TSTP Solution File: SYN710-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN710-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 23:57:01 EDT 2022
% Result : Unsatisfiable 0.20s 0.54s
% Output : Proof 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 43
% Syntax : Number of formulae : 75 ( 14 unt; 16 typ; 0 def)
% Number of atoms : 254 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 325 ( 142 ~; 155 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 12 ( 12 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 8 >; 8 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 166 ( 150 !; 0 ?; 166 :)
% Comments :
%------------------------------------------------------------------------------
tff(p33_type,type,
p33: ( $i * $i ) > $o ).
tff(f13_type,type,
f13: ( $i * $i ) > $i ).
tff(c50_type,type,
c50: $i ).
tff(f16_type,type,
f16: ( $i * $i ) > $i ).
tff(c49_type,type,
c49: $i ).
tff(c48_type,type,
c48: $i ).
tff(f18_type,type,
f18: ( $i * $i ) > $i ).
tff(f20_type,type,
f20: ( $i * $i ) > $i ).
tff(f9_type,type,
f9: ( $i * $i ) > $i ).
tff(c43_type,type,
c43: $i ).
tff(c47_type,type,
c47: $i ).
tff(f22_type,type,
f22: ( $i * $i ) > $i ).
tff(c52_type,type,
c52: $i ).
tff(c51_type,type,
c51: $i ).
tff(f11_type,type,
f11: ( $i * $i ) > $i ).
tff(c46_type,type,
c46: $i ).
tff(1,plain,
^ [X80: $i,X79: $i] :
refl(
( ( p33(f11(c46,X79),X80)
| p33(f18(c51,f20(f22(c52,X79),X80)),X79) )
<=> ( p33(f11(c46,X79),X80)
| p33(f18(c51,f20(f22(c52,X79),X80)),X79) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| p33(f18(c51,f20(f22(c52,X79),X80)),X79) )
<=> ! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| p33(f18(c51,f20(f22(c52,X79),X80)),X79) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| p33(f18(c51,f20(f22(c52,X79),X80)),X79) )
<=> ! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| p33(f18(c51,f20(f22(c52,X79),X80)),X79) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| p33(f18(c51,f20(f22(c52,X79),X80)),X79) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33_72) ).
tff(5,plain,
! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| p33(f18(c51,f20(f22(c52,X79),X80)),X79) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| p33(f18(c51,f20(f22(c52,X79),X80)),X79) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| p33(f18(c51,f20(f22(c52,X79),X80)),X79) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ p33(f11(c46,c50),f9(c47,c43))
<=> ~ p33(f11(c46,c50),f9(c47,c43)) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
~ p33(f11(c46,c50),f9(c47,c43)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p33_25) ).
tff(10,plain,
~ p33(f11(c46,c50),f9(c47,c43)),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| p33(f18(c51,f20(f22(c52,X79),X80)),X79) )
| p33(f11(c46,c50),f9(c47,c43))
| p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),c50) )
<=> ( ~ ! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| p33(f18(c51,f20(f22(c52,X79),X80)),X79) )
| p33(f11(c46,c50),f9(c47,c43))
| p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),c50) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| p33(f18(c51,f20(f22(c52,X79),X80)),X79) )
| p33(f11(c46,c50),f9(c47,c43))
| p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),c50) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| p33(f18(c51,f20(f22(c52,X79),X80)),X79) )
| p33(f11(c46,c50),f9(c47,c43))
| p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),c50) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),c50),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
^ [X14: $i,X13: $i,X15: $i] :
refl(
( ( ~ p33(f18(c51,X13),X15)
| p33(f18(c51,X13),f13(f16(c48,X14),X15)) )
<=> ( ~ p33(f18(c51,X13),X15)
| p33(f18(c51,X13),f13(f16(c48,X14),X15)) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [X14: $i,X13: $i,X15: $i] :
( ~ p33(f18(c51,X13),X15)
| p33(f18(c51,X13),f13(f16(c48,X14),X15)) )
<=> ! [X14: $i,X13: $i,X15: $i] :
( ~ p33(f18(c51,X13),X15)
| p33(f18(c51,X13),f13(f16(c48,X14),X15)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [X14: $i,X13: $i,X15: $i] :
( ~ p33(f18(c51,X13),X15)
| p33(f18(c51,X13),f13(f16(c48,X14),X15)) )
<=> ! [X14: $i,X13: $i,X15: $i] :
( ~ p33(f18(c51,X13),X15)
| p33(f18(c51,X13),f13(f16(c48,X14),X15)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
^ [X14: $i,X13: $i,X15: $i] :
rewrite(
( ( p33(f18(c51,X13),f13(f16(c48,X14),X15))
| ~ p33(f18(c51,X13),X15) )
<=> ( ~ p33(f18(c51,X13),X15)
| p33(f18(c51,X13),f13(f16(c48,X14),X15)) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [X14: $i,X13: $i,X15: $i] :
( p33(f18(c51,X13),f13(f16(c48,X14),X15))
| ~ p33(f18(c51,X13),X15) )
<=> ! [X14: $i,X13: $i,X15: $i] :
( ~ p33(f18(c51,X13),X15)
| p33(f18(c51,X13),f13(f16(c48,X14),X15)) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [X14: $i,X13: $i,X15: $i] :
( p33(f18(c51,X13),f13(f16(c48,X14),X15))
| ~ p33(f18(c51,X13),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33_75) ).
tff(21,plain,
! [X14: $i,X13: $i,X15: $i] :
( ~ p33(f18(c51,X13),X15)
| p33(f18(c51,X13),f13(f16(c48,X14),X15)) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [X14: $i,X13: $i,X15: $i] :
( ~ p33(f18(c51,X13),X15)
| p33(f18(c51,X13),f13(f16(c48,X14),X15)) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [X14: $i,X13: $i,X15: $i] :
( ~ p33(f18(c51,X13),X15)
| p33(f18(c51,X13),f13(f16(c48,X14),X15)) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [X14: $i,X13: $i,X15: $i] :
( ~ p33(f18(c51,X13),X15)
| p33(f18(c51,X13),f13(f16(c48,X14),X15)) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( ( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p33(f18(c51,X13),X15)
| p33(f18(c51,X13),f13(f16(c48,X14),X15)) )
| ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),c50)
| p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)) )
<=> ( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p33(f18(c51,X13),X15)
| p33(f18(c51,X13),f13(f16(c48,X14),X15)) )
| ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),c50)
| p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p33(f18(c51,X13),X15)
| p33(f18(c51,X13),f13(f16(c48,X14),X15)) )
| ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),c50)
| p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [X14: $i,X13: $i,X15: $i] :
( ~ p33(f18(c51,X13),X15)
| p33(f18(c51,X13),f13(f16(c48,X14),X15)) )
| ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),c50)
| p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)),
inference(unit_resolution,[status(thm)],[27,24,14]) ).
tff(29,plain,
^ [X80: $i,X79: $i] :
refl(
( ( p33(f11(c46,X79),X80)
| ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) )
<=> ( p33(f11(c46,X79),X80)
| ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) )
<=> ! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) )
<=> ! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33_73) ).
tff(33,plain,
! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ( ~ ! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) )
| p33(f11(c46,c50),f9(c47,c43))
| ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43)) )
<=> ( ~ ! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) )
| p33(f11(c46,c50),f9(c47,c43))
| ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ~ ! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) )
| p33(f11(c46,c50),f9(c47,c43))
| ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43)) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
( ~ ! [X80: $i,X79: $i] :
( p33(f11(c46,X79),X80)
| ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) )
| p33(f11(c46,c50),f9(c47,c43))
| ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43)) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43)),
inference(unit_resolution,[status(thm)],[38,10,35]) ).
tff(40,plain,
^ [X80: $i,X81: $i,X79: $i] :
refl(
( ( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) )
<=> ( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [X80: $i,X81: $i,X79: $i] :
( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) )
<=> ! [X80: $i,X81: $i,X79: $i] :
( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [X80: $i,X81: $i,X79: $i] :
( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) )
<=> ! [X80: $i,X81: $i,X79: $i] :
( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
^ [X80: $i,X81: $i,X79: $i] :
trans(
monotonicity(
rewrite(
( ( p33(f18(c51,X81),X80)
| ~ p33(f11(c46,X79),X80) )
<=> ( ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) ) )),
( ( p33(f18(c51,X81),X80)
| ~ p33(f11(c46,X79),X80)
| ~ p33(f18(c51,X81),X79) )
<=> ( ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80)
| ~ p33(f18(c51,X81),X79) ) )),
rewrite(
( ( ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80)
| ~ p33(f18(c51,X81),X79) )
<=> ( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) ) )),
( ( p33(f18(c51,X81),X80)
| ~ p33(f11(c46,X79),X80)
| ~ p33(f18(c51,X81),X79) )
<=> ( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [X80: $i,X81: $i,X79: $i] :
( p33(f18(c51,X81),X80)
| ~ p33(f11(c46,X79),X80)
| ~ p33(f18(c51,X81),X79) )
<=> ! [X80: $i,X81: $i,X79: $i] :
( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,axiom,
! [X80: $i,X81: $i,X79: $i] :
( p33(f18(c51,X81),X80)
| ~ p33(f11(c46,X79),X80)
| ~ p33(f18(c51,X81),X79) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33_80) ).
tff(46,plain,
! [X80: $i,X81: $i,X79: $i] :
( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [X80: $i,X81: $i,X79: $i] :
( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [X80: $i,X81: $i,X79: $i] :
( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [X80: $i,X81: $i,X79: $i] :
( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
<=> p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43)) ),
inference(rewrite,[status(thm)],]) ).
tff(51,axiom,
p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33_50) ).
tff(52,plain,
p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43)),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
( ( ~ ! [X80: $i,X81: $i,X79: $i] :
( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) )
| p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43))
| ~ p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
| ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)) )
<=> ( ~ ! [X80: $i,X81: $i,X79: $i] :
( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) )
| p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43))
| ~ p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
| ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ( ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50))
| ~ p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
| p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43)) )
<=> ( p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43))
| ~ p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
| ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ( ~ ! [X80: $i,X81: $i,X79: $i] :
( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) )
| ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50))
| ~ p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
| p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43)) )
<=> ( ~ ! [X80: $i,X81: $i,X79: $i] :
( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) )
| p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43))
| ~ p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
| ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)) ) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ( ~ ! [X80: $i,X81: $i,X79: $i] :
( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) )
| ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50))
| ~ p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
| p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43)) )
<=> ( ~ ! [X80: $i,X81: $i,X79: $i] :
( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) )
| p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43))
| ~ p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
| ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)) ) ),
inference(transitivity,[status(thm)],[55,53]) ).
tff(57,plain,
( ~ ! [X80: $i,X81: $i,X79: $i] :
( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) )
| ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50))
| ~ p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
| p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43)) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [X80: $i,X81: $i,X79: $i] :
( ~ p33(f18(c51,X81),X79)
| ~ p33(f11(c46,X79),X80)
| p33(f18(c51,X81),X80) )
| p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43))
| ~ p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
| ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
$false,
inference(unit_resolution,[status(thm)],[58,52,49,39,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN710-1 : 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 : n019.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 06:44:20 EDT 2022
% 0.13/0.34 % 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.
% 0.20/0.54 % SZS status Unsatisfiable
% 0.20/0.54 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------