TSTP Solution File: SYN577-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN577-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 23:56:29 EDT 2022
% Result : Unsatisfiable 10.33s 6.95s
% Output : Proof 10.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 84
% Syntax : Number of formulae : 159 ( 42 unt; 18 typ; 0 def)
% Number of atoms : 916 ( 0 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 1449 ( 711 ~; 660 |; 0 &)
% ( 78 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 37 ( 37 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 6 >; 5 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 12 con; 0-2 aty)
% Number of variables : 389 ( 368 !; 0 ?; 389 :)
% Comments :
%------------------------------------------------------------------------------
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(f5_type,type,
f5: ( $i * $i ) > $i ).
tff(c19_type,type,
c19: $i ).
tff(f6_type,type,
f6: $i > $i ).
tff(c9_type,type,
c9: $i ).
tff(f4_type,type,
f4: ( $i * $i ) > $i ).
tff(c14_type,type,
c14: $i ).
tff(f3_type,type,
f3: ( $i * $i ) > $i ).
tff(c11_type,type,
c11: $i ).
tff(c12_type,type,
c12: $i ).
tff(c17_type,type,
c17: $i ).
tff(c15_type,type,
c15: $i ).
tff(c20_type,type,
c20: $i ).
tff(c16_type,type,
c16: $i ).
tff(c18_type,type,
c18: $i ).
tff(c13_type,type,
c13: $i ).
tff(p7_type,type,
p7: ( $i * $i ) > $o ).
tff(c10_type,type,
c10: $i ).
tff(1,plain,
^ [X0: $i] :
refl(
( p2(X0,X0)
<=> p2(X0,X0) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X0: $i] : p2(X0,X0)
<=> ! [X0: $i] : p2(X0,X0) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X0: $i] : p2(X0,X0)
<=> ! [X0: $i] : p2(X0,X0) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X0: $i] : p2(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_1) ).
tff(5,plain,
! [X0: $i] : p2(X0,X0),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X0: $i] : p2(X0,X0),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X0: $i] : p2(X0,X0),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X0: $i] : p2(X0,X0)
| p2(c14,c14) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p2(c14,c14),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X14: $i,X17: $i,X16: $i,X15: $i] :
refl(
( ( ~ p2(X14,X16)
| ~ p2(X15,X17)
| p2(f4(X14,X15),f4(X16,X17)) )
<=> ( ~ p2(X14,X16)
| ~ p2(X15,X17)
| p2(f4(X14,X15),f4(X16,X17)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X14: $i,X17: $i,X16: $i,X15: $i] :
( ~ p2(X14,X16)
| ~ p2(X15,X17)
| p2(f4(X14,X15),f4(X16,X17)) )
<=> ! [X14: $i,X17: $i,X16: $i,X15: $i] :
( ~ p2(X14,X16)
| ~ p2(X15,X17)
| p2(f4(X14,X15),f4(X16,X17)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X14: $i,X17: $i,X16: $i,X15: $i] :
( ~ p2(X14,X16)
| ~ p2(X15,X17)
| p2(f4(X14,X15),f4(X16,X17)) )
<=> ! [X14: $i,X17: $i,X16: $i,X15: $i] :
( ~ p2(X14,X16)
| ~ p2(X15,X17)
| p2(f4(X14,X15),f4(X16,X17)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X14: $i,X17: $i,X16: $i,X15: $i] :
trans(
monotonicity(
rewrite(
( ( p2(f4(X14,X15),f4(X16,X17))
| ~ p2(X14,X16) )
<=> ( ~ p2(X14,X16)
| p2(f4(X14,X15),f4(X16,X17)) ) )),
( ( p2(f4(X14,X15),f4(X16,X17))
| ~ p2(X14,X16)
| ~ p2(X15,X17) )
<=> ( ~ p2(X14,X16)
| p2(f4(X14,X15),f4(X16,X17))
| ~ p2(X15,X17) ) )),
rewrite(
( ( ~ p2(X14,X16)
| p2(f4(X14,X15),f4(X16,X17))
| ~ p2(X15,X17) )
<=> ( ~ p2(X14,X16)
| ~ p2(X15,X17)
| p2(f4(X14,X15),f4(X16,X17)) ) )),
( ( p2(f4(X14,X15),f4(X16,X17))
| ~ p2(X14,X16)
| ~ p2(X15,X17) )
<=> ( ~ p2(X14,X16)
| ~ p2(X15,X17)
| p2(f4(X14,X15),f4(X16,X17)) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X14: $i,X17: $i,X16: $i,X15: $i] :
( p2(f4(X14,X15),f4(X16,X17))
| ~ p2(X14,X16)
| ~ p2(X15,X17) )
<=> ! [X14: $i,X17: $i,X16: $i,X15: $i] :
( ~ p2(X14,X16)
| ~ p2(X15,X17)
| p2(f4(X14,X15),f4(X16,X17)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X14: $i,X17: $i,X16: $i,X15: $i] :
( p2(f4(X14,X15),f4(X16,X17))
| ~ p2(X14,X16)
| ~ p2(X15,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_19) ).
tff(16,plain,
! [X14: $i,X17: $i,X16: $i,X15: $i] :
( ~ p2(X14,X16)
| ~ p2(X15,X17)
| p2(f4(X14,X15),f4(X16,X17)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X14: $i,X17: $i,X16: $i,X15: $i] :
( ~ p2(X14,X16)
| ~ p2(X15,X17)
| p2(f4(X14,X15),f4(X16,X17)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X14: $i,X17: $i,X16: $i,X15: $i] :
( ~ p2(X14,X16)
| ~ p2(X15,X17)
| p2(f4(X14,X15),f4(X16,X17)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X14: $i,X17: $i,X16: $i,X15: $i] :
( ~ p2(X14,X16)
| ~ p2(X15,X17)
| p2(f4(X14,X15),f4(X16,X17)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( p2(f3(c12,c11),c15)
<=> p2(f3(c12,c11),c15) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
p2(f3(c12,c11),c15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_7) ).
tff(22,plain,
p2(f3(c12,c11),c15),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [X14: $i,X17: $i,X16: $i,X15: $i] :
( ~ p2(X14,X16)
| ~ p2(X15,X17)
| p2(f4(X14,X15),f4(X16,X17)) )
| ~ p2(f3(c12,c11),c15)
| ~ p2(c14,c14)
| p2(f4(f3(c12,c11),c14),f4(c15,c14)) )
<=> ( ~ ! [X14: $i,X17: $i,X16: $i,X15: $i] :
( ~ p2(X14,X16)
| ~ p2(X15,X17)
| p2(f4(X14,X15),f4(X16,X17)) )
| ~ p2(f3(c12,c11),c15)
| ~ p2(c14,c14)
| p2(f4(f3(c12,c11),c14),f4(c15,c14)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ! [X14: $i,X17: $i,X16: $i,X15: $i] :
( ~ p2(X14,X16)
| ~ p2(X15,X17)
| p2(f4(X14,X15),f4(X16,X17)) )
| ~ p2(f3(c12,c11),c15)
| ~ p2(c14,c14)
| p2(f4(f3(c12,c11),c14),f4(c15,c14)) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [X14: $i,X17: $i,X16: $i,X15: $i] :
( ~ p2(X14,X16)
| ~ p2(X15,X17)
| p2(f4(X14,X15),f4(X16,X17)) )
| ~ p2(f3(c12,c11),c15)
| ~ p2(c14,c14)
| p2(f4(f3(c12,c11),c14),f4(c15,c14)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
p2(f4(f3(c12,c11),c14),f4(c15,c14)),
inference(unit_resolution,[status(thm)],[25,22,19,9]) ).
tff(27,plain,
( ~ ! [X0: $i] : p2(X0,X0)
| p2(f4(f3(c12,c11),c14),f4(f3(c12,c11),c14)) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
p2(f4(f3(c12,c11),c14),f4(f3(c12,c11),c14)),
inference(unit_resolution,[status(thm)],[27,7]) ).
tff(29,plain,
^ [X0: $i,X2: $i,X1: $i] :
refl(
( ( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
<=> ( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
^ [X0: $i,X2: $i,X1: $i] :
trans(
monotonicity(
rewrite(
( ( p2(X1,X2)
| ~ p2(X0,X1) )
<=> ( ~ p2(X0,X1)
| p2(X1,X2) ) )),
( ( p2(X1,X2)
| ~ p2(X0,X1)
| ~ p2(X0,X2) )
<=> ( ~ p2(X0,X1)
| p2(X1,X2)
| ~ p2(X0,X2) ) )),
rewrite(
( ( ~ p2(X0,X1)
| p2(X1,X2)
| ~ p2(X0,X2) )
<=> ( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ) )),
( ( p2(X1,X2)
| ~ p2(X0,X1)
| ~ p2(X0,X2) )
<=> ( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( p2(X1,X2)
| ~ p2(X0,X1)
| ~ p2(X0,X2) )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [X0: $i,X2: $i,X1: $i] :
( p2(X1,X2)
| ~ p2(X0,X1)
| ~ p2(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_14) ).
tff(35,plain,
! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| p2(f4(c15,c14),f4(f3(c12,c11),c14))
| ~ p2(f4(f3(c12,c11),c14),f4(f3(c12,c11),c14))
| ~ p2(f4(f3(c12,c11),c14),f4(c15,c14)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| p2(f4(c15,c14),f4(f3(c12,c11),c14))
| ~ p2(f4(f3(c12,c11),c14),f4(f3(c12,c11),c14))
| ~ p2(f4(f3(c12,c11),c14),f4(c15,c14)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ( ~ p2(f4(f3(c12,c11),c14),f4(f3(c12,c11),c14))
| ~ p2(f4(f3(c12,c11),c14),f4(c15,c14))
| p2(f4(c15,c14),f4(f3(c12,c11),c14)) )
<=> ( p2(f4(c15,c14),f4(f3(c12,c11),c14))
| ~ p2(f4(f3(c12,c11),c14),f4(f3(c12,c11),c14))
| ~ p2(f4(f3(c12,c11),c14),f4(c15,c14)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f4(f3(c12,c11),c14),f4(f3(c12,c11),c14))
| ~ p2(f4(f3(c12,c11),c14),f4(c15,c14))
| p2(f4(c15,c14),f4(f3(c12,c11),c14)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| p2(f4(c15,c14),f4(f3(c12,c11),c14))
| ~ p2(f4(f3(c12,c11),c14),f4(f3(c12,c11),c14))
| ~ p2(f4(f3(c12,c11),c14),f4(c15,c14)) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f4(f3(c12,c11),c14),f4(f3(c12,c11),c14))
| ~ p2(f4(f3(c12,c11),c14),f4(c15,c14))
| p2(f4(c15,c14),f4(f3(c12,c11),c14)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| p2(f4(c15,c14),f4(f3(c12,c11),c14))
| ~ p2(f4(f3(c12,c11),c14),f4(f3(c12,c11),c14))
| ~ p2(f4(f3(c12,c11),c14),f4(c15,c14)) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f4(f3(c12,c11),c14),f4(f3(c12,c11),c14))
| ~ p2(f4(f3(c12,c11),c14),f4(c15,c14))
| p2(f4(c15,c14),f4(f3(c12,c11),c14)) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| p2(f4(c15,c14),f4(f3(c12,c11),c14))
| ~ p2(f4(f3(c12,c11),c14),f4(f3(c12,c11),c14))
| ~ p2(f4(f3(c12,c11),c14),f4(c15,c14)) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
p2(f4(c15,c14),f4(f3(c12,c11),c14)),
inference(unit_resolution,[status(thm)],[44,38,28,26]) ).
tff(46,plain,
( p2(f4(c15,c14),c17)
<=> p2(f4(c15,c14),c17) ),
inference(rewrite,[status(thm)],]) ).
tff(47,axiom,
p2(f4(c15,c14),c17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_9) ).
tff(48,plain,
p2(f4(c15,c14),c17),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f4(c15,c14),c17)
| ~ p2(f4(c15,c14),f4(f3(c12,c11),c14))
| p2(c17,f4(f3(c12,c11),c14)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f4(c15,c14),c17)
| ~ p2(f4(c15,c14),f4(f3(c12,c11),c14))
| p2(c17,f4(f3(c12,c11),c14)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ( ~ p2(f4(c15,c14),f4(f3(c12,c11),c14))
| ~ p2(f4(c15,c14),c17)
| p2(c17,f4(f3(c12,c11),c14)) )
<=> ( ~ p2(f4(c15,c14),c17)
| ~ p2(f4(c15,c14),f4(f3(c12,c11),c14))
| p2(c17,f4(f3(c12,c11),c14)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f4(c15,c14),f4(f3(c12,c11),c14))
| ~ p2(f4(c15,c14),c17)
| p2(c17,f4(f3(c12,c11),c14)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f4(c15,c14),c17)
| ~ p2(f4(c15,c14),f4(f3(c12,c11),c14))
| p2(c17,f4(f3(c12,c11),c14)) ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f4(c15,c14),f4(f3(c12,c11),c14))
| ~ p2(f4(c15,c14),c17)
| p2(c17,f4(f3(c12,c11),c14)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f4(c15,c14),c17)
| ~ p2(f4(c15,c14),f4(f3(c12,c11),c14))
| p2(c17,f4(f3(c12,c11),c14)) ) ),
inference(transitivity,[status(thm)],[51,49]) ).
tff(53,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f4(c15,c14),f4(f3(c12,c11),c14))
| ~ p2(f4(c15,c14),c17)
| p2(c17,f4(f3(c12,c11),c14)) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f4(c15,c14),c17)
| ~ p2(f4(c15,c14),f4(f3(c12,c11),c14))
| p2(c17,f4(f3(c12,c11),c14)) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
p2(c17,f4(f3(c12,c11),c14)),
inference(unit_resolution,[status(thm)],[54,48,38,45]) ).
tff(56,plain,
( ~ ! [X0: $i] : p2(X0,X0)
| p2(f5(f6(c9),c19),f5(f6(c9),c19)) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
p2(f5(f6(c9),c19),f5(f6(c9),c19)),
inference(unit_resolution,[status(thm)],[56,7]) ).
tff(58,plain,
( p2(f5(f6(c9),c19),c17)
<=> p2(f5(f6(c9),c19),c17) ),
inference(rewrite,[status(thm)],]) ).
tff(59,axiom,
p2(f5(f6(c9),c19),c17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_11) ).
tff(60,plain,
p2(f5(f6(c9),c19),c17),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f5(f6(c9),c19),c17)
| p2(c17,f5(f6(c9),c19))
| ~ p2(f5(f6(c9),c19),f5(f6(c9),c19)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f5(f6(c9),c19),c17)
| p2(c17,f5(f6(c9),c19))
| ~ p2(f5(f6(c9),c19),f5(f6(c9),c19)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ( ~ p2(f5(f6(c9),c19),f5(f6(c9),c19))
| ~ p2(f5(f6(c9),c19),c17)
| p2(c17,f5(f6(c9),c19)) )
<=> ( ~ p2(f5(f6(c9),c19),c17)
| p2(c17,f5(f6(c9),c19))
| ~ p2(f5(f6(c9),c19),f5(f6(c9),c19)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f5(f6(c9),c19),f5(f6(c9),c19))
| ~ p2(f5(f6(c9),c19),c17)
| p2(c17,f5(f6(c9),c19)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f5(f6(c9),c19),c17)
| p2(c17,f5(f6(c9),c19))
| ~ p2(f5(f6(c9),c19),f5(f6(c9),c19)) ) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f5(f6(c9),c19),f5(f6(c9),c19))
| ~ p2(f5(f6(c9),c19),c17)
| p2(c17,f5(f6(c9),c19)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f5(f6(c9),c19),c17)
| p2(c17,f5(f6(c9),c19))
| ~ p2(f5(f6(c9),c19),f5(f6(c9),c19)) ) ),
inference(transitivity,[status(thm)],[63,61]) ).
tff(65,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f5(f6(c9),c19),f5(f6(c9),c19))
| ~ p2(f5(f6(c9),c19),c17)
| p2(c17,f5(f6(c9),c19)) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f5(f6(c9),c19),c17)
| p2(c17,f5(f6(c9),c19))
| ~ p2(f5(f6(c9),c19),f5(f6(c9),c19)) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
p2(c17,f5(f6(c9),c19)),
inference(unit_resolution,[status(thm)],[66,60,38,57]) ).
tff(68,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(c17,f5(f6(c9),c19))
| ~ p2(c17,f4(f3(c12,c11),c14))
| p2(f4(f3(c12,c11),c14),f5(f6(c9),c19)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(c17,f5(f6(c9),c19))
| ~ p2(c17,f4(f3(c12,c11),c14))
| p2(f4(f3(c12,c11),c14),f5(f6(c9),c19)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(c17,f5(f6(c9),c19))
| ~ p2(c17,f4(f3(c12,c11),c14))
| p2(f4(f3(c12,c11),c14),f5(f6(c9),c19)) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(c17,f5(f6(c9),c19))
| ~ p2(c17,f4(f3(c12,c11),c14))
| p2(f4(f3(c12,c11),c14),f5(f6(c9),c19)) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
p2(f4(f3(c12,c11),c14),f5(f6(c9),c19)),
inference(unit_resolution,[status(thm)],[70,38,67,55]) ).
tff(72,plain,
( ~ ! [X0: $i] : p2(X0,X0)
| p2(f5(f6(c9),c20),f5(f6(c9),c20)) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
p2(f5(f6(c9),c20),f5(f6(c9),c20)),
inference(unit_resolution,[status(thm)],[72,7]) ).
tff(74,plain,
( p2(f5(f6(c9),c20),c18)
<=> p2(f5(f6(c9),c20),c18) ),
inference(rewrite,[status(thm)],]) ).
tff(75,axiom,
p2(f5(f6(c9),c20),c18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_12) ).
tff(76,plain,
p2(f5(f6(c9),c20),c18),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| p2(c18,f5(f6(c9),c20))
| ~ p2(f5(f6(c9),c20),c18)
| ~ p2(f5(f6(c9),c20),f5(f6(c9),c20)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| p2(c18,f5(f6(c9),c20))
| ~ p2(f5(f6(c9),c20),c18)
| ~ p2(f5(f6(c9),c20),f5(f6(c9),c20)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
( ( ~ p2(f5(f6(c9),c20),f5(f6(c9),c20))
| ~ p2(f5(f6(c9),c20),c18)
| p2(c18,f5(f6(c9),c20)) )
<=> ( p2(c18,f5(f6(c9),c20))
| ~ p2(f5(f6(c9),c20),c18)
| ~ p2(f5(f6(c9),c20),f5(f6(c9),c20)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f5(f6(c9),c20),f5(f6(c9),c20))
| ~ p2(f5(f6(c9),c20),c18)
| p2(c18,f5(f6(c9),c20)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| p2(c18,f5(f6(c9),c20))
| ~ p2(f5(f6(c9),c20),c18)
| ~ p2(f5(f6(c9),c20),f5(f6(c9),c20)) ) ),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f5(f6(c9),c20),f5(f6(c9),c20))
| ~ p2(f5(f6(c9),c20),c18)
| p2(c18,f5(f6(c9),c20)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| p2(c18,f5(f6(c9),c20))
| ~ p2(f5(f6(c9),c20),c18)
| ~ p2(f5(f6(c9),c20),f5(f6(c9),c20)) ) ),
inference(transitivity,[status(thm)],[79,77]) ).
tff(81,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f5(f6(c9),c20),f5(f6(c9),c20))
| ~ p2(f5(f6(c9),c20),c18)
| p2(c18,f5(f6(c9),c20)) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| p2(c18,f5(f6(c9),c20))
| ~ p2(f5(f6(c9),c20),c18)
| ~ p2(f5(f6(c9),c20),f5(f6(c9),c20)) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
p2(c18,f5(f6(c9),c20)),
inference(unit_resolution,[status(thm)],[82,76,38,73]) ).
tff(84,plain,
( ~ ! [X0: $i] : p2(X0,X0)
| p2(f4(c16,c14),f4(c16,c14)) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
p2(f4(c16,c14),f4(c16,c14)),
inference(unit_resolution,[status(thm)],[84,7]) ).
tff(86,plain,
( p2(f4(c16,c14),c18)
<=> p2(f4(c16,c14),c18) ),
inference(rewrite,[status(thm)],]) ).
tff(87,axiom,
p2(f4(c16,c14),c18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_8) ).
tff(88,plain,
p2(f4(c16,c14),c18),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f4(c16,c14),c18)
| ~ p2(f4(c16,c14),f4(c16,c14))
| p2(c18,f4(c16,c14)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f4(c16,c14),c18)
| ~ p2(f4(c16,c14),f4(c16,c14))
| p2(c18,f4(c16,c14)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ( ~ p2(f4(c16,c14),f4(c16,c14))
| ~ p2(f4(c16,c14),c18)
| p2(c18,f4(c16,c14)) )
<=> ( ~ p2(f4(c16,c14),c18)
| ~ p2(f4(c16,c14),f4(c16,c14))
| p2(c18,f4(c16,c14)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f4(c16,c14),f4(c16,c14))
| ~ p2(f4(c16,c14),c18)
| p2(c18,f4(c16,c14)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f4(c16,c14),c18)
| ~ p2(f4(c16,c14),f4(c16,c14))
| p2(c18,f4(c16,c14)) ) ),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f4(c16,c14),f4(c16,c14))
| ~ p2(f4(c16,c14),c18)
| p2(c18,f4(c16,c14)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f4(c16,c14),c18)
| ~ p2(f4(c16,c14),f4(c16,c14))
| p2(c18,f4(c16,c14)) ) ),
inference(transitivity,[status(thm)],[91,89]) ).
tff(93,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f4(c16,c14),f4(c16,c14))
| ~ p2(f4(c16,c14),c18)
| p2(c18,f4(c16,c14)) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f4(c16,c14),c18)
| ~ p2(f4(c16,c14),f4(c16,c14))
| p2(c18,f4(c16,c14)) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
p2(c18,f4(c16,c14)),
inference(unit_resolution,[status(thm)],[94,88,38,85]) ).
tff(96,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| p2(f4(c16,c14),f5(f6(c9),c20))
| ~ p2(c18,f4(c16,c14))
| ~ p2(c18,f5(f6(c9),c20)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| p2(f4(c16,c14),f5(f6(c9),c20))
| ~ p2(c18,f4(c16,c14))
| ~ p2(c18,f5(f6(c9),c20)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,plain,
( ( ~ p2(c18,f5(f6(c9),c20))
| ~ p2(c18,f4(c16,c14))
| p2(f4(c16,c14),f5(f6(c9),c20)) )
<=> ( p2(f4(c16,c14),f5(f6(c9),c20))
| ~ p2(c18,f4(c16,c14))
| ~ p2(c18,f5(f6(c9),c20)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(c18,f5(f6(c9),c20))
| ~ p2(c18,f4(c16,c14))
| p2(f4(c16,c14),f5(f6(c9),c20)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| p2(f4(c16,c14),f5(f6(c9),c20))
| ~ p2(c18,f4(c16,c14))
| ~ p2(c18,f5(f6(c9),c20)) ) ),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(c18,f5(f6(c9),c20))
| ~ p2(c18,f4(c16,c14))
| p2(f4(c16,c14),f5(f6(c9),c20)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| p2(f4(c16,c14),f5(f6(c9),c20))
| ~ p2(c18,f4(c16,c14))
| ~ p2(c18,f5(f6(c9),c20)) ) ),
inference(transitivity,[status(thm)],[98,96]) ).
tff(100,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(c18,f5(f6(c9),c20))
| ~ p2(c18,f4(c16,c14))
| p2(f4(c16,c14),f5(f6(c9),c20)) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| p2(f4(c16,c14),f5(f6(c9),c20))
| ~ p2(c18,f4(c16,c14))
| ~ p2(c18,f5(f6(c9),c20)) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
p2(f4(c16,c14),f5(f6(c9),c20)),
inference(unit_resolution,[status(thm)],[101,38,95,83]) ).
tff(103,plain,
( ~ ! [X0: $i] : p2(X0,X0)
| p2(f3(c12,c11),f3(c12,c11)) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
p2(f3(c12,c11),f3(c12,c11)),
inference(unit_resolution,[status(thm)],[103,7]) ).
tff(105,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(c12,c11),c15)
| p2(c15,f3(c12,c11))
| ~ p2(f3(c12,c11),f3(c12,c11)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(c12,c11),c15)
| p2(c15,f3(c12,c11))
| ~ p2(f3(c12,c11),f3(c12,c11)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
( ( ~ p2(f3(c12,c11),f3(c12,c11))
| ~ p2(f3(c12,c11),c15)
| p2(c15,f3(c12,c11)) )
<=> ( ~ p2(f3(c12,c11),c15)
| p2(c15,f3(c12,c11))
| ~ p2(f3(c12,c11),f3(c12,c11)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(c12,c11),f3(c12,c11))
| ~ p2(f3(c12,c11),c15)
| p2(c15,f3(c12,c11)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(c12,c11),c15)
| p2(c15,f3(c12,c11))
| ~ p2(f3(c12,c11),f3(c12,c11)) ) ),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(c12,c11),f3(c12,c11))
| ~ p2(f3(c12,c11),c15)
| p2(c15,f3(c12,c11)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(c12,c11),c15)
| p2(c15,f3(c12,c11))
| ~ p2(f3(c12,c11),f3(c12,c11)) ) ),
inference(transitivity,[status(thm)],[107,105]) ).
tff(109,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(c12,c11),f3(c12,c11))
| ~ p2(f3(c12,c11),c15)
| p2(c15,f3(c12,c11)) ),
inference(quant_inst,[status(thm)],]) ).
tff(110,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(c12,c11),c15)
| p2(c15,f3(c12,c11))
| ~ p2(f3(c12,c11),f3(c12,c11)) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
p2(c15,f3(c12,c11)),
inference(unit_resolution,[status(thm)],[110,22,38,104]) ).
tff(112,plain,
( p2(f3(c12,c13),c16)
<=> p2(f3(c12,c13),c16) ),
inference(rewrite,[status(thm)],]) ).
tff(113,axiom,
p2(f3(c12,c13),c16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_10) ).
tff(114,plain,
p2(f3(c12,c13),c16),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(c12,c13),c16)
| p2(c16,c16) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(c12,c13),c16)
| p2(c16,c16) ) ),
inference(rewrite,[status(thm)],]) ).
tff(116,plain,
( ( ~ p2(f3(c12,c13),c16)
| ~ p2(f3(c12,c13),c16)
| p2(c16,c16) )
<=> ( ~ p2(f3(c12,c13),c16)
| p2(c16,c16) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(c12,c13),c16)
| ~ p2(f3(c12,c13),c16)
| p2(c16,c16) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(c12,c13),c16)
| p2(c16,c16) ) ),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(c12,c13),c16)
| ~ p2(f3(c12,c13),c16)
| p2(c16,c16) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(c12,c13),c16)
| p2(c16,c16) ) ),
inference(transitivity,[status(thm)],[117,115]) ).
tff(119,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(c12,c13),c16)
| ~ p2(f3(c12,c13),c16)
| p2(c16,c16) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(c12,c13),c16)
| p2(c16,c16) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
p2(c16,c16),
inference(unit_resolution,[status(thm)],[120,114,38]) ).
tff(122,plain,
^ [X32: $i,X34: $i,X33: $i] :
refl(
( ( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) )
<=> ( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) ) )),
inference(bind,[status(th)],]) ).
tff(123,plain,
( ! [X32: $i,X34: $i,X33: $i] :
( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) )
<=> ! [X32: $i,X34: $i,X33: $i] :
( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
( ! [X32: $i,X34: $i,X33: $i] :
( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) )
<=> ! [X32: $i,X34: $i,X33: $i] :
( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,plain,
^ [X32: $i,X34: $i,X33: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ p7(X34,c10)
| ~ p2(c15,X32) )
<=> ( ~ p2(c15,X32)
| ~ p7(X34,c10) ) )),
( ( ~ p7(X34,c10)
| ~ p2(c15,X32)
| ~ p2(c16,X33) )
<=> ( ~ p2(c15,X32)
| ~ p7(X34,c10)
| ~ p2(c16,X33) ) )),
rewrite(
( ( ~ p2(c15,X32)
| ~ p7(X34,c10)
| ~ p2(c16,X33) )
<=> ( ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) ) )),
( ( ~ p7(X34,c10)
| ~ p2(c15,X32)
| ~ p2(c16,X33) )
<=> ( ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) ) )),
( ( ~ p7(X34,c10)
| ~ p2(c15,X32)
| ~ p2(c16,X33)
| ~ p2(f4(X32,c14),f5(f6(X34),c19)) )
<=> ( ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10)
| ~ p2(f4(X32,c14),f5(f6(X34),c19)) ) )),
rewrite(
( ( ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10)
| ~ p2(f4(X32,c14),f5(f6(X34),c19)) )
<=> ( ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) ) )),
( ( ~ p7(X34,c10)
| ~ p2(c15,X32)
| ~ p2(c16,X33)
| ~ p2(f4(X32,c14),f5(f6(X34),c19)) )
<=> ( ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) ) )),
( ( ~ p7(X34,c10)
| ~ p2(c15,X32)
| ~ p2(c16,X33)
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(f4(X33,c14),f5(f6(X34),c20)) )
<=> ( ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10)
| ~ p2(f4(X33,c14),f5(f6(X34),c20)) ) )),
rewrite(
( ( ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10)
| ~ p2(f4(X33,c14),f5(f6(X34),c20)) )
<=> ( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) ) )),
( ( ~ p7(X34,c10)
| ~ p2(c15,X32)
| ~ p2(c16,X33)
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(f4(X33,c14),f5(f6(X34),c20)) )
<=> ( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) ) )),
inference(bind,[status(th)],]) ).
tff(126,plain,
( ! [X32: $i,X34: $i,X33: $i] :
( ~ p7(X34,c10)
| ~ p2(c15,X32)
| ~ p2(c16,X33)
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(f4(X33,c14),f5(f6(X34),c20)) )
<=> ! [X32: $i,X34: $i,X33: $i] :
( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,axiom,
! [X32: $i,X34: $i,X33: $i] :
( ~ p7(X34,c10)
| ~ p2(c15,X32)
| ~ p2(c16,X33)
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(f4(X33,c14),f5(f6(X34),c20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p7_20) ).
tff(128,plain,
! [X32: $i,X34: $i,X33: $i] :
( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
! [X32: $i,X34: $i,X33: $i] :
( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) ),
inference(modus_ponens,[status(thm)],[128,124]) ).
tff(130,plain,
! [X32: $i,X34: $i,X33: $i] :
( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) ),
inference(skolemize,[status(sab)],[129]) ).
tff(131,plain,
! [X32: $i,X34: $i,X33: $i] :
( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) ),
inference(modus_ponens,[status(thm)],[130,123]) ).
tff(132,plain,
( p7(c9,c10)
<=> p7(c9,c10) ),
inference(rewrite,[status(thm)],]) ).
tff(133,axiom,
p7(c9,c10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_5) ).
tff(134,plain,
p7(c9,c10),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
( ( ~ ! [X32: $i,X34: $i,X33: $i] :
( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) )
| ~ p2(c16,c16)
| ~ p7(c9,c10)
| ~ p2(f4(c16,c14),f5(f6(c9),c20))
| ~ p2(c15,f3(c12,c11))
| ~ p2(f4(f3(c12,c11),c14),f5(f6(c9),c19)) )
<=> ( ~ ! [X32: $i,X34: $i,X33: $i] :
( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) )
| ~ p2(c16,c16)
| ~ p7(c9,c10)
| ~ p2(f4(c16,c14),f5(f6(c9),c20))
| ~ p2(c15,f3(c12,c11))
| ~ p2(f4(f3(c12,c11),c14),f5(f6(c9),c19)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(136,plain,
( ( ~ p2(f4(c16,c14),f5(f6(c9),c20))
| ~ p2(f4(f3(c12,c11),c14),f5(f6(c9),c19))
| ~ p2(c16,c16)
| ~ p2(c15,f3(c12,c11))
| ~ p7(c9,c10) )
<=> ( ~ p2(c16,c16)
| ~ p7(c9,c10)
| ~ p2(f4(c16,c14),f5(f6(c9),c20))
| ~ p2(c15,f3(c12,c11))
| ~ p2(f4(f3(c12,c11),c14),f5(f6(c9),c19)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(137,plain,
( ( ~ ! [X32: $i,X34: $i,X33: $i] :
( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) )
| ~ p2(f4(c16,c14),f5(f6(c9),c20))
| ~ p2(f4(f3(c12,c11),c14),f5(f6(c9),c19))
| ~ p2(c16,c16)
| ~ p2(c15,f3(c12,c11))
| ~ p7(c9,c10) )
<=> ( ~ ! [X32: $i,X34: $i,X33: $i] :
( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) )
| ~ p2(c16,c16)
| ~ p7(c9,c10)
| ~ p2(f4(c16,c14),f5(f6(c9),c20))
| ~ p2(c15,f3(c12,c11))
| ~ p2(f4(f3(c12,c11),c14),f5(f6(c9),c19)) ) ),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
( ( ~ ! [X32: $i,X34: $i,X33: $i] :
( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) )
| ~ p2(f4(c16,c14),f5(f6(c9),c20))
| ~ p2(f4(f3(c12,c11),c14),f5(f6(c9),c19))
| ~ p2(c16,c16)
| ~ p2(c15,f3(c12,c11))
| ~ p7(c9,c10) )
<=> ( ~ ! [X32: $i,X34: $i,X33: $i] :
( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) )
| ~ p2(c16,c16)
| ~ p7(c9,c10)
| ~ p2(f4(c16,c14),f5(f6(c9),c20))
| ~ p2(c15,f3(c12,c11))
| ~ p2(f4(f3(c12,c11),c14),f5(f6(c9),c19)) ) ),
inference(transitivity,[status(thm)],[137,135]) ).
tff(139,plain,
( ~ ! [X32: $i,X34: $i,X33: $i] :
( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) )
| ~ p2(f4(c16,c14),f5(f6(c9),c20))
| ~ p2(f4(f3(c12,c11),c14),f5(f6(c9),c19))
| ~ p2(c16,c16)
| ~ p2(c15,f3(c12,c11))
| ~ p7(c9,c10) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
( ~ ! [X32: $i,X34: $i,X33: $i] :
( ~ p2(f4(X33,c14),f5(f6(X34),c20))
| ~ p2(f4(X32,c14),f5(f6(X34),c19))
| ~ p2(c16,X33)
| ~ p2(c15,X32)
| ~ p7(X34,c10) )
| ~ p2(c16,c16)
| ~ p7(c9,c10)
| ~ p2(f4(c16,c14),f5(f6(c9),c20))
| ~ p2(c15,f3(c12,c11))
| ~ p2(f4(f3(c12,c11),c14),f5(f6(c9),c19)) ),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
$false,
inference(unit_resolution,[status(thm)],[140,134,131,121,111,102,71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN577-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Sep 5 06:13:40 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 10.33/6.95 % SZS status Unsatisfiable
% 10.33/6.95 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------