TSTP Solution File: SYN569-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN569-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 23:56:27 EDT 2022
% Result : Unsatisfiable 2.77s 2.00s
% Output : Proof 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 72
% Syntax : Number of formulae : 143 ( 37 unt; 13 typ; 0 def)
% Number of atoms : 697 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 1018 ( 494 ~; 454 |; 0 &)
% ( 70 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 43 ( 43 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 8 >; 8 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 327 ( 296 !; 0 ?; 327 :)
% Comments :
%------------------------------------------------------------------------------
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(f4_type,type,
f4: ( $i * $i ) > $i ).
tff(f3_type,type,
f3: $i > $i ).
tff(c14_type,type,
c14: $i ).
tff(f5_type,type,
f5: ( $i * $i ) > $i ).
tff(c11_type,type,
c11: $i ).
tff(c12_type,type,
c12: $i ).
tff(c15_type,type,
c15: $i ).
tff(p9_type,type,
p9: ( $i * $i * $i ) > $o ).
tff(c13_type,type,
c13: $i ).
tff(p10_type,type,
p10: ( $i * $i ) > $o ).
tff(p8_type,type,
p8: ( $i * $i ) > $o ).
tff(f7_type,type,
f7: ( $i * $i ) > $i ).
tff(1,plain,
^ [X6: $i] :
refl(
( p2(X6,X6)
<=> p2(X6,X6) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X6: $i] : p2(X6,X6)
<=> ! [X6: $i] : p2(X6,X6) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X6: $i] : p2(X6,X6)
<=> ! [X6: $i] : p2(X6,X6) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X6: $i] : p2(X6,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_1) ).
tff(5,plain,
! [X6: $i] : p2(X6,X6),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X6: $i] : p2(X6,X6),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X6: $i] : p2(X6,X6),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X6: $i] : p2(X6,X6)
| p2(f5(c12,c11),f5(c12,c11)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p2(f5(c12,c11),f5(c12,c11)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X4: $i,X5: $i] :
refl(
( ( ~ p8(X4,X5)
| p10(X4,X5) )
<=> ( ~ p8(X4,X5)
| p10(X4,X5) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X4: $i,X5: $i] :
( ~ p8(X4,X5)
| p10(X4,X5) )
<=> ! [X4: $i,X5: $i] :
( ~ p8(X4,X5)
| p10(X4,X5) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X4: $i,X5: $i] :
( ~ p8(X4,X5)
| p10(X4,X5) )
<=> ! [X4: $i,X5: $i] :
( ~ p8(X4,X5)
| p10(X4,X5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X4: $i,X5: $i] :
rewrite(
( ( p10(X4,X5)
| ~ p8(X4,X5) )
<=> ( ~ p8(X4,X5)
| p10(X4,X5) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X4: $i,X5: $i] :
( p10(X4,X5)
| ~ p8(X4,X5) )
<=> ! [X4: $i,X5: $i] :
( ~ p8(X4,X5)
| p10(X4,X5) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X4: $i,X5: $i] :
( p10(X4,X5)
| ~ p8(X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10_7) ).
tff(16,plain,
! [X4: $i,X5: $i] :
( ~ p8(X4,X5)
| p10(X4,X5) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X4: $i,X5: $i] :
( ~ p8(X4,X5)
| p10(X4,X5) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X4: $i,X5: $i] :
( ~ p8(X4,X5)
| p10(X4,X5) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X4: $i,X5: $i] :
( ~ p8(X4,X5)
| p10(X4,X5) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( p8(c11,c14)
<=> p8(c11,c14) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
p8(c11,c14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8_5) ).
tff(22,plain,
p8(c11,c14),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [X4: $i,X5: $i] :
( ~ p8(X4,X5)
| p10(X4,X5) )
| ~ p8(c11,c14)
| p10(c11,c14) )
<=> ( ~ ! [X4: $i,X5: $i] :
( ~ p8(X4,X5)
| p10(X4,X5) )
| ~ p8(c11,c14)
| p10(c11,c14) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ! [X4: $i,X5: $i] :
( ~ p8(X4,X5)
| p10(X4,X5) )
| ~ p8(c11,c14)
| p10(c11,c14) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [X4: $i,X5: $i] :
( ~ p8(X4,X5)
| p10(X4,X5) )
| ~ p8(c11,c14)
| p10(c11,c14) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
p10(c11,c14),
inference(unit_resolution,[status(thm)],[25,22,19]) ).
tff(27,plain,
( p8(c14,c12)
<=> p8(c14,c12) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
p8(c14,c12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8_3) ).
tff(29,plain,
p8(c14,c12),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
( ( ~ ! [X4: $i,X5: $i] :
( ~ p8(X4,X5)
| p10(X4,X5) )
| ~ p8(c14,c12)
| p10(c14,c12) )
<=> ( ~ ! [X4: $i,X5: $i] :
( ~ p8(X4,X5)
| p10(X4,X5) )
| ~ p8(c14,c12)
| p10(c14,c12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ~ ! [X4: $i,X5: $i] :
( ~ p8(X4,X5)
| p10(X4,X5) )
| ~ p8(c14,c12)
| p10(c14,c12) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
( ~ ! [X4: $i,X5: $i] :
( ~ p8(X4,X5)
| p10(X4,X5) )
| ~ p8(c14,c12)
| p10(c14,c12) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
p10(c14,c12),
inference(unit_resolution,[status(thm)],[32,29,19]) ).
tff(34,plain,
^ [X40: $i] :
refl(
( ( ~ p10(c11,X40)
| ~ p10(X40,c12)
| p9(c13,f3(X40),X40) )
<=> ( ~ p10(c11,X40)
| ~ p10(X40,c12)
| p9(c13,f3(X40),X40) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [X40: $i] :
( ~ p10(c11,X40)
| ~ p10(X40,c12)
| p9(c13,f3(X40),X40) )
<=> ! [X40: $i] :
( ~ p10(c11,X40)
| ~ p10(X40,c12)
| p9(c13,f3(X40),X40) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [X40: $i] :
( ~ p10(c11,X40)
| ~ p10(X40,c12)
| p9(c13,f3(X40),X40) )
<=> ! [X40: $i] :
( ~ p10(c11,X40)
| ~ p10(X40,c12)
| p9(c13,f3(X40),X40) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
^ [X40: $i] :
trans(
monotonicity(
rewrite(
( ( p9(c13,f3(X40),X40)
| ~ p10(X40,c12) )
<=> ( ~ p10(X40,c12)
| p9(c13,f3(X40),X40) ) )),
( ( p9(c13,f3(X40),X40)
| ~ p10(X40,c12)
| ~ p10(c11,X40) )
<=> ( ~ p10(X40,c12)
| p9(c13,f3(X40),X40)
| ~ p10(c11,X40) ) )),
rewrite(
( ( ~ p10(X40,c12)
| p9(c13,f3(X40),X40)
| ~ p10(c11,X40) )
<=> ( ~ p10(c11,X40)
| ~ p10(X40,c12)
| p9(c13,f3(X40),X40) ) )),
( ( p9(c13,f3(X40),X40)
| ~ p10(X40,c12)
| ~ p10(c11,X40) )
<=> ( ~ p10(c11,X40)
| ~ p10(X40,c12)
| p9(c13,f3(X40),X40) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [X40: $i] :
( p9(c13,f3(X40),X40)
| ~ p10(X40,c12)
| ~ p10(c11,X40) )
<=> ! [X40: $i] :
( ~ p10(c11,X40)
| ~ p10(X40,c12)
| p9(c13,f3(X40),X40) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,axiom,
! [X40: $i] :
( p9(c13,f3(X40),X40)
| ~ p10(X40,c12)
| ~ p10(c11,X40) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9_12) ).
tff(40,plain,
! [X40: $i] :
( ~ p10(c11,X40)
| ~ p10(X40,c12)
| p9(c13,f3(X40),X40) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [X40: $i] :
( ~ p10(c11,X40)
| ~ p10(X40,c12)
| p9(c13,f3(X40),X40) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
! [X40: $i] :
( ~ p10(c11,X40)
| ~ p10(X40,c12)
| p9(c13,f3(X40),X40) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [X40: $i] :
( ~ p10(c11,X40)
| ~ p10(X40,c12)
| p9(c13,f3(X40),X40) ),
inference(modus_ponens,[status(thm)],[42,35]) ).
tff(44,plain,
( ( ~ ! [X40: $i] :
( ~ p10(c11,X40)
| ~ p10(X40,c12)
| p9(c13,f3(X40),X40) )
| ~ p10(c11,c14)
| ~ p10(c14,c12)
| p9(c13,f3(c14),c14) )
<=> ( ~ ! [X40: $i] :
( ~ p10(c11,X40)
| ~ p10(X40,c12)
| p9(c13,f3(X40),X40) )
| ~ p10(c11,c14)
| ~ p10(c14,c12)
| p9(c13,f3(c14),c14) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ~ ! [X40: $i] :
( ~ p10(c11,X40)
| ~ p10(X40,c12)
| p9(c13,f3(X40),X40) )
| ~ p10(c11,c14)
| ~ p10(c14,c12)
| p9(c13,f3(c14),c14) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
( ~ ! [X40: $i] :
( ~ p10(c11,X40)
| ~ p10(X40,c12)
| p9(c13,f3(X40),X40) )
| ~ p10(c11,c14)
| ~ p10(c14,c12)
| p9(c13,f3(c14),c14) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
p9(c13,f3(c14),c14),
inference(unit_resolution,[status(thm)],[46,43,33,26]) ).
tff(48,plain,
^ [X9: $i,X12: $i,X11: $i,X10: $i] :
refl(
( ( ~ p9(X11,X10,X12)
| ~ p9(X11,X9,X12)
| p2(X9,X10) )
<=> ( ~ p9(X11,X10,X12)
| ~ p9(X11,X9,X12)
| p2(X9,X10) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p9(X11,X10,X12)
| ~ p9(X11,X9,X12)
| p2(X9,X10) )
<=> ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p9(X11,X10,X12)
| ~ p9(X11,X9,X12)
| p2(X9,X10) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p9(X11,X10,X12)
| ~ p9(X11,X9,X12)
| p2(X9,X10) )
<=> ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p9(X11,X10,X12)
| ~ p9(X11,X9,X12)
| p2(X9,X10) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
^ [X9: $i,X12: $i,X11: $i,X10: $i] :
trans(
monotonicity(
rewrite(
( ( p2(X9,X10)
| ~ p9(X11,X9,X12) )
<=> ( ~ p9(X11,X9,X12)
| p2(X9,X10) ) )),
( ( p2(X9,X10)
| ~ p9(X11,X9,X12)
| ~ p9(X11,X10,X12) )
<=> ( ~ p9(X11,X9,X12)
| p2(X9,X10)
| ~ p9(X11,X10,X12) ) )),
rewrite(
( ( ~ p9(X11,X9,X12)
| p2(X9,X10)
| ~ p9(X11,X10,X12) )
<=> ( ~ p9(X11,X10,X12)
| ~ p9(X11,X9,X12)
| p2(X9,X10) ) )),
( ( p2(X9,X10)
| ~ p9(X11,X9,X12)
| ~ p9(X11,X10,X12) )
<=> ( ~ p9(X11,X10,X12)
| ~ p9(X11,X9,X12)
| p2(X9,X10) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( p2(X9,X10)
| ~ p9(X11,X9,X12)
| ~ p9(X11,X10,X12) )
<=> ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p9(X11,X10,X12)
| ~ p9(X11,X9,X12)
| p2(X9,X10) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,axiom,
! [X9: $i,X12: $i,X11: $i,X10: $i] :
( p2(X9,X10)
| ~ p9(X11,X9,X12)
| ~ p9(X11,X10,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_11) ).
tff(54,plain,
! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p9(X11,X10,X12)
| ~ p9(X11,X9,X12)
| p2(X9,X10) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p9(X11,X10,X12)
| ~ p9(X11,X9,X12)
| p2(X9,X10) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p9(X11,X10,X12)
| ~ p9(X11,X9,X12)
| p2(X9,X10) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p9(X11,X10,X12)
| ~ p9(X11,X9,X12)
| p2(X9,X10) ),
inference(modus_ponens,[status(thm)],[56,49]) ).
tff(58,plain,
( p9(c13,c15,c14)
<=> p9(c13,c15,c14) ),
inference(rewrite,[status(thm)],]) ).
tff(59,axiom,
p9(c13,c15,c14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9_6) ).
tff(60,plain,
p9(c13,c15,c14),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( ( ~ ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p9(X11,X10,X12)
| ~ p9(X11,X9,X12)
| p2(X9,X10) )
| ~ p9(c13,c15,c14)
| ~ p9(c13,f3(c14),c14)
| p2(f3(c14),c15) )
<=> ( ~ ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p9(X11,X10,X12)
| ~ p9(X11,X9,X12)
| p2(X9,X10) )
| ~ p9(c13,c15,c14)
| ~ p9(c13,f3(c14),c14)
| p2(f3(c14),c15) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ~ ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p9(X11,X10,X12)
| ~ p9(X11,X9,X12)
| p2(X9,X10) )
| ~ p9(c13,c15,c14)
| ~ p9(c13,f3(c14),c14)
| p2(f3(c14),c15) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( ~ ! [X9: $i,X12: $i,X11: $i,X10: $i] :
( ~ p9(X11,X10,X12)
| ~ p9(X11,X9,X12)
| p2(X9,X10) )
| ~ p9(c13,c15,c14)
| ~ p9(c13,f3(c14),c14)
| p2(f3(c14),c15) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
p2(f3(c14),c15),
inference(unit_resolution,[status(thm)],[63,60,57,47]) ).
tff(65,plain,
^ [X17: $i,X16: $i,X18: $i,X15: $i] :
refl(
( ( ~ p2(X16,X18)
| ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) )
<=> ( ~ p2(X16,X18)
| ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( ~ p2(X16,X18)
| ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) )
<=> ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( ~ p2(X16,X18)
| ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( ~ p2(X16,X18)
| ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) )
<=> ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( ~ p2(X16,X18)
| ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
^ [X17: $i,X16: $i,X18: $i,X15: $i] :
trans(
monotonicity(
rewrite(
( ( p2(f4(X15,X16),f4(X17,X18))
| ~ p2(X15,X17) )
<=> ( ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) ) )),
( ( p2(f4(X15,X16),f4(X17,X18))
| ~ p2(X15,X17)
| ~ p2(X16,X18) )
<=> ( ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18))
| ~ p2(X16,X18) ) )),
rewrite(
( ( ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18))
| ~ p2(X16,X18) )
<=> ( ~ p2(X16,X18)
| ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) ) )),
( ( p2(f4(X15,X16),f4(X17,X18))
| ~ p2(X15,X17)
| ~ p2(X16,X18) )
<=> ( ~ p2(X16,X18)
| ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(f4(X15,X16),f4(X17,X18))
| ~ p2(X15,X17)
| ~ p2(X16,X18) )
<=> ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( ~ p2(X16,X18)
| ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,axiom,
! [X17: $i,X16: $i,X18: $i,X15: $i] :
( p2(f4(X15,X16),f4(X17,X18))
| ~ p2(X15,X17)
| ~ p2(X16,X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_16) ).
tff(71,plain,
! [X17: $i,X16: $i,X18: $i,X15: $i] :
( ~ p2(X16,X18)
| ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [X17: $i,X16: $i,X18: $i,X15: $i] :
( ~ p2(X16,X18)
| ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
! [X17: $i,X16: $i,X18: $i,X15: $i] :
( ~ p2(X16,X18)
| ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [X17: $i,X16: $i,X18: $i,X15: $i] :
( ~ p2(X16,X18)
| ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) ),
inference(modus_ponens,[status(thm)],[73,66]) ).
tff(75,plain,
( ( ~ ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( ~ p2(X16,X18)
| ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) )
| ~ p2(f3(c14),c15)
| ~ p2(f5(c12,c11),f5(c12,c11))
| p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),c15)) )
<=> ( ~ ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( ~ p2(X16,X18)
| ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) )
| ~ p2(f3(c14),c15)
| ~ p2(f5(c12,c11),f5(c12,c11))
| p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),c15)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
( ~ ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( ~ p2(X16,X18)
| ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) )
| ~ p2(f3(c14),c15)
| ~ p2(f5(c12,c11),f5(c12,c11))
| p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),c15)) ),
inference(quant_inst,[status(thm)],]) ).
tff(77,plain,
( ~ ! [X17: $i,X16: $i,X18: $i,X15: $i] :
( ~ p2(X16,X18)
| ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) )
| ~ p2(f3(c14),c15)
| ~ p2(f5(c12,c11),f5(c12,c11))
| p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),c15)) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),c15)),
inference(unit_resolution,[status(thm)],[77,74,64,9]) ).
tff(79,plain,
( ~ ! [X6: $i] : p2(X6,X6)
| p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),f3(c14))) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),f3(c14))),
inference(unit_resolution,[status(thm)],[79,7]) ).
tff(81,plain,
^ [X6: $i,X7: $i,X8: $i] :
refl(
( ( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
<=> ( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
<=> ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
<=> ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
^ [X6: $i,X7: $i,X8: $i] :
trans(
monotonicity(
rewrite(
( ( p2(X7,X8)
| ~ p2(X6,X7) )
<=> ( ~ p2(X6,X7)
| p2(X7,X8) ) )),
( ( p2(X7,X8)
| ~ p2(X6,X7)
| ~ p2(X6,X8) )
<=> ( ~ p2(X6,X7)
| p2(X7,X8)
| ~ p2(X6,X8) ) )),
rewrite(
( ( ~ p2(X6,X7)
| p2(X7,X8)
| ~ p2(X6,X8) )
<=> ( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) ) )),
( ( p2(X7,X8)
| ~ p2(X6,X7)
| ~ p2(X6,X8) )
<=> ( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) ) )),
inference(bind,[status(th)],]) ).
tff(85,plain,
( ! [X6: $i,X7: $i,X8: $i] :
( p2(X7,X8)
| ~ p2(X6,X7)
| ~ p2(X6,X8) )
<=> ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,axiom,
! [X6: $i,X7: $i,X8: $i] :
( p2(X7,X8)
| ~ p2(X6,X7)
| ~ p2(X6,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_10) ).
tff(87,plain,
! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) ),
inference(modus_ponens,[status(thm)],[89,82]) ).
tff(91,plain,
( ( ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
| ~ p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),c15))
| ~ p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),f3(c14)))
| p2(f4(f5(c12,c11),c15),f4(f5(c12,c11),f3(c14))) )
<=> ( ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
| ~ p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),c15))
| ~ p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),f3(c14)))
| p2(f4(f5(c12,c11),c15),f4(f5(c12,c11),f3(c14))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( ( ~ p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),f3(c14)))
| ~ p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),c15))
| p2(f4(f5(c12,c11),c15),f4(f5(c12,c11),f3(c14))) )
<=> ( ~ p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),c15))
| ~ p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),f3(c14)))
| p2(f4(f5(c12,c11),c15),f4(f5(c12,c11),f3(c14))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ( ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
| ~ p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),f3(c14)))
| ~ p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),c15))
| p2(f4(f5(c12,c11),c15),f4(f5(c12,c11),f3(c14))) )
<=> ( ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
| ~ p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),c15))
| ~ p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),f3(c14)))
| p2(f4(f5(c12,c11),c15),f4(f5(c12,c11),f3(c14))) ) ),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
( ( ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
| ~ p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),f3(c14)))
| ~ p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),c15))
| p2(f4(f5(c12,c11),c15),f4(f5(c12,c11),f3(c14))) )
<=> ( ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
| ~ p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),c15))
| ~ p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),f3(c14)))
| p2(f4(f5(c12,c11),c15),f4(f5(c12,c11),f3(c14))) ) ),
inference(transitivity,[status(thm)],[93,91]) ).
tff(95,plain,
( ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
| ~ p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),f3(c14)))
| ~ p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),c15))
| p2(f4(f5(c12,c11),c15),f4(f5(c12,c11),f3(c14))) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
( ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
| ~ p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),c15))
| ~ p2(f4(f5(c12,c11),f3(c14)),f4(f5(c12,c11),f3(c14)))
| p2(f4(f5(c12,c11),c15),f4(f5(c12,c11),f3(c14))) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
p2(f4(f5(c12,c11),c15),f4(f5(c12,c11),f3(c14))),
inference(unit_resolution,[status(thm)],[96,90,80,78]) ).
tff(98,plain,
( ~ ! [X6: $i] : p2(X6,X6)
| p2(f5(f7(c13,c12),f7(c13,c11)),f5(f7(c13,c12),f7(c13,c11))) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
p2(f5(f7(c13,c12),f7(c13,c11)),f5(f7(c13,c12),f7(c13,c11))),
inference(unit_resolution,[status(thm)],[98,7]) ).
tff(100,plain,
( p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),c15))
<=> p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),c15)) ),
inference(rewrite,[status(thm)],]) ).
tff(101,axiom,
p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),c15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_15) ).
tff(102,plain,
p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),c15)),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
( ( ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),c15))
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f5(f7(c13,c12),f7(c13,c11)))
| p2(f4(f5(c12,c11),c15),f5(f7(c13,c12),f7(c13,c11))) )
<=> ( ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),c15))
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f5(f7(c13,c12),f7(c13,c11)))
| p2(f4(f5(c12,c11),c15),f5(f7(c13,c12),f7(c13,c11))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f5(f7(c13,c12),f7(c13,c11)))
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),c15))
| p2(f4(f5(c12,c11),c15),f5(f7(c13,c12),f7(c13,c11))) )
<=> ( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),c15))
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f5(f7(c13,c12),f7(c13,c11)))
| p2(f4(f5(c12,c11),c15),f5(f7(c13,c12),f7(c13,c11))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ( ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f5(f7(c13,c12),f7(c13,c11)))
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),c15))
| p2(f4(f5(c12,c11),c15),f5(f7(c13,c12),f7(c13,c11))) )
<=> ( ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),c15))
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f5(f7(c13,c12),f7(c13,c11)))
| p2(f4(f5(c12,c11),c15),f5(f7(c13,c12),f7(c13,c11))) ) ),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( ( ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f5(f7(c13,c12),f7(c13,c11)))
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),c15))
| p2(f4(f5(c12,c11),c15),f5(f7(c13,c12),f7(c13,c11))) )
<=> ( ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),c15))
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f5(f7(c13,c12),f7(c13,c11)))
| p2(f4(f5(c12,c11),c15),f5(f7(c13,c12),f7(c13,c11))) ) ),
inference(transitivity,[status(thm)],[105,103]) ).
tff(107,plain,
( ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f5(f7(c13,c12),f7(c13,c11)))
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),c15))
| p2(f4(f5(c12,c11),c15),f5(f7(c13,c12),f7(c13,c11))) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
( ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),c15))
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f5(f7(c13,c12),f7(c13,c11)))
| p2(f4(f5(c12,c11),c15),f5(f7(c13,c12),f7(c13,c11))) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
p2(f4(f5(c12,c11),c15),f5(f7(c13,c12),f7(c13,c11))),
inference(unit_resolution,[status(thm)],[108,90,102,99]) ).
tff(110,plain,
^ [X41: $i] :
refl(
( ( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) )
<=> ( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) ) )),
inference(bind,[status(th)],]) ).
tff(111,plain,
( ! [X41: $i] :
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) )
<=> ! [X41: $i] :
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) ) ),
inference(quant_intro,[status(thm)],[110]) ).
tff(112,plain,
( ! [X41: $i] :
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) )
<=> ! [X41: $i] :
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
^ [X41: $i] :
trans(
monotonicity(
rewrite(
( ( ~ p8(X41,c12)
| ~ p8(c11,X41) )
<=> ( ~ p8(X41,c12)
| ~ p8(c11,X41) ) )),
( ( ~ p8(X41,c12)
| ~ p8(c11,X41)
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41))) )
<=> ( ~ p8(X41,c12)
| ~ p8(c11,X41)
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41))) ) )),
rewrite(
( ( ~ p8(X41,c12)
| ~ p8(c11,X41)
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41))) )
<=> ( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) ) )),
( ( ~ p8(X41,c12)
| ~ p8(c11,X41)
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41))) )
<=> ( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) ) )),
inference(bind,[status(th)],]) ).
tff(114,plain,
( ! [X41: $i] :
( ~ p8(X41,c12)
| ~ p8(c11,X41)
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41))) )
<=> ! [X41: $i] :
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,axiom,
! [X41: $i] :
( ~ p8(X41,c12)
| ~ p8(c11,X41)
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p8_20) ).
tff(116,plain,
! [X41: $i] :
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
! [X41: $i] :
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) ),
inference(modus_ponens,[status(thm)],[116,112]) ).
tff(118,plain,
! [X41: $i] :
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) ),
inference(skolemize,[status(sab)],[117]) ).
tff(119,plain,
! [X41: $i] :
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) ),
inference(modus_ponens,[status(thm)],[118,111]) ).
tff(120,plain,
( ( ~ ! [X41: $i] :
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) )
| ~ p8(c14,c12)
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(c14)))
| ~ p8(c11,c14) )
<=> ( ~ ! [X41: $i] :
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) )
| ~ p8(c14,c12)
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(c14)))
| ~ p8(c11,c14) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,plain,
( ( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(c14)))
| ~ p8(c14,c12)
| ~ p8(c11,c14) )
<=> ( ~ p8(c14,c12)
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(c14)))
| ~ p8(c11,c14) ) ),
inference(rewrite,[status(thm)],]) ).
tff(122,plain,
( ( ~ ! [X41: $i] :
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) )
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(c14)))
| ~ p8(c14,c12)
| ~ p8(c11,c14) )
<=> ( ~ ! [X41: $i] :
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) )
| ~ p8(c14,c12)
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(c14)))
| ~ p8(c11,c14) ) ),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
( ( ~ ! [X41: $i] :
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) )
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(c14)))
| ~ p8(c14,c12)
| ~ p8(c11,c14) )
<=> ( ~ ! [X41: $i] :
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) )
| ~ p8(c14,c12)
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(c14)))
| ~ p8(c11,c14) ) ),
inference(transitivity,[status(thm)],[122,120]) ).
tff(124,plain,
( ~ ! [X41: $i] :
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) )
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(c14)))
| ~ p8(c14,c12)
| ~ p8(c11,c14) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
( ~ ! [X41: $i] :
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(X41,c12)
| ~ p8(c11,X41) )
| ~ p8(c14,c12)
| ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(c14)))
| ~ p8(c11,c14) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(c14))),
inference(unit_resolution,[status(thm)],[125,29,22,119]) ).
tff(127,plain,
( ( ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
| ~ p2(f4(f5(c12,c11),c15),f4(f5(c12,c11),f3(c14)))
| ~ p2(f4(f5(c12,c11),c15),f5(f7(c13,c12),f7(c13,c11)))
| p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(c14))) )
<=> ( ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
| ~ p2(f4(f5(c12,c11),c15),f4(f5(c12,c11),f3(c14)))
| ~ p2(f4(f5(c12,c11),c15),f5(f7(c13,c12),f7(c13,c11)))
| p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(c14))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(128,plain,
( ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
| ~ p2(f4(f5(c12,c11),c15),f4(f5(c12,c11),f3(c14)))
| ~ p2(f4(f5(c12,c11),c15),f5(f7(c13,c12),f7(c13,c11)))
| p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(c14))) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
( ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) )
| ~ p2(f4(f5(c12,c11),c15),f4(f5(c12,c11),f3(c14)))
| ~ p2(f4(f5(c12,c11),c15),f5(f7(c13,c12),f7(c13,c11)))
| p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(c14))) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
$false,
inference(unit_resolution,[status(thm)],[129,90,126,109,97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN569-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 06:02:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 2.77/2.00 % SZS status Unsatisfiable
% 2.77/2.00 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------