( ( ~ ! [X: $i] :
( p_3(X)
| ~ q_4(X)
| ~ q_5(X) )
| p_3(a)
| ~ q_4(a)
| ~ q_5(a) )
<=> ( ~ ! [X: $i] :
( p_3(X)
| ~ q_4(X)
| ~ q_5(X) )
| p_3(a)
| ~ q_4(a)
| ~ q_5(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(167,plain,
( ~ ! [X: $i] :
( p_3(X)
| ~ q_4(X)
| ~ q_5(X) )
| p_3(a)
| ~ q_4(a)
| ~ q_5(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(168,plain,
( ~ ! [X: $i] :
( p_3(X)
| ~ q_4(X)
| ~ q_5(X) )
| p_3(a)
| ~ q_4(a)
| ~ q_5(a) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
p_3(a),
inference(unit_resolution,[status(thm)],[168,165,51,124]) ).
tff(170,plain,
^ [X: $i] :
refl(
( ( q_2(X)
| ~ p_3(X)
| ~ q_4(X) )
<=> ( q_2(X)
| ~ p_3(X)
| ~ q_4(X) ) )),
inference(bind,[status(th)],]) ).
tff(171,plain,
( ! [X: $i] :
( q_2(X)
| ~ p_3(X)
| ~ q_4(X) )
<=> ! [X: $i] :
( q_2(X)
| ~ p_3(X)
| ~ q_4(X) ) ),
inference(quant_intro,[status(thm)],[170]) ).
tff(172,plain,
( ! [X: $i] :
( q_2(X)
| ~ p_3(X)
| ~ q_4(X) )
<=> ! [X: $i] :
( q_2(X)
| ~ p_3(X)
| ~ q_4(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(173,plain,
^ [X: $i] :
rewrite(
( ( q_2(X)
| ~ p_3(X)
| ~ q_4(X) )
<=> ( q_2(X)
| ~ p_3(X)
| ~ q_4(X) ) )),
inference(bind,[status(th)],]) ).
tff(174,plain,
( ! [X: $i] :
( q_2(X)
| ~ p_3(X)
| ~ q_4(X) )
<=> ! [X: $i] :
( q_2(X)
| ~ p_3(X)
| ~ q_4(X) ) ),
inference(quant_intro,[status(thm)],[173]) ).
tff(175,axiom,
! [X: $i] :
( q_2(X)
| ~ p_3(X)
| ~ q_4(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type12_5) ).
tff(176,plain,
! [X: $i] :
( q_2(X)
| ~ p_3(X)
| ~ q_4(X) ),
inference(modus_ponens,[status(thm)],[175,174]) ).
tff(177,plain,
! [X: $i] :
( q_2(X)
| ~ p_3(X)
| ~ q_4(X) ),
inference(modus_ponens,[status(thm)],[176,172]) ).
tff(178,plain,
! [X: $i] :
( q_2(X)
| ~ p_3(X)
| ~ q_4(X) ),
inference(skolemize,[status(sab)],[177]) ).
tff(179,plain,
! [X: $i] :
( q_2(X)
| ~ p_3(X)
| ~ q_4(X) ),
inference(modus_ponens,[status(thm)],[178,171]) ).
tff(180,plain,
( ( ~ ! [X: $i] :
( q_2(X)
| ~ p_3(X)
| ~ q_4(X) )
| q_2(a)
| ~ p_3(a)
| ~ q_4(a) )
<=> ( ~ ! [X: $i] :
( q_2(X)
| ~ p_3(X)
| ~ q_4(X) )
| q_2(a)
| ~ p_3(a)
| ~ q_4(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(181,plain,
( ~ ! [X: $i] :
( q_2(X)
| ~ p_3(X)
| ~ q_4(X) )
| q_2(a)
| ~ p_3(a)
| ~ q_4(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(182,plain,
( ~ ! [X: $i] :
( q_2(X)
| ~ p_3(X)
| ~ q_4(X) )
| q_2(a)
| ~ p_3(a)
| ~ q_4(a) ),
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
q_2(a),
inference(unit_resolution,[status(thm)],[182,179,124,169]) ).
tff(184,plain,
^ [X: $i] :
refl(
( ( p_0(X)
| ~ q_2(X)
| ~ q_1(X) )
<=> ( p_0(X)
| ~ q_2(X)
| ~ q_1(X) ) )),
inference(bind,[status(th)],]) ).
tff(185,plain,
( ! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) )
<=> ! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) ) ),
inference(quant_intro,[status(thm)],[184]) ).
tff(186,plain,
( ! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) )
<=> ! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(187,plain,
^ [X: $i] :
rewrite(
( ( p_0(X)
| ~ q_1(X)
| ~ q_2(X) )
<=> ( p_0(X)
| ~ q_2(X)
| ~ q_1(X) ) )),
inference(bind,[status(th)],]) ).
tff(188,plain,
( ! [X: $i] :
( p_0(X)
| ~ q_1(X)
| ~ q_2(X) )
<=> ! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) ) ),
inference(quant_intro,[status(thm)],[187]) ).
tff(189,axiom,
! [X: $i] :
( p_0(X)
| ~ q_1(X)
| ~ q_2(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type11_2) ).
tff(190,plain,
! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) ),
inference(modus_ponens,[status(thm)],[189,188]) ).
tff(191,plain,
! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) ),
inference(modus_ponens,[status(thm)],[190,186]) ).
tff(192,plain,
! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) ),
inference(skolemize,[status(sab)],[191]) ).
tff(193,plain,
! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) ),
inference(modus_ponens,[status(thm)],[192,185]) ).
tff(194,plain,
( ( ~ ! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) )
| ~ q_2(a)
| p_0(a)
| ~ q_1(a) )
<=> ( ~ ! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) )
| ~ q_2(a)
| p_0(a)
| ~ q_1(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(195,plain,
( ( p_0(a)
| ~ q_2(a)
| ~ q_1(a) )
<=> ( ~ q_2(a)
| p_0(a)
| ~ q_1(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(196,plain,
( ( ~ ! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) )
| p_0(a)
| ~ q_2(a)
| ~ q_1(a) )
<=> ( ~ ! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) )
| ~ q_2(a)
| p_0(a)
| ~ q_1(a) ) ),
inference(monotonicity,[status(thm)],[195]) ).
tff(197,plain,
( ( ~ ! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) )
| p_0(a)
| ~ q_2(a)
| ~ q_1(a) )
<=> ( ~ ! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) )
| ~ q_2(a)
| p_0(a)
| ~ q_1(a) ) ),
inference(transitivity,[status(thm)],[196,194]) ).
tff(198,plain,
( ~ ! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) )
| p_0(a)
| ~ q_2(a)
| ~ q_1(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(199,plain,
( ~ ! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) )
| ~ q_2(a)
| p_0(a)
| ~ q_1(a) ),
inference(modus_ponens,[status(thm)],[198,197]) ).
tff(200,plain,
p_0(a),
inference(unit_resolution,[status(thm)],[199,193,183,155]) ).
tff(201,plain,
^ [X: $i] :
refl(
( ( p_1(X)
| ~ q_2(X)
| ~ q_3(X) )
<=> ( p_1(X)
| ~ q_2(X)
| ~ q_3(X) ) )),
inference(bind,[status(th)],]) ).
tff(202,plain,
( ! [X: $i] :
( p_1(X)
| ~ q_2(X)
| ~ q_3(X) )
<=> ! [X: $i] :
( p_1(X)
| ~ q_2(X)
| ~ q_3(X) ) ),
inference(quant_intro,[status(thm)],[201]) ).
tff(203,plain,
( ! [X: $i] :
( p_1(X)
| ~ q_2(X)
| ~ q_3(X) )
<=> ! [X: $i] :
( p_1(X)
| ~ q_2(X)
| ~ q_3(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(204,plain,
^ [X: $i] :
rewrite(
( ( p_1(X)
| ~ q_2(X)
| ~ q_3(X) )
<=> ( p_1(X)
| ~ q_2(X)
| ~ q_3(X) ) )),
inference(bind,[status(th)],]) ).
tff(205,plain,
( ! [X: $i] :
( p_1(X)
| ~ q_2(X)
| ~ q_3(X) )
<=> ! [X: $i] :
( p_1(X)
| ~ q_2(X)
| ~ q_3(X) ) ),
inference(quant_intro,[status(thm)],[204]) ).
tff(206,axiom,
! [X: $i] :
( p_1(X)
| ~ q_2(X)
| ~ q_3(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type11_4) ).
tff(207,plain,
! [X: $i] :
( p_1(X)
| ~ q_2(X)
| ~ q_3(X) ),
inference(modus_ponens,[status(thm)],[206,205]) ).
tff(208,plain,
! [X: $i] :
( p_1(X)
| ~ q_2(X)
| ~ q_3(X) ),
inference(modus_ponens,[status(thm)],[207,203]) ).
tff(209,plain,
! [X: $i] :
( p_1(X)
| ~ q_2(X)
| ~ q_3(X) ),
inference(skolemize,[status(sab)],[208]) ).
tff(210,plain,
! [X: $i] :
( p_1(X)
| ~ q_2(X)
| ~ q_3(X) ),
inference(modus_ponens,[status(thm)],[209,202]) ).
tff(211,plain,
( ( ~ ! [X: $i] :
( p_1(X)
| ~ q_2(X)
| ~ q_3(X) )
| p_1(a)
| ~ q_2(a)
| ~ q_3(a) )
<=> ( ~ ! [X: $i] :
( p_1(X)
| ~ q_2(X)
| ~ q_3(X) )
| p_1(a)
| ~ q_2(a)
| ~ q_3(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(212,plain,
( ~ ! [X: $i] :
( p_1(X)
| ~ q_2(X)
| ~ q_3(X) )
| p_1(a)
| ~ q_2(a)
| ~ q_3(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(213,plain,
( ~ ! [X: $i] :
( p_1(X)
| ~ q_2(X)
| ~ q_3(X) )
| p_1(a)
| ~ q_2(a)
| ~ q_3(a) ),
inference(modus_ponens,[status(thm)],[212,211]) ).
tff(214,plain,
p_1(a),
inference(unit_resolution,[status(thm)],[213,210,96,183]) ).
tff(215,plain,
^ [X: $i] :
refl(
( ( q_0(X)
| ~ p_1(X)
| ~ q_2(X) )
<=> ( q_0(X)
| ~ p_1(X)
| ~ q_2(X) ) )),
inference(bind,[status(th)],]) ).
tff(216,plain,
( ! [X: $i] :
( q_0(X)
| ~ p_1(X)
| ~ q_2(X) )
<=> ! [X: $i] :
( q_0(X)
| ~ p_1(X)
| ~ q_2(X) ) ),
inference(quant_intro,[status(thm)],[215]) ).
tff(217,plain,
( ! [X: $i] :
( q_0(X)
| ~ p_1(X)
| ~ q_2(X) )
<=> ! [X: $i] :
( q_0(X)
| ~ p_1(X)
| ~ q_2(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(218,plain,
^ [X: $i] :
rewrite(
( ( q_0(X)
| ~ p_1(X)
| ~ q_2(X) )
<=> ( q_0(X)
| ~ p_1(X)
| ~ q_2(X) ) )),
inference(bind,[status(th)],]) ).
tff(219,plain,
( ! [X: $i] :
( q_0(X)
| ~ p_1(X)
| ~ q_2(X) )
<=> ! [X: $i] :
( q_0(X)
| ~ p_1(X)
| ~ q_2(X) ) ),
inference(quant_intro,[status(thm)],[218]) ).
tff(220,axiom,
! [X: $i] :
( q_0(X)
| ~ p_1(X)
| ~ q_2(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_type12_1) ).
tff(221,plain,
! [X: $i] :
( q_0(X)
| ~ p_1(X)
| ~ q_2(X) ),
inference(modus_ponens,[status(thm)],[220,219]) ).
tff(222,plain,
! [X: $i] :
( q_0(X)
| ~ p_1(X)
| ~ q_2(X) ),
inference(modus_ponens,[status(thm)],[221,217]) ).
tff(223,plain,
! [X: $i] :
( q_0(X)
| ~ p_1(X)
| ~ q_2(X) ),
inference(skolemize,[status(sab)],[222]) ).
tff(224,plain,
! [X: $i] :
( q_0(X)
| ~ p_1(X)
| ~ q_2(X) ),
inference(modus_ponens,[status(thm)],[223,216]) ).
tff(225,plain,
( ( ~ ! [X: $i] :
( q_0(X)
| ~ p_1(X)
| ~ q_2(X) )
| q_0(a)
| ~ p_1(a)
| ~ q_2(a) )
<=> ( ~ ! [X: $i] :
( q_0(X)
| ~ p_1(X)
| ~ q_2(X) )
| q_0(a)
| ~ p_1(a)
| ~ q_2(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(226,plain,
( ~ ! [X: $i] :
( q_0(X)
| ~ p_1(X)
| ~ q_2(X) )
| q_0(a)
| ~ p_1(a)
| ~ q_2(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(227,plain,
( ~ ! [X: $i] :
( q_0(X)
| ~ p_1(X)
| ~ q_2(X) )
| q_0(a)
| ~ p_1(a)
| ~ q_2(a) ),
inference(modus_ponens,[status(thm)],[226,225]) ).
tff(228,plain,
q_0(a),
inference(unit_resolution,[status(thm)],[227,224,183,214]) ).
tff(229,plain,
^ [X: $i] :
refl(
( ( ~ p_0(X)
| ~ q_0(X) )
<=> ( ~ p_0(X)
| ~ q_0(X) ) )),
inference(bind,[status(th)],]) ).
tff(230,plain,
( ! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) )
<=> ! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) ) ),
inference(quant_intro,[status(thm)],[229]) ).
tff(231,plain,
( ! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) )
<=> ! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(232,axiom,
! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_s3_goal_1) ).
tff(233,plain,
! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) ),
inference(modus_ponens,[status(thm)],[232,231]) ).
tff(234,plain,
! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) ),
inference(skolemize,[status(sab)],[233]) ).
tff(235,plain,
! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) ),
inference(modus_ponens,[status(thm)],[234,230]) ).
tff(236,plain,
( ( ~ ! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) )
| ~ p_0(a)
| ~ q_0(a) )
<=> ( ~ ! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) )
| ~ p_0(a)
| ~ q_0(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(237,plain,
( ~ ! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) )
| ~ p_0(a)
| ~ q_0(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(238,plain,
( ~ ! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) )
| ~ p_0(a)
| ~ q_0(a) ),
inference(modus_ponens,[status(thm)],[237,236]) ).
tff(239,plain,
$false,
inference(unit_resolution,[status(thm)],[238,235,228,200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN100-1.005 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n029.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Sep 5 01:56:46 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------