TSTP Solution File: SYN590-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN590-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 23:56:33 EDT 2022
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 51
% Syntax : Number of formulae : 104 ( 22 unt; 10 typ; 0 def)
% Number of atoms : 457 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 655 ( 316 ~; 292 |; 0 &)
% ( 47 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 8 >; 3 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-1 aty)
% Number of variables : 203 ( 181 !; 0 ?; 203 :)
% Comments :
%------------------------------------------------------------------------------
tff(p12_type,type,
p12: ( $i * $i ) > $o ).
tff(c15_type,type,
c15: $i ).
tff(f8_type,type,
f8: $i > $i ).
tff(f9_type,type,
f9: $i > $i ).
tff(c16_type,type,
c16: $i ).
tff(p3_type,type,
p3: ( $i * $i ) > $o ).
tff(f6_type,type,
f6: $i > $i ).
tff(f4_type,type,
f4: $i > $i ).
tff(p11_type,type,
p11: $i > $o ).
tff(p10_type,type,
p10: ( $i * $i ) > $o ).
tff(1,plain,
^ [X4: $i] :
refl(
( ( ~ p11(X4)
| p11(f9(X4)) )
<=> ( ~ p11(X4)
| p11(f9(X4)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X4: $i] :
( ~ p11(X4)
| p11(f9(X4)) )
<=> ! [X4: $i] :
( ~ p11(X4)
| p11(f9(X4)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X4: $i] :
( ~ p11(X4)
| p11(f9(X4)) )
<=> ! [X4: $i] :
( ~ p11(X4)
| p11(f9(X4)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
^ [X4: $i] :
rewrite(
( ( p11(f9(X4))
| ~ p11(X4) )
<=> ( ~ p11(X4)
| p11(f9(X4)) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X4: $i] :
( p11(f9(X4))
| ~ p11(X4) )
<=> ! [X4: $i] :
( ~ p11(X4)
| p11(f9(X4)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [X4: $i] :
( p11(f9(X4))
| ~ p11(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11_9) ).
tff(7,plain,
! [X4: $i] :
( ~ p11(X4)
| p11(f9(X4)) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X4: $i] :
( ~ p11(X4)
| p11(f9(X4)) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [X4: $i] :
( ~ p11(X4)
| p11(f9(X4)) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X4: $i] :
( ~ p11(X4)
| p11(f9(X4)) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( p11(c16)
<=> p11(c16) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
p11(c16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c16_is_p11_3) ).
tff(13,plain,
p11(c16),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [X4: $i] :
( ~ p11(X4)
| p11(f9(X4)) )
| ~ p11(c16)
| p11(f9(c16)) )
<=> ( ~ ! [X4: $i] :
( ~ p11(X4)
| p11(f9(X4)) )
| ~ p11(c16)
| p11(f9(c16)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [X4: $i] :
( ~ p11(X4)
| p11(f9(X4)) )
| ~ p11(c16)
| p11(f9(c16)) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [X4: $i] :
( ~ p11(X4)
| p11(f9(X4)) )
| ~ p11(c16)
| p11(f9(c16)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
p11(f9(c16)),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [X24: $i] :
refl(
( ( ~ p11(X24)
| p3(f4(X24),f6(f8(X24))) )
<=> ( ~ p11(X24)
| p3(f4(X24),f6(f8(X24))) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [X24: $i] :
( ~ p11(X24)
| p3(f4(X24),f6(f8(X24))) )
<=> ! [X24: $i] :
( ~ p11(X24)
| p3(f4(X24),f6(f8(X24))) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [X24: $i] :
( ~ p11(X24)
| p3(f4(X24),f6(f8(X24))) )
<=> ! [X24: $i] :
( ~ p11(X24)
| p3(f4(X24),f6(f8(X24))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
^ [X24: $i] :
rewrite(
( ( p3(f4(X24),f6(f8(X24)))
| ~ p11(X24) )
<=> ( ~ p11(X24)
| p3(f4(X24),f6(f8(X24))) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [X24: $i] :
( p3(f4(X24),f6(f8(X24)))
| ~ p11(X24) )
<=> ! [X24: $i] :
( ~ p11(X24)
| p3(f4(X24),f6(f8(X24))) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [X24: $i] :
( p3(f4(X24),f6(f8(X24)))
| ~ p11(X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_18) ).
tff(24,plain,
! [X24: $i] :
( ~ p11(X24)
| p3(f4(X24),f6(f8(X24))) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [X24: $i] :
( ~ p11(X24)
| p3(f4(X24),f6(f8(X24))) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [X24: $i] :
( ~ p11(X24)
| p3(f4(X24),f6(f8(X24))) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X24: $i] :
( ~ p11(X24)
| p3(f4(X24),f6(f8(X24))) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [X24: $i] :
( ~ p11(X24)
| p3(f4(X24),f6(f8(X24))) )
| ~ p11(f9(c16))
| p3(f4(f9(c16)),f6(f8(f9(c16)))) )
<=> ( ~ ! [X24: $i] :
( ~ p11(X24)
| p3(f4(X24),f6(f8(X24))) )
| ~ p11(f9(c16))
| p3(f4(f9(c16)),f6(f8(f9(c16)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ ! [X24: $i] :
( ~ p11(X24)
| p3(f4(X24),f6(f8(X24))) )
| ~ p11(f9(c16))
| p3(f4(f9(c16)),f6(f8(f9(c16)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [X24: $i] :
( ~ p11(X24)
| p3(f4(X24),f6(f8(X24))) )
| ~ p11(f9(c16))
| p3(f4(f9(c16)),f6(f8(f9(c16)))) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
( ~ p11(f9(c16))
| p3(f4(f9(c16)),f6(f8(f9(c16)))) ),
inference(unit_resolution,[status(thm)],[30,27]) ).
tff(32,plain,
p3(f4(f9(c16)),f6(f8(f9(c16)))),
inference(unit_resolution,[status(thm)],[31,17]) ).
tff(33,plain,
^ [X35: $i,X34: $i] :
refl(
( ( ~ p11(X34)
| ~ p3(f4(X34),f6(X35))
| ~ p12(X35,c15) )
<=> ( ~ p11(X34)
| ~ p3(f4(X34),f6(X35))
| ~ p12(X35,c15) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [X35: $i,X34: $i] :
( ~ p11(X34)
| ~ p3(f4(X34),f6(X35))
| ~ p12(X35,c15) )
<=> ! [X35: $i,X34: $i] :
( ~ p11(X34)
| ~ p3(f4(X34),f6(X35))
| ~ p12(X35,c15) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [X35: $i,X34: $i] :
( ~ p11(X34)
| ~ p3(f4(X34),f6(X35))
| ~ p12(X35,c15) )
<=> ! [X35: $i,X34: $i] :
( ~ p11(X34)
| ~ p3(f4(X34),f6(X35))
| ~ p12(X35,c15) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
^ [X35: $i,X34: $i] :
rewrite(
( ( ~ p11(X34)
| ~ p12(X35,c15)
| ~ p3(f4(X34),f6(X35)) )
<=> ( ~ p11(X34)
| ~ p3(f4(X34),f6(X35))
| ~ p12(X35,c15) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X35: $i,X34: $i] :
( ~ p11(X34)
| ~ p12(X35,c15)
| ~ p3(f4(X34),f6(X35)) )
<=> ! [X35: $i,X34: $i] :
( ~ p11(X34)
| ~ p3(f4(X34),f6(X35))
| ~ p12(X35,c15) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [X35: $i,X34: $i] :
( ~ p11(X34)
| ~ p12(X35,c15)
| ~ p3(f4(X34),f6(X35)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p11_25) ).
tff(39,plain,
! [X35: $i,X34: $i] :
( ~ p11(X34)
| ~ p3(f4(X34),f6(X35))
| ~ p12(X35,c15) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [X35: $i,X34: $i] :
( ~ p11(X34)
| ~ p3(f4(X34),f6(X35))
| ~ p12(X35,c15) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [X35: $i,X34: $i] :
( ~ p11(X34)
| ~ p3(f4(X34),f6(X35))
| ~ p12(X35,c15) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [X35: $i,X34: $i] :
( ~ p11(X34)
| ~ p3(f4(X34),f6(X35))
| ~ p12(X35,c15) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
( ( ~ ! [X35: $i,X34: $i] :
( ~ p11(X34)
| ~ p3(f4(X34),f6(X35))
| ~ p12(X35,c15) )
| ~ p11(f9(c16))
| ~ p3(f4(f9(c16)),f6(f8(f9(c16))))
| ~ p12(f8(f9(c16)),c15) )
<=> ( ~ ! [X35: $i,X34: $i] :
( ~ p11(X34)
| ~ p3(f4(X34),f6(X35))
| ~ p12(X35,c15) )
| ~ p11(f9(c16))
| ~ p3(f4(f9(c16)),f6(f8(f9(c16))))
| ~ p12(f8(f9(c16)),c15) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ~ ! [X35: $i,X34: $i] :
( ~ p11(X34)
| ~ p3(f4(X34),f6(X35))
| ~ p12(X35,c15) )
| ~ p11(f9(c16))
| ~ p3(f4(f9(c16)),f6(f8(f9(c16))))
| ~ p12(f8(f9(c16)),c15) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
( ~ ! [X35: $i,X34: $i] :
( ~ p11(X34)
| ~ p3(f4(X34),f6(X35))
| ~ p12(X35,c15) )
| ~ p11(f9(c16))
| ~ p3(f4(f9(c16)),f6(f8(f9(c16))))
| ~ p12(f8(f9(c16)),c15) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
~ p12(f8(f9(c16)),c15),
inference(unit_resolution,[status(thm)],[45,42,17,32]) ).
tff(47,plain,
^ [X4: $i] :
refl(
( ( ~ p11(X4)
| p10(f4(f9(X4)),f4(X4)) )
<=> ( ~ p11(X4)
| p10(f4(f9(X4)),f4(X4)) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [X4: $i] :
( ~ p11(X4)
| p10(f4(f9(X4)),f4(X4)) )
<=> ! [X4: $i] :
( ~ p11(X4)
| p10(f4(f9(X4)),f4(X4)) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [X4: $i] :
( ~ p11(X4)
| p10(f4(f9(X4)),f4(X4)) )
<=> ! [X4: $i] :
( ~ p11(X4)
| p10(f4(f9(X4)),f4(X4)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
^ [X4: $i] :
rewrite(
( ( p10(f4(f9(X4)),f4(X4))
| ~ p11(X4) )
<=> ( ~ p11(X4)
| p10(f4(f9(X4)),f4(X4)) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [X4: $i] :
( p10(f4(f9(X4)),f4(X4))
| ~ p11(X4) )
<=> ! [X4: $i] :
( ~ p11(X4)
| p10(f4(f9(X4)),f4(X4)) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,axiom,
! [X4: $i] :
( p10(f4(f9(X4)),f4(X4))
| ~ p11(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10_19) ).
tff(53,plain,
! [X4: $i] :
( ~ p11(X4)
| p10(f4(f9(X4)),f4(X4)) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [X4: $i] :
( ~ p11(X4)
| p10(f4(f9(X4)),f4(X4)) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
! [X4: $i] :
( ~ p11(X4)
| p10(f4(f9(X4)),f4(X4)) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [X4: $i] :
( ~ p11(X4)
| p10(f4(f9(X4)),f4(X4)) ),
inference(modus_ponens,[status(thm)],[55,48]) ).
tff(57,plain,
( ( ~ ! [X4: $i] :
( ~ p11(X4)
| p10(f4(f9(X4)),f4(X4)) )
| ~ p11(c16)
| p10(f4(f9(c16)),f4(c16)) )
<=> ( ~ ! [X4: $i] :
( ~ p11(X4)
| p10(f4(f9(X4)),f4(X4)) )
| ~ p11(c16)
| p10(f4(f9(c16)),f4(c16)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ~ ! [X4: $i] :
( ~ p11(X4)
| p10(f4(f9(X4)),f4(X4)) )
| ~ p11(c16)
| p10(f4(f9(c16)),f4(c16)) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
( ~ ! [X4: $i] :
( ~ p11(X4)
| p10(f4(f9(X4)),f4(X4)) )
| ~ p11(c16)
| p10(f4(f9(c16)),f4(c16)) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
p10(f4(f9(c16)),f4(c16)),
inference(unit_resolution,[status(thm)],[59,13,56]) ).
tff(61,plain,
^ [X0: $i,X3: $i,X2: $i,X1: $i] :
refl(
( ( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) )
<=> ( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) )
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) )
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
^ [X0: $i,X3: $i,X2: $i,X1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p10(X0,X1)
| ~ p3(X2,X0) )
<=> ( ~ p3(X2,X0)
| p10(X0,X1) ) )),
( ( p10(X0,X1)
| ~ p3(X2,X0)
| ~ p3(X3,X1) )
<=> ( ~ p3(X2,X0)
| p10(X0,X1)
| ~ p3(X3,X1) ) )),
rewrite(
( ( ~ p3(X2,X0)
| p10(X0,X1)
| ~ p3(X3,X1) )
<=> ( ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) ) )),
( ( p10(X0,X1)
| ~ p3(X2,X0)
| ~ p3(X3,X1) )
<=> ( ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) ) )),
( ( p10(X0,X1)
| ~ p3(X2,X0)
| ~ p3(X3,X1)
| ~ p10(X2,X3) )
<=> ( ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1)
| ~ p10(X2,X3) ) )),
rewrite(
( ( ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1)
| ~ p10(X2,X3) )
<=> ( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) ) )),
( ( p10(X0,X1)
| ~ p3(X2,X0)
| ~ p3(X3,X1)
| ~ p10(X2,X3) )
<=> ( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( p10(X0,X1)
| ~ p3(X2,X0)
| ~ p3(X3,X1)
| ~ p10(X2,X3) )
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,axiom,
! [X0: $i,X3: $i,X2: $i,X1: $i] :
( p10(X0,X1)
| ~ p3(X2,X0)
| ~ p3(X3,X1)
| ~ p10(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10_26) ).
tff(67,plain,
! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) ),
inference(modus_ponens,[status(thm)],[69,62]) ).
tff(71,plain,
( p3(f4(c16),f6(c15))
<=> p3(f4(c16),f6(c15)) ),
inference(rewrite,[status(thm)],]) ).
tff(72,axiom,
p3(f4(c16),f6(c15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_8) ).
tff(73,plain,
p3(f4(c16),f6(c15)),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
( ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) )
| ~ p3(f4(c16),f6(c15))
| ~ p10(f4(f9(c16)),f4(c16))
| ~ p3(f4(f9(c16)),f6(f8(f9(c16))))
| p10(f6(f8(f9(c16))),f6(c15)) )
<=> ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) )
| ~ p3(f4(c16),f6(c15))
| ~ p10(f4(f9(c16)),f4(c16))
| ~ p3(f4(f9(c16)),f6(f8(f9(c16))))
| p10(f6(f8(f9(c16))),f6(c15)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ( ~ p10(f4(f9(c16)),f4(c16))
| ~ p3(f4(c16),f6(c15))
| ~ p3(f4(f9(c16)),f6(f8(f9(c16))))
| p10(f6(f8(f9(c16))),f6(c15)) )
<=> ( ~ p3(f4(c16),f6(c15))
| ~ p10(f4(f9(c16)),f4(c16))
| ~ p3(f4(f9(c16)),f6(f8(f9(c16))))
| p10(f6(f8(f9(c16))),f6(c15)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
( ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) )
| ~ p10(f4(f9(c16)),f4(c16))
| ~ p3(f4(c16),f6(c15))
| ~ p3(f4(f9(c16)),f6(f8(f9(c16))))
| p10(f6(f8(f9(c16))),f6(c15)) )
<=> ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) )
| ~ p3(f4(c16),f6(c15))
| ~ p10(f4(f9(c16)),f4(c16))
| ~ p3(f4(f9(c16)),f6(f8(f9(c16))))
| p10(f6(f8(f9(c16))),f6(c15)) ) ),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
( ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) )
| ~ p10(f4(f9(c16)),f4(c16))
| ~ p3(f4(c16),f6(c15))
| ~ p3(f4(f9(c16)),f6(f8(f9(c16))))
| p10(f6(f8(f9(c16))),f6(c15)) )
<=> ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) )
| ~ p3(f4(c16),f6(c15))
| ~ p10(f4(f9(c16)),f4(c16))
| ~ p3(f4(f9(c16)),f6(f8(f9(c16))))
| p10(f6(f8(f9(c16))),f6(c15)) ) ),
inference(transitivity,[status(thm)],[76,74]) ).
tff(78,plain,
( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) )
| ~ p10(f4(f9(c16)),f4(c16))
| ~ p3(f4(c16),f6(c15))
| ~ p3(f4(f9(c16)),f6(f8(f9(c16))))
| p10(f6(f8(f9(c16))),f6(c15)) ),
inference(quant_inst,[status(thm)],]) ).
tff(79,plain,
( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p3(X3,X1)
| ~ p3(X2,X0)
| p10(X0,X1) )
| ~ p3(f4(c16),f6(c15))
| ~ p10(f4(f9(c16)),f4(c16))
| ~ p3(f4(f9(c16)),f6(f8(f9(c16))))
| p10(f6(f8(f9(c16))),f6(c15)) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
p10(f6(f8(f9(c16))),f6(c15)),
inference(unit_resolution,[status(thm)],[79,73,70,60,32]) ).
tff(81,plain,
^ [X6: $i,X5: $i] :
refl(
( ( ~ p10(f6(X5),f6(X6))
| p12(X5,X6) )
<=> ( ~ p10(f6(X5),f6(X6))
| p12(X5,X6) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [X6: $i,X5: $i] :
( ~ p10(f6(X5),f6(X6))
| p12(X5,X6) )
<=> ! [X6: $i,X5: $i] :
( ~ p10(f6(X5),f6(X6))
| p12(X5,X6) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [X6: $i,X5: $i] :
( ~ p10(f6(X5),f6(X6))
| p12(X5,X6) )
<=> ! [X6: $i,X5: $i] :
( ~ p10(f6(X5),f6(X6))
| p12(X5,X6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
^ [X6: $i,X5: $i] :
rewrite(
( ( p12(X5,X6)
| ~ p10(f6(X5),f6(X6)) )
<=> ( ~ p10(f6(X5),f6(X6))
| p12(X5,X6) ) )),
inference(bind,[status(th)],]) ).
tff(85,plain,
( ! [X6: $i,X5: $i] :
( p12(X5,X6)
| ~ p10(f6(X5),f6(X6)) )
<=> ! [X6: $i,X5: $i] :
( ~ p10(f6(X5),f6(X6))
| p12(X5,X6) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,axiom,
! [X6: $i,X5: $i] :
( p12(X5,X6)
| ~ p10(f6(X5),f6(X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12_11) ).
tff(87,plain,
! [X6: $i,X5: $i] :
( ~ p10(f6(X5),f6(X6))
| p12(X5,X6) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [X6: $i,X5: $i] :
( ~ p10(f6(X5),f6(X6))
| p12(X5,X6) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
! [X6: $i,X5: $i] :
( ~ p10(f6(X5),f6(X6))
| p12(X5,X6) ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [X6: $i,X5: $i] :
( ~ p10(f6(X5),f6(X6))
| p12(X5,X6) ),
inference(modus_ponens,[status(thm)],[89,82]) ).
tff(91,plain,
( ( ~ ! [X6: $i,X5: $i] :
( ~ p10(f6(X5),f6(X6))
| p12(X5,X6) )
| ~ p10(f6(f8(f9(c16))),f6(c15))
| p12(f8(f9(c16)),c15) )
<=> ( ~ ! [X6: $i,X5: $i] :
( ~ p10(f6(X5),f6(X6))
| p12(X5,X6) )
| ~ p10(f6(f8(f9(c16))),f6(c15))
| p12(f8(f9(c16)),c15) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( ~ ! [X6: $i,X5: $i] :
( ~ p10(f6(X5),f6(X6))
| p12(X5,X6) )
| ~ p10(f6(f8(f9(c16))),f6(c15))
| p12(f8(f9(c16)),c15) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
( ~ ! [X6: $i,X5: $i] :
( ~ p10(f6(X5),f6(X6))
| p12(X5,X6) )
| ~ p10(f6(f8(f9(c16))),f6(c15))
| p12(f8(f9(c16)),c15) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
$false,
inference(unit_resolution,[status(thm)],[93,90,80,46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN590-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 05:58:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------