TSTP Solution File: SYN096-1.008 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN096-1.008 : 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 23:53:44 EDT 2022
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 208
% Syntax : Number of formulae : 441 ( 89 unt; 31 typ; 0 def)
% Number of atoms : 2114 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 3135 (1486 ~;1468 |; 0 &)
% ( 181 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 55 ( 55 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of predicates : 33 ( 32 usr; 1 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 488 ( 433 !; 0 ?; 488 :)
% 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(p_8_type,type,
p_8: $i > $o ).
tff(q_9_type,type,
q_9: $i > $o ).
tff(p_10_type,type,
p_10: $i > $o ).
tff(q_11_type,type,
q_11: $i > $o ).
tff(p_12_type,type,
p_12: $i > $o ).
tff(q_13_type,type,
q_13: $i > $o ).
tff(q_15_type,type,
q_15: $i > $o ).
tff(p_14_type,type,
p_14: $i > $o ).
tff(q_14_type,type,
q_14: $i > $o ).
tff(q_12_type,type,
q_12: $i > $o ).
tff(q_10_type,type,
q_10: $i > $o ).
tff(p_11_type,type,
p_11: $i > $o ).
tff(q_8_type,type,
q_8: $i > $o ).
tff(p_9_type,type,
p_9: $i > $o ).
tff(q_6_type,type,
q_6: $i > $o ).
tff(p_7_type,type,
p_7: $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_15(a)
<=> q_15(a) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
q_15(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_t3_4) ).
tff(3,plain,
q_15(a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( p_14(a)
<=> p_14(a) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
p_14(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_t3_1) ).
tff(6,plain,
p_14(a),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [X: $i] :
refl(
( ( q_13(X)
| ~ p_14(X)
| ~ q_15(X) )
<=> ( q_13(X)
| ~ p_14(X)
| ~ q_15(X) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [X: $i] :
( q_13(X)
| ~ p_14(X)
| ~ q_15(X) )
<=> ! [X: $i] :
( q_13(X)
| ~ p_14(X)
| ~ q_15(X) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [X: $i] :
( q_13(X)
| ~ p_14(X)
| ~ q_15(X) )
<=> ! [X: $i] :
( q_13(X)
| ~ p_14(X)
| ~ q_15(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
^ [X: $i] :
rewrite(
( ( q_13(X)
| ~ p_14(X)
| ~ q_15(X) )
<=> ( q_13(X)
| ~ p_14(X)
| ~ q_15(X) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] :
( q_13(X)
| ~ p_14(X)
| ~ q_15(X) )
<=> ! [X: $i] :
( q_13(X)
| ~ p_14(X)
| ~ q_15(X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [X: $i] :
( q_13(X)
| ~ p_14(X)
| ~ q_15(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type12_27) ).
tff(13,plain,
! [X: $i] :
( q_13(X)
| ~ p_14(X)
| ~ q_15(X) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [X: $i] :
( q_13(X)
| ~ p_14(X)
| ~ q_15(X) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [X: $i] :
( q_13(X)
| ~ p_14(X)
| ~ q_15(X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] :
( q_13(X)
| ~ p_14(X)
| ~ q_15(X) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [X: $i] :
( q_13(X)
| ~ p_14(X)
| ~ q_15(X) )
| q_13(a)
| ~ p_14(a)
| ~ q_15(a) )
<=> ( ~ ! [X: $i] :
( q_13(X)
| ~ p_14(X)
| ~ q_15(X) )
| q_13(a)
| ~ p_14(a)
| ~ q_15(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [X: $i] :
( q_13(X)
| ~ p_14(X)
| ~ q_15(X) )
| q_13(a)
| ~ p_14(a)
| ~ q_15(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [X: $i] :
( q_13(X)
| ~ p_14(X)
| ~ q_15(X) )
| q_13(a)
| ~ p_14(a)
| ~ q_15(a) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
q_13(a),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
( q_14(a)
<=> q_14(a) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
q_14(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_t3_3) ).
tff(23,plain,
q_14(a),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [X: $i] :
refl(
( ( p_12(X)
| ~ q_13(X)
| ~ q_14(X) )
<=> ( p_12(X)
| ~ q_13(X)
| ~ q_14(X) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [X: $i] :
( p_12(X)
| ~ q_13(X)
| ~ q_14(X) )
<=> ! [X: $i] :
( p_12(X)
| ~ q_13(X)
| ~ q_14(X) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [X: $i] :
( p_12(X)
| ~ q_13(X)
| ~ q_14(X) )
<=> ! [X: $i] :
( p_12(X)
| ~ q_13(X)
| ~ q_14(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
^ [X: $i] :
rewrite(
( ( p_12(X)
| ~ q_13(X)
| ~ q_14(X) )
<=> ( p_12(X)
| ~ q_13(X)
| ~ q_14(X) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [X: $i] :
( p_12(X)
| ~ q_13(X)
| ~ q_14(X) )
<=> ! [X: $i] :
( p_12(X)
| ~ q_13(X)
| ~ q_14(X) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [X: $i] :
( p_12(X)
| ~ q_13(X)
| ~ q_14(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type11_26) ).
tff(30,plain,
! [X: $i] :
( p_12(X)
| ~ q_13(X)
| ~ q_14(X) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [X: $i] :
( p_12(X)
| ~ q_13(X)
| ~ q_14(X) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [X: $i] :
( p_12(X)
| ~ q_13(X)
| ~ q_14(X) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [X: $i] :
( p_12(X)
| ~ q_13(X)
| ~ q_14(X) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [X: $i] :
( p_12(X)
| ~ q_13(X)
| ~ q_14(X) )
| p_12(a)
| ~ q_13(a)
| ~ q_14(a) )
<=> ( ~ ! [X: $i] :
( p_12(X)
| ~ q_13(X)
| ~ q_14(X) )
| p_12(a)
| ~ q_13(a)
| ~ q_14(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ~ ! [X: $i] :
( p_12(X)
| ~ q_13(X)
| ~ q_14(X) )
| p_12(a)
| ~ q_13(a)
| ~ q_14(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ~ ! [X: $i] :
( p_12(X)
| ~ q_13(X)
| ~ q_14(X) )
| p_12(a)
| ~ q_13(a)
| ~ q_14(a) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
p_12(a),
inference(unit_resolution,[status(thm)],[36,33,23,20]) ).
tff(38,plain,
^ [X: $i] :
refl(
( ( q_11(X)
| ~ p_12(X)
| ~ q_13(X) )
<=> ( q_11(X)
| ~ p_12(X)
| ~ q_13(X) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [X: $i] :
( q_11(X)
| ~ p_12(X)
| ~ q_13(X) )
<=> ! [X: $i] :
( q_11(X)
| ~ p_12(X)
| ~ q_13(X) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [X: $i] :
( q_11(X)
| ~ p_12(X)
| ~ q_13(X) )
<=> ! [X: $i] :
( q_11(X)
| ~ p_12(X)
| ~ q_13(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
^ [X: $i] :
rewrite(
( ( q_11(X)
| ~ p_12(X)
| ~ q_13(X) )
<=> ( q_11(X)
| ~ p_12(X)
| ~ q_13(X) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [X: $i] :
( q_11(X)
| ~ p_12(X)
| ~ q_13(X) )
<=> ! [X: $i] :
( q_11(X)
| ~ p_12(X)
| ~ q_13(X) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [X: $i] :
( q_11(X)
| ~ p_12(X)
| ~ q_13(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type12_23) ).
tff(44,plain,
! [X: $i] :
( q_11(X)
| ~ p_12(X)
| ~ q_13(X) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [X: $i] :
( q_11(X)
| ~ p_12(X)
| ~ q_13(X) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [X: $i] :
( q_11(X)
| ~ p_12(X)
| ~ q_13(X) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [X: $i] :
( q_11(X)
| ~ p_12(X)
| ~ q_13(X) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ( ~ ! [X: $i] :
( q_11(X)
| ~ p_12(X)
| ~ q_13(X) )
| q_11(a)
| ~ p_12(a)
| ~ q_13(a) )
<=> ( ~ ! [X: $i] :
( q_11(X)
| ~ p_12(X)
| ~ q_13(X) )
| q_11(a)
| ~ p_12(a)
| ~ q_13(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ~ ! [X: $i] :
( q_11(X)
| ~ p_12(X)
| ~ q_13(X) )
| q_11(a)
| ~ p_12(a)
| ~ q_13(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
( ~ ! [X: $i] :
( q_11(X)
| ~ p_12(X)
| ~ q_13(X) )
| q_11(a)
| ~ p_12(a)
| ~ q_13(a) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
q_11(a),
inference(unit_resolution,[status(thm)],[50,47,20,37]) ).
tff(52,plain,
^ [X: $i] :
refl(
( ( q_12(X)
| ~ q_13(X)
| ~ p_14(X) )
<=> ( q_12(X)
| ~ q_13(X)
| ~ p_14(X) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [X: $i] :
( q_12(X)
| ~ q_13(X)
| ~ p_14(X) )
<=> ! [X: $i] :
( q_12(X)
| ~ q_13(X)
| ~ p_14(X) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [X: $i] :
( q_12(X)
| ~ q_13(X)
| ~ p_14(X) )
<=> ! [X: $i] :
( q_12(X)
| ~ q_13(X)
| ~ p_14(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
^ [X: $i] :
rewrite(
( ( q_12(X)
| ~ q_13(X)
| ~ p_14(X) )
<=> ( q_12(X)
| ~ q_13(X)
| ~ p_14(X) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [X: $i] :
( q_12(X)
| ~ q_13(X)
| ~ p_14(X) )
<=> ! [X: $i] :
( q_12(X)
| ~ q_13(X)
| ~ p_14(X) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,axiom,
! [X: $i] :
( q_12(X)
| ~ q_13(X)
| ~ p_14(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type12_26) ).
tff(58,plain,
! [X: $i] :
( q_12(X)
| ~ q_13(X)
| ~ p_14(X) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [X: $i] :
( q_12(X)
| ~ q_13(X)
| ~ p_14(X) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
! [X: $i] :
( q_12(X)
| ~ q_13(X)
| ~ p_14(X) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [X: $i] :
( q_12(X)
| ~ q_13(X)
| ~ p_14(X) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
( ( ~ ! [X: $i] :
( q_12(X)
| ~ q_13(X)
| ~ p_14(X) )
| ~ p_14(a)
| q_12(a)
| ~ q_13(a) )
<=> ( ~ ! [X: $i] :
( q_12(X)
| ~ q_13(X)
| ~ p_14(X) )
| ~ p_14(a)
| q_12(a)
| ~ q_13(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ( q_12(a)
| ~ q_13(a)
| ~ p_14(a) )
<=> ( ~ p_14(a)
| q_12(a)
| ~ q_13(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
( ( ~ ! [X: $i] :
( q_12(X)
| ~ q_13(X)
| ~ p_14(X) )
| q_12(a)
| ~ q_13(a)
| ~ p_14(a) )
<=> ( ~ ! [X: $i] :
( q_12(X)
| ~ q_13(X)
| ~ p_14(X) )
| ~ p_14(a)
| q_12(a)
| ~ q_13(a) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( ~ ! [X: $i] :
( q_12(X)
| ~ q_13(X)
| ~ p_14(X) )
| q_12(a)
| ~ q_13(a)
| ~ p_14(a) )
<=> ( ~ ! [X: $i] :
( q_12(X)
| ~ q_13(X)
| ~ p_14(X) )
| ~ p_14(a)
| q_12(a)
| ~ q_13(a) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
( ~ ! [X: $i] :
( q_12(X)
| ~ q_13(X)
| ~ p_14(X) )
| q_12(a)
| ~ q_13(a)
| ~ p_14(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
( ~ ! [X: $i] :
( q_12(X)
| ~ q_13(X)
| ~ p_14(X) )
| ~ p_14(a)
| q_12(a)
| ~ q_13(a) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
q_12(a),
inference(unit_resolution,[status(thm)],[67,61,6,20]) ).
tff(69,plain,
^ [X: $i] :
refl(
( ( p_10(X)
| ~ q_11(X)
| ~ q_12(X) )
<=> ( p_10(X)
| ~ q_11(X)
| ~ q_12(X) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [X: $i] :
( p_10(X)
| ~ q_11(X)
| ~ q_12(X) )
<=> ! [X: $i] :
( p_10(X)
| ~ q_11(X)
| ~ q_12(X) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [X: $i] :
( p_10(X)
| ~ q_11(X)
| ~ q_12(X) )
<=> ! [X: $i] :
( p_10(X)
| ~ q_11(X)
| ~ q_12(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
^ [X: $i] :
rewrite(
( ( p_10(X)
| ~ q_11(X)
| ~ q_12(X) )
<=> ( p_10(X)
| ~ q_11(X)
| ~ q_12(X) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [X: $i] :
( p_10(X)
| ~ q_11(X)
| ~ q_12(X) )
<=> ! [X: $i] :
( p_10(X)
| ~ q_11(X)
| ~ q_12(X) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,axiom,
! [X: $i] :
( p_10(X)
| ~ q_11(X)
| ~ q_12(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type11_22) ).
tff(75,plain,
! [X: $i] :
( p_10(X)
| ~ q_11(X)
| ~ q_12(X) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [X: $i] :
( p_10(X)
| ~ q_11(X)
| ~ q_12(X) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
! [X: $i] :
( p_10(X)
| ~ q_11(X)
| ~ q_12(X) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [X: $i] :
( p_10(X)
| ~ q_11(X)
| ~ q_12(X) ),
inference(modus_ponens,[status(thm)],[77,70]) ).
tff(79,plain,
( ( ~ ! [X: $i] :
( p_10(X)
| ~ q_11(X)
| ~ q_12(X) )
| p_10(a)
| ~ q_11(a)
| ~ q_12(a) )
<=> ( ~ ! [X: $i] :
( p_10(X)
| ~ q_11(X)
| ~ q_12(X) )
| p_10(a)
| ~ q_11(a)
| ~ q_12(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ~ ! [X: $i] :
( p_10(X)
| ~ q_11(X)
| ~ q_12(X) )
| p_10(a)
| ~ q_11(a)
| ~ q_12(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
( ~ ! [X: $i] :
( p_10(X)
| ~ q_11(X)
| ~ q_12(X) )
| p_10(a)
| ~ q_11(a)
| ~ q_12(a) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
p_10(a),
inference(unit_resolution,[status(thm)],[81,78,68,51]) ).
tff(83,plain,
^ [X: $i] :
refl(
( ( q_9(X)
| ~ p_10(X)
| ~ q_11(X) )
<=> ( q_9(X)
| ~ p_10(X)
| ~ q_11(X) ) )),
inference(bind,[status(th)],]) ).
tff(84,plain,
( ! [X: $i] :
( q_9(X)
| ~ p_10(X)
| ~ q_11(X) )
<=> ! [X: $i] :
( q_9(X)
| ~ p_10(X)
| ~ q_11(X) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [X: $i] :
( q_9(X)
| ~ p_10(X)
| ~ q_11(X) )
<=> ! [X: $i] :
( q_9(X)
| ~ p_10(X)
| ~ q_11(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
^ [X: $i] :
rewrite(
( ( q_9(X)
| ~ p_10(X)
| ~ q_11(X) )
<=> ( q_9(X)
| ~ p_10(X)
| ~ q_11(X) ) )),
inference(bind,[status(th)],]) ).
tff(87,plain,
( ! [X: $i] :
( q_9(X)
| ~ p_10(X)
| ~ q_11(X) )
<=> ! [X: $i] :
( q_9(X)
| ~ p_10(X)
| ~ q_11(X) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,axiom,
! [X: $i] :
( q_9(X)
| ~ p_10(X)
| ~ q_11(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type12_19) ).
tff(89,plain,
! [X: $i] :
( q_9(X)
| ~ p_10(X)
| ~ q_11(X) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [X: $i] :
( q_9(X)
| ~ p_10(X)
| ~ q_11(X) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
! [X: $i] :
( q_9(X)
| ~ p_10(X)
| ~ q_11(X) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [X: $i] :
( q_9(X)
| ~ p_10(X)
| ~ q_11(X) ),
inference(modus_ponens,[status(thm)],[91,84]) ).
tff(93,plain,
( ( ~ ! [X: $i] :
( q_9(X)
| ~ p_10(X)
| ~ q_11(X) )
| q_9(a)
| ~ p_10(a)
| ~ q_11(a) )
<=> ( ~ ! [X: $i] :
( q_9(X)
| ~ p_10(X)
| ~ q_11(X) )
| q_9(a)
| ~ p_10(a)
| ~ q_11(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ~ ! [X: $i] :
( q_9(X)
| ~ p_10(X)
| ~ q_11(X) )
| q_9(a)
| ~ p_10(a)
| ~ q_11(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
( ~ ! [X: $i] :
( q_9(X)
| ~ p_10(X)
| ~ q_11(X) )
| q_9(a)
| ~ p_10(a)
| ~ q_11(a) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
q_9(a),
inference(unit_resolution,[status(thm)],[95,92,51,82]) ).
tff(97,plain,
^ [X: $i] :
refl(
( ( p_11(X)
| ~ q_12(X)
| ~ q_13(X) )
<=> ( p_11(X)
| ~ q_12(X)
| ~ q_13(X) ) )),
inference(bind,[status(th)],]) ).
tff(98,plain,
( ! [X: $i] :
( p_11(X)
| ~ q_12(X)
| ~ q_13(X) )
<=> ! [X: $i] :
( p_11(X)
| ~ q_12(X)
| ~ q_13(X) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
( ! [X: $i] :
( p_11(X)
| ~ q_12(X)
| ~ q_13(X) )
<=> ! [X: $i] :
( p_11(X)
| ~ q_12(X)
| ~ q_13(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
^ [X: $i] :
rewrite(
( ( p_11(X)
| ~ q_12(X)
| ~ q_13(X) )
<=> ( p_11(X)
| ~ q_12(X)
| ~ q_13(X) ) )),
inference(bind,[status(th)],]) ).
tff(101,plain,
( ! [X: $i] :
( p_11(X)
| ~ q_12(X)
| ~ q_13(X) )
<=> ! [X: $i] :
( p_11(X)
| ~ q_12(X)
| ~ q_13(X) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,axiom,
! [X: $i] :
( p_11(X)
| ~ q_12(X)
| ~ q_13(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type11_24) ).
tff(103,plain,
! [X: $i] :
( p_11(X)
| ~ q_12(X)
| ~ q_13(X) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
! [X: $i] :
( p_11(X)
| ~ q_12(X)
| ~ q_13(X) ),
inference(modus_ponens,[status(thm)],[103,99]) ).
tff(105,plain,
! [X: $i] :
( p_11(X)
| ~ q_12(X)
| ~ q_13(X) ),
inference(skolemize,[status(sab)],[104]) ).
tff(106,plain,
! [X: $i] :
( p_11(X)
| ~ q_12(X)
| ~ q_13(X) ),
inference(modus_ponens,[status(thm)],[105,98]) ).
tff(107,plain,
( ( ~ ! [X: $i] :
( p_11(X)
| ~ q_12(X)
| ~ q_13(X) )
| p_11(a)
| ~ q_12(a)
| ~ q_13(a) )
<=> ( ~ ! [X: $i] :
( p_11(X)
| ~ q_12(X)
| ~ q_13(X) )
| p_11(a)
| ~ q_12(a)
| ~ q_13(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
( ~ ! [X: $i] :
( p_11(X)
| ~ q_12(X)
| ~ q_13(X) )
| p_11(a)
| ~ q_12(a)
| ~ q_13(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(109,plain,
( ~ ! [X: $i] :
( p_11(X)
| ~ q_12(X)
| ~ q_13(X) )
| p_11(a)
| ~ q_12(a)
| ~ q_13(a) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
p_11(a),
inference(unit_resolution,[status(thm)],[109,106,20,68]) ).
tff(111,plain,
^ [X: $i] :
refl(
( ( q_10(X)
| ~ p_11(X)
| ~ q_12(X) )
<=> ( q_10(X)
| ~ p_11(X)
| ~ q_12(X) ) )),
inference(bind,[status(th)],]) ).
tff(112,plain,
( ! [X: $i] :
( q_10(X)
| ~ p_11(X)
| ~ q_12(X) )
<=> ! [X: $i] :
( q_10(X)
| ~ p_11(X)
| ~ q_12(X) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,plain,
( ! [X: $i] :
( q_10(X)
| ~ p_11(X)
| ~ q_12(X) )
<=> ! [X: $i] :
( q_10(X)
| ~ p_11(X)
| ~ q_12(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
^ [X: $i] :
rewrite(
( ( q_10(X)
| ~ p_11(X)
| ~ q_12(X) )
<=> ( q_10(X)
| ~ p_11(X)
| ~ q_12(X) ) )),
inference(bind,[status(th)],]) ).
tff(115,plain,
( ! [X: $i] :
( q_10(X)
| ~ p_11(X)
| ~ q_12(X) )
<=> ! [X: $i] :
( q_10(X)
| ~ p_11(X)
| ~ q_12(X) ) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,axiom,
! [X: $i] :
( q_10(X)
| ~ p_11(X)
| ~ q_12(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type12_21) ).
tff(117,plain,
! [X: $i] :
( q_10(X)
| ~ p_11(X)
| ~ q_12(X) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
! [X: $i] :
( q_10(X)
| ~ p_11(X)
| ~ q_12(X) ),
inference(modus_ponens,[status(thm)],[117,113]) ).
tff(119,plain,
! [X: $i] :
( q_10(X)
| ~ p_11(X)
| ~ q_12(X) ),
inference(skolemize,[status(sab)],[118]) ).
tff(120,plain,
! [X: $i] :
( q_10(X)
| ~ p_11(X)
| ~ q_12(X) ),
inference(modus_ponens,[status(thm)],[119,112]) ).
tff(121,plain,
( ( ~ ! [X: $i] :
( q_10(X)
| ~ p_11(X)
| ~ q_12(X) )
| q_10(a)
| ~ p_11(a)
| ~ q_12(a) )
<=> ( ~ ! [X: $i] :
( q_10(X)
| ~ p_11(X)
| ~ q_12(X) )
| q_10(a)
| ~ p_11(a)
| ~ q_12(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(122,plain,
( ~ ! [X: $i] :
( q_10(X)
| ~ p_11(X)
| ~ q_12(X) )
| q_10(a)
| ~ p_11(a)
| ~ q_12(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(123,plain,
( ~ ! [X: $i] :
( q_10(X)
| ~ p_11(X)
| ~ q_12(X) )
| q_10(a)
| ~ p_11(a)
| ~ q_12(a) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
q_10(a),
inference(unit_resolution,[status(thm)],[123,120,68,110]) ).
tff(125,plain,
^ [X: $i] :
refl(
( ( p_8(X)
| ~ q_9(X)
| ~ q_10(X) )
<=> ( p_8(X)
| ~ q_9(X)
| ~ q_10(X) ) )),
inference(bind,[status(th)],]) ).
tff(126,plain,
( ! [X: $i] :
( p_8(X)
| ~ q_9(X)
| ~ q_10(X) )
<=> ! [X: $i] :
( p_8(X)
| ~ q_9(X)
| ~ q_10(X) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,plain,
( ! [X: $i] :
( p_8(X)
| ~ q_9(X)
| ~ q_10(X) )
<=> ! [X: $i] :
( p_8(X)
| ~ q_9(X)
| ~ q_10(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(128,plain,
^ [X: $i] :
rewrite(
( ( p_8(X)
| ~ q_9(X)
| ~ q_10(X) )
<=> ( p_8(X)
| ~ q_9(X)
| ~ q_10(X) ) )),
inference(bind,[status(th)],]) ).
tff(129,plain,
( ! [X: $i] :
( p_8(X)
| ~ q_9(X)
| ~ q_10(X) )
<=> ! [X: $i] :
( p_8(X)
| ~ q_9(X)
| ~ q_10(X) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,axiom,
! [X: $i] :
( p_8(X)
| ~ q_9(X)
| ~ q_10(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type11_18) ).
tff(131,plain,
! [X: $i] :
( p_8(X)
| ~ q_9(X)
| ~ q_10(X) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
! [X: $i] :
( p_8(X)
| ~ q_9(X)
| ~ q_10(X) ),
inference(modus_ponens,[status(thm)],[131,127]) ).
tff(133,plain,
! [X: $i] :
( p_8(X)
| ~ q_9(X)
| ~ q_10(X) ),
inference(skolemize,[status(sab)],[132]) ).
tff(134,plain,
! [X: $i] :
( p_8(X)
| ~ q_9(X)
| ~ q_10(X) ),
inference(modus_ponens,[status(thm)],[133,126]) ).
tff(135,plain,
( ( ~ ! [X: $i] :
( p_8(X)
| ~ q_9(X)
| ~ q_10(X) )
| ~ q_10(a)
| p_8(a)
| ~ q_9(a) )
<=> ( ~ ! [X: $i] :
( p_8(X)
| ~ q_9(X)
| ~ q_10(X) )
| ~ q_10(a)
| p_8(a)
| ~ q_9(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(136,plain,
( ( p_8(a)
| ~ q_9(a)
| ~ q_10(a) )
<=> ( ~ q_10(a)
| p_8(a)
| ~ q_9(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(137,plain,
( ( ~ ! [X: $i] :
( p_8(X)
| ~ q_9(X)
| ~ q_10(X) )
| p_8(a)
| ~ q_9(a)
| ~ q_10(a) )
<=> ( ~ ! [X: $i] :
( p_8(X)
| ~ q_9(X)
| ~ q_10(X) )
| ~ q_10(a)
| p_8(a)
| ~ q_9(a) ) ),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
( ( ~ ! [X: $i] :
( p_8(X)
| ~ q_9(X)
| ~ q_10(X) )
| p_8(a)
| ~ q_9(a)
| ~ q_10(a) )
<=> ( ~ ! [X: $i] :
( p_8(X)
| ~ q_9(X)
| ~ q_10(X) )
| ~ q_10(a)
| p_8(a)
| ~ q_9(a) ) ),
inference(transitivity,[status(thm)],[137,135]) ).
tff(139,plain,
( ~ ! [X: $i] :
( p_8(X)
| ~ q_9(X)
| ~ q_10(X) )
| p_8(a)
| ~ q_9(a)
| ~ q_10(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
( ~ ! [X: $i] :
( p_8(X)
| ~ q_9(X)
| ~ q_10(X) )
| ~ q_10(a)
| p_8(a)
| ~ q_9(a) ),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
p_8(a),
inference(unit_resolution,[status(thm)],[140,134,124,96]) ).
tff(142,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(143,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)],[142]) ).
tff(144,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(145,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(146,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)],[145]) ).
tff(147,axiom,
! [X: $i] :
( q_7(X)
| ~ p_8(X)
| ~ q_9(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type12_15) ).
tff(148,plain,
! [X: $i] :
( q_7(X)
| ~ p_8(X)
| ~ q_9(X) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
! [X: $i] :
( q_7(X)
| ~ p_8(X)
| ~ q_9(X) ),
inference(modus_ponens,[status(thm)],[148,144]) ).
tff(150,plain,
! [X: $i] :
( q_7(X)
| ~ p_8(X)
| ~ q_9(X) ),
inference(skolemize,[status(sab)],[149]) ).
tff(151,plain,
! [X: $i] :
( q_7(X)
| ~ p_8(X)
| ~ q_9(X) ),
inference(modus_ponens,[status(thm)],[150,143]) ).
tff(152,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(153,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(154,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)],[153,152]) ).
tff(155,plain,
q_7(a),
inference(unit_resolution,[status(thm)],[154,151,96,141]) ).
tff(156,plain,
^ [X: $i] :
refl(
( ( p_9(X)
| ~ q_10(X)
| ~ q_11(X) )
<=> ( p_9(X)
| ~ q_10(X)
| ~ q_11(X) ) )),
inference(bind,[status(th)],]) ).
tff(157,plain,
( ! [X: $i] :
( p_9(X)
| ~ q_10(X)
| ~ q_11(X) )
<=> ! [X: $i] :
( p_9(X)
| ~ q_10(X)
| ~ q_11(X) ) ),
inference(quant_intro,[status(thm)],[156]) ).
tff(158,plain,
( ! [X: $i] :
( p_9(X)
| ~ q_10(X)
| ~ q_11(X) )
<=> ! [X: $i] :
( p_9(X)
| ~ q_10(X)
| ~ q_11(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(159,plain,
^ [X: $i] :
rewrite(
( ( p_9(X)
| ~ q_10(X)
| ~ q_11(X) )
<=> ( p_9(X)
| ~ q_10(X)
| ~ q_11(X) ) )),
inference(bind,[status(th)],]) ).
tff(160,plain,
( ! [X: $i] :
( p_9(X)
| ~ q_10(X)
| ~ q_11(X) )
<=> ! [X: $i] :
( p_9(X)
| ~ q_10(X)
| ~ q_11(X) ) ),
inference(quant_intro,[status(thm)],[159]) ).
tff(161,axiom,
! [X: $i] :
( p_9(X)
| ~ q_10(X)
| ~ q_11(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type11_20) ).
tff(162,plain,
! [X: $i] :
( p_9(X)
| ~ q_10(X)
| ~ q_11(X) ),
inference(modus_ponens,[status(thm)],[161,160]) ).
tff(163,plain,
! [X: $i] :
( p_9(X)
| ~ q_10(X)
| ~ q_11(X) ),
inference(modus_ponens,[status(thm)],[162,158]) ).
tff(164,plain,
! [X: $i] :
( p_9(X)
| ~ q_10(X)
| ~ q_11(X) ),
inference(skolemize,[status(sab)],[163]) ).
tff(165,plain,
! [X: $i] :
( p_9(X)
| ~ q_10(X)
| ~ q_11(X) ),
inference(modus_ponens,[status(thm)],[164,157]) ).
tff(166,plain,
( ( ~ ! [X: $i] :
( p_9(X)
| ~ q_10(X)
| ~ q_11(X) )
| p_9(a)
| ~ q_10(a)
| ~ q_11(a) )
<=> ( ~ ! [X: $i] :
( p_9(X)
| ~ q_10(X)
| ~ q_11(X) )
| p_9(a)
| ~ q_10(a)
| ~ q_11(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(167,plain,
( ~ ! [X: $i] :
( p_9(X)
| ~ q_10(X)
| ~ q_11(X) )
| p_9(a)
| ~ q_10(a)
| ~ q_11(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(168,plain,
( ~ ! [X: $i] :
( p_9(X)
| ~ q_10(X)
| ~ q_11(X) )
| p_9(a)
| ~ q_10(a)
| ~ q_11(a) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
p_9(a),
inference(unit_resolution,[status(thm)],[168,165,51,124]) ).
tff(170,plain,
^ [X: $i] :
refl(
( ( q_8(X)
| ~ p_9(X)
| ~ q_10(X) )
<=> ( q_8(X)
| ~ p_9(X)
| ~ q_10(X) ) )),
inference(bind,[status(th)],]) ).
tff(171,plain,
( ! [X: $i] :
( q_8(X)
| ~ p_9(X)
| ~ q_10(X) )
<=> ! [X: $i] :
( q_8(X)
| ~ p_9(X)
| ~ q_10(X) ) ),
inference(quant_intro,[status(thm)],[170]) ).
tff(172,plain,
( ! [X: $i] :
( q_8(X)
| ~ p_9(X)
| ~ q_10(X) )
<=> ! [X: $i] :
( q_8(X)
| ~ p_9(X)
| ~ q_10(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(173,plain,
^ [X: $i] :
rewrite(
( ( q_8(X)
| ~ p_9(X)
| ~ q_10(X) )
<=> ( q_8(X)
| ~ p_9(X)
| ~ q_10(X) ) )),
inference(bind,[status(th)],]) ).
tff(174,plain,
( ! [X: $i] :
( q_8(X)
| ~ p_9(X)
| ~ q_10(X) )
<=> ! [X: $i] :
( q_8(X)
| ~ p_9(X)
| ~ q_10(X) ) ),
inference(quant_intro,[status(thm)],[173]) ).
tff(175,axiom,
! [X: $i] :
( q_8(X)
| ~ p_9(X)
| ~ q_10(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type12_17) ).
tff(176,plain,
! [X: $i] :
( q_8(X)
| ~ p_9(X)
| ~ q_10(X) ),
inference(modus_ponens,[status(thm)],[175,174]) ).
tff(177,plain,
! [X: $i] :
( q_8(X)
| ~ p_9(X)
| ~ q_10(X) ),
inference(modus_ponens,[status(thm)],[176,172]) ).
tff(178,plain,
! [X: $i] :
( q_8(X)
| ~ p_9(X)
| ~ q_10(X) ),
inference(skolemize,[status(sab)],[177]) ).
tff(179,plain,
! [X: $i] :
( q_8(X)
| ~ p_9(X)
| ~ q_10(X) ),
inference(modus_ponens,[status(thm)],[178,171]) ).
tff(180,plain,
( ( ~ ! [X: $i] :
( q_8(X)
| ~ p_9(X)
| ~ q_10(X) )
| q_8(a)
| ~ p_9(a)
| ~ q_10(a) )
<=> ( ~ ! [X: $i] :
( q_8(X)
| ~ p_9(X)
| ~ q_10(X) )
| q_8(a)
| ~ p_9(a)
| ~ q_10(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(181,plain,
( ~ ! [X: $i] :
( q_8(X)
| ~ p_9(X)
| ~ q_10(X) )
| q_8(a)
| ~ p_9(a)
| ~ q_10(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(182,plain,
( ~ ! [X: $i] :
( q_8(X)
| ~ p_9(X)
| ~ q_10(X) )
| q_8(a)
| ~ p_9(a)
| ~ q_10(a) ),
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
q_8(a),
inference(unit_resolution,[status(thm)],[182,179,124,169]) ).
tff(184,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(185,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)],[184]) ).
tff(186,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(187,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(188,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)],[187]) ).
tff(189,axiom,
! [X: $i] :
( p_6(X)
| ~ q_7(X)
| ~ q_8(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type11_14) ).
tff(190,plain,
! [X: $i] :
( p_6(X)
| ~ q_7(X)
| ~ q_8(X) ),
inference(modus_ponens,[status(thm)],[189,188]) ).
tff(191,plain,
! [X: $i] :
( p_6(X)
| ~ q_7(X)
| ~ q_8(X) ),
inference(modus_ponens,[status(thm)],[190,186]) ).
tff(192,plain,
! [X: $i] :
( p_6(X)
| ~ q_7(X)
| ~ q_8(X) ),
inference(skolemize,[status(sab)],[191]) ).
tff(193,plain,
! [X: $i] :
( p_6(X)
| ~ q_7(X)
| ~ q_8(X) ),
inference(modus_ponens,[status(thm)],[192,185]) ).
tff(194,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(195,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(196,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)],[195,194]) ).
tff(197,plain,
p_6(a),
inference(unit_resolution,[status(thm)],[196,193,183,155]) ).
tff(198,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(199,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)],[198]) ).
tff(200,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(201,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(202,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)],[201]) ).
tff(203,axiom,
! [X: $i] :
( q_5(X)
| ~ p_6(X)
| ~ q_7(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type12_11) ).
tff(204,plain,
! [X: $i] :
( q_5(X)
| ~ p_6(X)
| ~ q_7(X) ),
inference(modus_ponens,[status(thm)],[203,202]) ).
tff(205,plain,
! [X: $i] :
( q_5(X)
| ~ p_6(X)
| ~ q_7(X) ),
inference(modus_ponens,[status(thm)],[204,200]) ).
tff(206,plain,
! [X: $i] :
( q_5(X)
| ~ p_6(X)
| ~ q_7(X) ),
inference(skolemize,[status(sab)],[205]) ).
tff(207,plain,
! [X: $i] :
( q_5(X)
| ~ p_6(X)
| ~ q_7(X) ),
inference(modus_ponens,[status(thm)],[206,199]) ).
tff(208,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(209,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(210,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)],[209,208]) ).
tff(211,plain,
q_5(a),
inference(unit_resolution,[status(thm)],[210,207,155,197]) ).
tff(212,plain,
^ [X: $i] :
refl(
( ( p_7(X)
| ~ q_8(X)
| ~ q_9(X) )
<=> ( p_7(X)
| ~ q_8(X)
| ~ q_9(X) ) )),
inference(bind,[status(th)],]) ).
tff(213,plain,
( ! [X: $i] :
( p_7(X)
| ~ q_8(X)
| ~ q_9(X) )
<=> ! [X: $i] :
( p_7(X)
| ~ q_8(X)
| ~ q_9(X) ) ),
inference(quant_intro,[status(thm)],[212]) ).
tff(214,plain,
( ! [X: $i] :
( p_7(X)
| ~ q_8(X)
| ~ q_9(X) )
<=> ! [X: $i] :
( p_7(X)
| ~ q_8(X)
| ~ q_9(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(215,plain,
^ [X: $i] :
rewrite(
( ( p_7(X)
| ~ q_8(X)
| ~ q_9(X) )
<=> ( p_7(X)
| ~ q_8(X)
| ~ q_9(X) ) )),
inference(bind,[status(th)],]) ).
tff(216,plain,
( ! [X: $i] :
( p_7(X)
| ~ q_8(X)
| ~ q_9(X) )
<=> ! [X: $i] :
( p_7(X)
| ~ q_8(X)
| ~ q_9(X) ) ),
inference(quant_intro,[status(thm)],[215]) ).
tff(217,axiom,
! [X: $i] :
( p_7(X)
| ~ q_8(X)
| ~ q_9(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type11_16) ).
tff(218,plain,
! [X: $i] :
( p_7(X)
| ~ q_8(X)
| ~ q_9(X) ),
inference(modus_ponens,[status(thm)],[217,216]) ).
tff(219,plain,
! [X: $i] :
( p_7(X)
| ~ q_8(X)
| ~ q_9(X) ),
inference(modus_ponens,[status(thm)],[218,214]) ).
tff(220,plain,
! [X: $i] :
( p_7(X)
| ~ q_8(X)
| ~ q_9(X) ),
inference(skolemize,[status(sab)],[219]) ).
tff(221,plain,
! [X: $i] :
( p_7(X)
| ~ q_8(X)
| ~ q_9(X) ),
inference(modus_ponens,[status(thm)],[220,213]) ).
tff(222,plain,
( ( ~ ! [X: $i] :
( p_7(X)
| ~ q_8(X)
| ~ q_9(X) )
| p_7(a)
| ~ q_8(a)
| ~ q_9(a) )
<=> ( ~ ! [X: $i] :
( p_7(X)
| ~ q_8(X)
| ~ q_9(X) )
| p_7(a)
| ~ q_8(a)
| ~ q_9(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(223,plain,
( ~ ! [X: $i] :
( p_7(X)
| ~ q_8(X)
| ~ q_9(X) )
| p_7(a)
| ~ q_8(a)
| ~ q_9(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(224,plain,
( ~ ! [X: $i] :
( p_7(X)
| ~ q_8(X)
| ~ q_9(X) )
| p_7(a)
| ~ q_8(a)
| ~ q_9(a) ),
inference(modus_ponens,[status(thm)],[223,222]) ).
tff(225,plain,
p_7(a),
inference(unit_resolution,[status(thm)],[224,221,96,183]) ).
tff(226,plain,
^ [X: $i] :
refl(
( ( q_6(X)
| ~ p_7(X)
| ~ q_8(X) )
<=> ( q_6(X)
| ~ p_7(X)
| ~ q_8(X) ) )),
inference(bind,[status(th)],]) ).
tff(227,plain,
( ! [X: $i] :
( q_6(X)
| ~ p_7(X)
| ~ q_8(X) )
<=> ! [X: $i] :
( q_6(X)
| ~ p_7(X)
| ~ q_8(X) ) ),
inference(quant_intro,[status(thm)],[226]) ).
tff(228,plain,
( ! [X: $i] :
( q_6(X)
| ~ p_7(X)
| ~ q_8(X) )
<=> ! [X: $i] :
( q_6(X)
| ~ p_7(X)
| ~ q_8(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(229,plain,
^ [X: $i] :
rewrite(
( ( q_6(X)
| ~ p_7(X)
| ~ q_8(X) )
<=> ( q_6(X)
| ~ p_7(X)
| ~ q_8(X) ) )),
inference(bind,[status(th)],]) ).
tff(230,plain,
( ! [X: $i] :
( q_6(X)
| ~ p_7(X)
| ~ q_8(X) )
<=> ! [X: $i] :
( q_6(X)
| ~ p_7(X)
| ~ q_8(X) ) ),
inference(quant_intro,[status(thm)],[229]) ).
tff(231,axiom,
! [X: $i] :
( q_6(X)
| ~ p_7(X)
| ~ q_8(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type12_13) ).
tff(232,plain,
! [X: $i] :
( q_6(X)
| ~ p_7(X)
| ~ q_8(X) ),
inference(modus_ponens,[status(thm)],[231,230]) ).
tff(233,plain,
! [X: $i] :
( q_6(X)
| ~ p_7(X)
| ~ q_8(X) ),
inference(modus_ponens,[status(thm)],[232,228]) ).
tff(234,plain,
! [X: $i] :
( q_6(X)
| ~ p_7(X)
| ~ q_8(X) ),
inference(skolemize,[status(sab)],[233]) ).
tff(235,plain,
! [X: $i] :
( q_6(X)
| ~ p_7(X)
| ~ q_8(X) ),
inference(modus_ponens,[status(thm)],[234,227]) ).
tff(236,plain,
( ( ~ ! [X: $i] :
( q_6(X)
| ~ p_7(X)
| ~ q_8(X) )
| q_6(a)
| ~ p_7(a)
| ~ q_8(a) )
<=> ( ~ ! [X: $i] :
( q_6(X)
| ~ p_7(X)
| ~ q_8(X) )
| q_6(a)
| ~ p_7(a)
| ~ q_8(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(237,plain,
( ~ ! [X: $i] :
( q_6(X)
| ~ p_7(X)
| ~ q_8(X) )
| q_6(a)
| ~ p_7(a)
| ~ q_8(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(238,plain,
( ~ ! [X: $i] :
( q_6(X)
| ~ p_7(X)
| ~ q_8(X) )
| q_6(a)
| ~ p_7(a)
| ~ q_8(a) ),
inference(modus_ponens,[status(thm)],[237,236]) ).
tff(239,plain,
q_6(a),
inference(unit_resolution,[status(thm)],[238,235,183,225]) ).
tff(240,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(241,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)],[240]) ).
tff(242,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(243,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(244,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)],[243]) ).
tff(245,axiom,
! [X: $i] :
( p_4(X)
| ~ q_5(X)
| ~ q_6(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type11_10) ).
tff(246,plain,
! [X: $i] :
( p_4(X)
| ~ q_5(X)
| ~ q_6(X) ),
inference(modus_ponens,[status(thm)],[245,244]) ).
tff(247,plain,
! [X: $i] :
( p_4(X)
| ~ q_5(X)
| ~ q_6(X) ),
inference(modus_ponens,[status(thm)],[246,242]) ).
tff(248,plain,
! [X: $i] :
( p_4(X)
| ~ q_5(X)
| ~ q_6(X) ),
inference(skolemize,[status(sab)],[247]) ).
tff(249,plain,
! [X: $i] :
( p_4(X)
| ~ q_5(X)
| ~ q_6(X) ),
inference(modus_ponens,[status(thm)],[248,241]) ).
tff(250,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(251,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(252,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)],[251,250]) ).
tff(253,plain,
p_4(a),
inference(unit_resolution,[status(thm)],[252,249,239,211]) ).
tff(254,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(255,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)],[254]) ).
tff(256,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(257,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(258,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)],[257]) ).
tff(259,axiom,
! [X: $i] :
( q_3(X)
| ~ p_4(X)
| ~ q_5(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type12_7) ).
tff(260,plain,
! [X: $i] :
( q_3(X)
| ~ p_4(X)
| ~ q_5(X) ),
inference(modus_ponens,[status(thm)],[259,258]) ).
tff(261,plain,
! [X: $i] :
( q_3(X)
| ~ p_4(X)
| ~ q_5(X) ),
inference(modus_ponens,[status(thm)],[260,256]) ).
tff(262,plain,
! [X: $i] :
( q_3(X)
| ~ p_4(X)
| ~ q_5(X) ),
inference(skolemize,[status(sab)],[261]) ).
tff(263,plain,
! [X: $i] :
( q_3(X)
| ~ p_4(X)
| ~ q_5(X) ),
inference(modus_ponens,[status(thm)],[262,255]) ).
tff(264,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(265,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(266,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)],[265,264]) ).
tff(267,plain,
q_3(a),
inference(unit_resolution,[status(thm)],[266,263,211,253]) ).
tff(268,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(269,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)],[268]) ).
tff(270,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(271,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(272,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)],[271]) ).
tff(273,axiom,
! [X: $i] :
( p_5(X)
| ~ q_6(X)
| ~ q_7(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type11_12) ).
tff(274,plain,
! [X: $i] :
( p_5(X)
| ~ q_6(X)
| ~ q_7(X) ),
inference(modus_ponens,[status(thm)],[273,272]) ).
tff(275,plain,
! [X: $i] :
( p_5(X)
| ~ q_6(X)
| ~ q_7(X) ),
inference(modus_ponens,[status(thm)],[274,270]) ).
tff(276,plain,
! [X: $i] :
( p_5(X)
| ~ q_6(X)
| ~ q_7(X) ),
inference(skolemize,[status(sab)],[275]) ).
tff(277,plain,
! [X: $i] :
( p_5(X)
| ~ q_6(X)
| ~ q_7(X) ),
inference(modus_ponens,[status(thm)],[276,269]) ).
tff(278,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(279,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(280,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)],[279,278]) ).
tff(281,plain,
p_5(a),
inference(unit_resolution,[status(thm)],[280,277,155,239]) ).
tff(282,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(283,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)],[282]) ).
tff(284,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(285,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(286,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)],[285]) ).
tff(287,axiom,
! [X: $i] :
( q_4(X)
| ~ p_5(X)
| ~ q_6(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type12_9) ).
tff(288,plain,
! [X: $i] :
( q_4(X)
| ~ p_5(X)
| ~ q_6(X) ),
inference(modus_ponens,[status(thm)],[287,286]) ).
tff(289,plain,
! [X: $i] :
( q_4(X)
| ~ p_5(X)
| ~ q_6(X) ),
inference(modus_ponens,[status(thm)],[288,284]) ).
tff(290,plain,
! [X: $i] :
( q_4(X)
| ~ p_5(X)
| ~ q_6(X) ),
inference(skolemize,[status(sab)],[289]) ).
tff(291,plain,
! [X: $i] :
( q_4(X)
| ~ p_5(X)
| ~ q_6(X) ),
inference(modus_ponens,[status(thm)],[290,283]) ).
tff(292,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(293,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(294,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)],[293,292]) ).
tff(295,plain,
q_4(a),
inference(unit_resolution,[status(thm)],[294,291,239,281]) ).
tff(296,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(297,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)],[296]) ).
tff(298,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(299,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(300,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)],[299]) ).
tff(301,axiom,
! [X: $i] :
( p_2(X)
| ~ q_3(X)
| ~ q_4(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type11_6) ).
tff(302,plain,
! [X: $i] :
( p_2(X)
| ~ q_3(X)
| ~ q_4(X) ),
inference(modus_ponens,[status(thm)],[301,300]) ).
tff(303,plain,
! [X: $i] :
( p_2(X)
| ~ q_3(X)
| ~ q_4(X) ),
inference(modus_ponens,[status(thm)],[302,298]) ).
tff(304,plain,
! [X: $i] :
( p_2(X)
| ~ q_3(X)
| ~ q_4(X) ),
inference(skolemize,[status(sab)],[303]) ).
tff(305,plain,
! [X: $i] :
( p_2(X)
| ~ q_3(X)
| ~ q_4(X) ),
inference(modus_ponens,[status(thm)],[304,297]) ).
tff(306,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(307,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(308,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)],[307,306]) ).
tff(309,plain,
p_2(a),
inference(unit_resolution,[status(thm)],[308,305,295,267]) ).
tff(310,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(311,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)],[310]) ).
tff(312,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(313,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(314,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)],[313]) ).
tff(315,axiom,
! [X: $i] :
( q_1(X)
| ~ p_2(X)
| ~ q_3(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type12_3) ).
tff(316,plain,
! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) ),
inference(modus_ponens,[status(thm)],[315,314]) ).
tff(317,plain,
! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) ),
inference(modus_ponens,[status(thm)],[316,312]) ).
tff(318,plain,
! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) ),
inference(skolemize,[status(sab)],[317]) ).
tff(319,plain,
! [X: $i] :
( ~ p_2(X)
| q_1(X)
| ~ q_3(X) ),
inference(modus_ponens,[status(thm)],[318,311]) ).
tff(320,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(321,plain,
( ( ~ p_2(a)
| q_1(a)
| ~ q_3(a) )
<=> ( ~ q_3(a)
| ~ p_2(a)
| q_1(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(322,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)],[321]) ).
tff(323,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)],[322,320]) ).
tff(324,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(325,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)],[324,323]) ).
tff(326,plain,
q_1(a),
inference(unit_resolution,[status(thm)],[325,319,267,309]) ).
tff(327,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(328,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)],[327]) ).
tff(329,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(330,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(331,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)],[330]) ).
tff(332,axiom,
! [X: $i] :
( p_3(X)
| ~ q_4(X)
| ~ q_5(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type11_8) ).
tff(333,plain,
! [X: $i] :
( p_3(X)
| ~ q_4(X)
| ~ q_5(X) ),
inference(modus_ponens,[status(thm)],[332,331]) ).
tff(334,plain,
! [X: $i] :
( p_3(X)
| ~ q_4(X)
| ~ q_5(X) ),
inference(modus_ponens,[status(thm)],[333,329]) ).
tff(335,plain,
! [X: $i] :
( p_3(X)
| ~ q_4(X)
| ~ q_5(X) ),
inference(skolemize,[status(sab)],[334]) ).
tff(336,plain,
! [X: $i] :
( p_3(X)
| ~ q_4(X)
| ~ q_5(X) ),
inference(modus_ponens,[status(thm)],[335,328]) ).
tff(337,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(338,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(339,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)],[338,337]) ).
tff(340,plain,
p_3(a),
inference(unit_resolution,[status(thm)],[339,336,211,295]) ).
tff(341,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(342,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)],[341]) ).
tff(343,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(344,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(345,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)],[344]) ).
tff(346,axiom,
! [X: $i] :
( q_2(X)
| ~ p_3(X)
| ~ q_4(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type12_5) ).
tff(347,plain,
! [X: $i] :
( q_2(X)
| ~ p_3(X)
| ~ q_4(X) ),
inference(modus_ponens,[status(thm)],[346,345]) ).
tff(348,plain,
! [X: $i] :
( q_2(X)
| ~ p_3(X)
| ~ q_4(X) ),
inference(modus_ponens,[status(thm)],[347,343]) ).
tff(349,plain,
! [X: $i] :
( q_2(X)
| ~ p_3(X)
| ~ q_4(X) ),
inference(skolemize,[status(sab)],[348]) ).
tff(350,plain,
! [X: $i] :
( q_2(X)
| ~ p_3(X)
| ~ q_4(X) ),
inference(modus_ponens,[status(thm)],[349,342]) ).
tff(351,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(352,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(353,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)],[352,351]) ).
tff(354,plain,
q_2(a),
inference(unit_resolution,[status(thm)],[353,350,295,340]) ).
tff(355,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(356,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)],[355]) ).
tff(357,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(358,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(359,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)],[358]) ).
tff(360,axiom,
! [X: $i] :
( p_0(X)
| ~ q_1(X)
| ~ q_2(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type11_2) ).
tff(361,plain,
! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) ),
inference(modus_ponens,[status(thm)],[360,359]) ).
tff(362,plain,
! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) ),
inference(modus_ponens,[status(thm)],[361,357]) ).
tff(363,plain,
! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) ),
inference(skolemize,[status(sab)],[362]) ).
tff(364,plain,
! [X: $i] :
( p_0(X)
| ~ q_2(X)
| ~ q_1(X) ),
inference(modus_ponens,[status(thm)],[363,356]) ).
tff(365,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(366,plain,
( ( p_0(a)
| ~ q_2(a)
| ~ q_1(a) )
<=> ( ~ q_2(a)
| p_0(a)
| ~ q_1(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(367,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)],[366]) ).
tff(368,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)],[367,365]) ).
tff(369,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(370,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)],[369,368]) ).
tff(371,plain,
p_0(a),
inference(unit_resolution,[status(thm)],[370,364,354,326]) ).
tff(372,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(373,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)],[372]) ).
tff(374,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(375,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(376,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)],[375]) ).
tff(377,axiom,
! [X: $i] :
( p_1(X)
| ~ q_2(X)
| ~ q_3(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type11_4) ).
tff(378,plain,
! [X: $i] :
( p_1(X)
| ~ q_2(X)
| ~ q_3(X) ),
inference(modus_ponens,[status(thm)],[377,376]) ).
tff(379,plain,
! [X: $i] :
( p_1(X)
| ~ q_2(X)
| ~ q_3(X) ),
inference(modus_ponens,[status(thm)],[378,374]) ).
tff(380,plain,
! [X: $i] :
( p_1(X)
| ~ q_2(X)
| ~ q_3(X) ),
inference(skolemize,[status(sab)],[379]) ).
tff(381,plain,
! [X: $i] :
( p_1(X)
| ~ q_2(X)
| ~ q_3(X) ),
inference(modus_ponens,[status(thm)],[380,373]) ).
tff(382,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(383,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(384,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)],[383,382]) ).
tff(385,plain,
p_1(a),
inference(unit_resolution,[status(thm)],[384,381,267,354]) ).
tff(386,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(387,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)],[386]) ).
tff(388,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(389,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(390,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)],[389]) ).
tff(391,axiom,
! [X: $i] :
( q_0(X)
| ~ p_1(X)
| ~ q_2(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_type12_1) ).
tff(392,plain,
! [X: $i] :
( q_0(X)
| ~ p_1(X)
| ~ q_2(X) ),
inference(modus_ponens,[status(thm)],[391,390]) ).
tff(393,plain,
! [X: $i] :
( q_0(X)
| ~ p_1(X)
| ~ q_2(X) ),
inference(modus_ponens,[status(thm)],[392,388]) ).
tff(394,plain,
! [X: $i] :
( q_0(X)
| ~ p_1(X)
| ~ q_2(X) ),
inference(skolemize,[status(sab)],[393]) ).
tff(395,plain,
! [X: $i] :
( q_0(X)
| ~ p_1(X)
| ~ q_2(X) ),
inference(modus_ponens,[status(thm)],[394,387]) ).
tff(396,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(397,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(398,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)],[397,396]) ).
tff(399,plain,
q_0(a),
inference(unit_resolution,[status(thm)],[398,395,354,385]) ).
tff(400,plain,
^ [X: $i] :
refl(
( ( ~ p_0(X)
| ~ q_0(X) )
<=> ( ~ p_0(X)
| ~ q_0(X) ) )),
inference(bind,[status(th)],]) ).
tff(401,plain,
( ! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) )
<=> ! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) ) ),
inference(quant_intro,[status(thm)],[400]) ).
tff(402,plain,
( ! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) )
<=> ! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(403,axiom,
! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s3_goal_1) ).
tff(404,plain,
! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) ),
inference(modus_ponens,[status(thm)],[403,402]) ).
tff(405,plain,
! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) ),
inference(skolemize,[status(sab)],[404]) ).
tff(406,plain,
! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) ),
inference(modus_ponens,[status(thm)],[405,401]) ).
tff(407,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(408,plain,
( ~ ! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) )
| ~ p_0(a)
| ~ q_0(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(409,plain,
( ~ ! [X: $i] :
( ~ p_0(X)
| ~ q_0(X) )
| ~ p_0(a)
| ~ q_0(a) ),
inference(modus_ponens,[status(thm)],[408,407]) ).
tff(410,plain,
$false,
inference(unit_resolution,[status(thm)],[409,406,399,371]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN096-1.008 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 01:55:31 EDT 2022
% 0.13/0.33 % 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.
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------