TSTP Solution File: SYN656-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN656-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 23:56:49 EDT 2022
% Result : Unsatisfiable 0.22s 0.46s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 59
% Syntax : Number of formulae : 116 ( 34 unt; 15 typ; 0 def)
% Number of atoms : 496 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 651 ( 292 ~; 306 |; 0 &)
% ( 53 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 36 ( 36 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 8 >; 8 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 297 ( 265 !; 0 ?; 297 :)
% Comments :
%------------------------------------------------------------------------------
tff(p3_type,type,
p3: ( $i * $i ) > $o ).
tff(f13_type,type,
f13: ( $i * $i ) > $i ).
tff(c34_type,type,
c34: $i ).
tff(c31_type,type,
c31: $i ).
tff(f15_type,type,
f15: ( $i * $i ) > $i ).
tff(c35_type,type,
c35: $i ).
tff(f17_type,type,
f17: ( $i * $i ) > $i ).
tff(c33_type,type,
c33: $i ).
tff(p25_type,type,
p25: ( $i * $i ) > $o ).
tff(f5_type,type,
f5: ( $i * $i ) > $i ).
tff(f7_type,type,
f7: ( $i * $i ) > $i ).
tff(c29_type,type,
c29: $i ).
tff(c28_type,type,
c28: $i ).
tff(c32_type,type,
c32: $i ).
tff(p4_type,type,
p4: ( $i * $i ) > $o ).
tff(1,plain,
^ [X64: $i] :
refl(
( p3(X64,X64)
<=> p3(X64,X64) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X64: $i] : p3(X64,X64)
<=> ! [X64: $i] : p3(X64,X64) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X64: $i] : p3(X64,X64)
<=> ! [X64: $i] : p3(X64,X64) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X64: $i] : p3(X64,X64),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_6) ).
tff(5,plain,
! [X64: $i] : p3(X64,X64),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X64: $i] : p3(X64,X64),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X64: $i] : p3(X64,X64),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X64: $i] : p3(X64,X64)
| p3(f13(c31,c34),f13(c31,c34)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p3(f13(c31,c34),f13(c31,c34)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X58: $i] :
refl(
( p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58))
<=> p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58)) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X58: $i] : p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58))
<=> ! [X58: $i] : p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58)) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X58: $i] : p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58))
<=> ! [X58: $i] : p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58)) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X58: $i] : p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25_31) ).
tff(14,plain,
! [X58: $i] : p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58)),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X58: $i] : p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58)),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X58: $i] : p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58)),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X58: $i] : p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58))
| p25(f5(c29,f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
p25(f5(c29,f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [X62: $i,X57: $i,X56: $i,X55: $i] :
refl(
( ( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(f7(c28,X55),X62),X57)
| ~ p25(f5(X55,X56),X62) )
<=> ( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(f7(c28,X55),X62),X57)
| ~ p25(f5(X55,X56),X62) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X62: $i,X57: $i,X56: $i,X55: $i] :
( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(f7(c28,X55),X62),X57)
| ~ p25(f5(X55,X56),X62) )
<=> ! [X62: $i,X57: $i,X56: $i,X55: $i] :
( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(f7(c28,X55),X62),X57)
| ~ p25(f5(X55,X56),X62) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X62: $i,X57: $i,X56: $i,X55: $i] :
( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(f7(c28,X55),X62),X57)
| ~ p25(f5(X55,X56),X62) )
<=> ! [X62: $i,X57: $i,X56: $i,X55: $i] :
( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(f7(c28,X55),X62),X57)
| ~ p25(f5(X55,X56),X62) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
^ [X62: $i,X57: $i,X56: $i,X55: $i] :
trans(
monotonicity(
rewrite(
( ( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(X55,X56),X62) )
<=> ( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(X55,X56),X62) ) )),
( ( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(X55,X56),X62)
| ~ p25(f5(f7(c28,X55),X62),X57) )
<=> ( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(X55,X56),X62)
| ~ p25(f5(f7(c28,X55),X62),X57) ) )),
rewrite(
( ( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(X55,X56),X62)
| ~ p25(f5(f7(c28,X55),X62),X57) )
<=> ( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(f7(c28,X55),X62),X57)
| ~ p25(f5(X55,X56),X62) ) )),
( ( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(X55,X56),X62)
| ~ p25(f5(f7(c28,X55),X62),X57) )
<=> ( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(f7(c28,X55),X62),X57)
| ~ p25(f5(X55,X56),X62) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [X62: $i,X57: $i,X56: $i,X55: $i] :
( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(X55,X56),X62)
| ~ p25(f5(f7(c28,X55),X62),X57) )
<=> ! [X62: $i,X57: $i,X56: $i,X55: $i] :
( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(f7(c28,X55),X62),X57)
| ~ p25(f5(X55,X56),X62) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [X62: $i,X57: $i,X56: $i,X55: $i] :
( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(X55,X56),X62)
| ~ p25(f5(f7(c28,X55),X62),X57) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25_46) ).
tff(25,plain,
! [X62: $i,X57: $i,X56: $i,X55: $i] :
( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(f7(c28,X55),X62),X57)
| ~ p25(f5(X55,X56),X62) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X62: $i,X57: $i,X56: $i,X55: $i] :
( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(f7(c28,X55),X62),X57)
| ~ p25(f5(X55,X56),X62) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [X62: $i,X57: $i,X56: $i,X55: $i] :
( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(f7(c28,X55),X62),X57)
| ~ p25(f5(X55,X56),X62) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [X62: $i,X57: $i,X56: $i,X55: $i] :
( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(f7(c28,X55),X62),X57)
| ~ p25(f5(X55,X56),X62) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
<=> ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34)) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p25_45) ).
tff(31,plain,
~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34)),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( ( ~ ! [X62: $i,X57: $i,X56: $i,X55: $i] :
( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(f7(c28,X55),X62),X57)
| ~ p25(f5(X55,X56),X62) )
| p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
| ~ p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),c35))),f13(c31,c34))
| ~ p25(f5(c29,f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))) )
<=> ( ~ ! [X62: $i,X57: $i,X56: $i,X55: $i] :
( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(f7(c28,X55),X62),X57)
| ~ p25(f5(X55,X56),X62) )
| p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
| ~ p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),c35))),f13(c31,c34))
| ~ p25(f5(c29,f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ~ ! [X62: $i,X57: $i,X56: $i,X55: $i] :
( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(f7(c28,X55),X62),X57)
| ~ p25(f5(X55,X56),X62) )
| p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
| ~ p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),c35))),f13(c31,c34))
| ~ p25(f5(c29,f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [X62: $i,X57: $i,X56: $i,X55: $i] :
( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(f7(c28,X55),X62),X57)
| ~ p25(f5(X55,X56),X62) )
| p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
| ~ p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),c35))),f13(c31,c34))
| ~ p25(f5(c29,f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
~ p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),c35))),f13(c31,c34)),
inference(unit_resolution,[status(thm)],[34,31,28,18]) ).
tff(36,plain,
^ [X63: $i] :
refl(
( ( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
| p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) )
<=> ( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
| p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X63: $i] :
( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
| p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) )
<=> ! [X63: $i] :
( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
| p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X63: $i] :
( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
| p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) )
<=> ! [X63: $i] :
( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
| p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
! [X63: $i] :
( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
| p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_49) ).
tff(40,plain,
! [X63: $i] :
( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
| p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [X63: $i] :
( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
| p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [X63: $i] :
( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
| p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ( ~ ! [X63: $i] :
( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
| p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) )
| p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),c35)))
| p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),c35))),f13(c31,c34)) )
<=> ( ~ ! [X63: $i] :
( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
| p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) )
| p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),c35)))
| p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),c35))),f13(c31,c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ~ ! [X63: $i] :
( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
| p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) )
| p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),c35)))
| p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),c35))),f13(c31,c34)) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
( ~ ! [X63: $i] :
( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
| p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) )
| p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),c35)))
| p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),c35))),f13(c31,c34)) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),c35)))
| p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),c35))),f13(c31,c34)) ),
inference(unit_resolution,[status(thm)],[45,42]) ).
tff(47,plain,
p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),c35))),
inference(unit_resolution,[status(thm)],[46,35]) ).
tff(48,plain,
^ [X64: $i,X66: $i,X65: $i] :
refl(
( ( ~ p3(X64,X66)
| ~ p3(X64,X65)
| p3(X65,X66) )
<=> ( ~ p3(X64,X66)
| ~ p3(X64,X65)
| p3(X65,X66) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [X64: $i,X66: $i,X65: $i] :
( ~ p3(X64,X66)
| ~ p3(X64,X65)
| p3(X65,X66) )
<=> ! [X64: $i,X66: $i,X65: $i] :
( ~ p3(X64,X66)
| ~ p3(X64,X65)
| p3(X65,X66) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [X64: $i,X66: $i,X65: $i] :
( ~ p3(X64,X66)
| ~ p3(X64,X65)
| p3(X65,X66) )
<=> ! [X64: $i,X66: $i,X65: $i] :
( ~ p3(X64,X66)
| ~ p3(X64,X65)
| p3(X65,X66) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
^ [X64: $i,X66: $i,X65: $i] :
trans(
monotonicity(
rewrite(
( ( p3(X65,X66)
| ~ p3(X64,X65) )
<=> ( ~ p3(X64,X65)
| p3(X65,X66) ) )),
( ( p3(X65,X66)
| ~ p3(X64,X65)
| ~ p3(X64,X66) )
<=> ( ~ p3(X64,X65)
| p3(X65,X66)
| ~ p3(X64,X66) ) )),
rewrite(
( ( ~ p3(X64,X65)
| p3(X65,X66)
| ~ p3(X64,X66) )
<=> ( ~ p3(X64,X66)
| ~ p3(X64,X65)
| p3(X65,X66) ) )),
( ( p3(X65,X66)
| ~ p3(X64,X65)
| ~ p3(X64,X66) )
<=> ( ~ p3(X64,X66)
| ~ p3(X64,X65)
| p3(X65,X66) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [X64: $i,X66: $i,X65: $i] :
( p3(X65,X66)
| ~ p3(X64,X65)
| ~ p3(X64,X66) )
<=> ! [X64: $i,X66: $i,X65: $i] :
( ~ p3(X64,X66)
| ~ p3(X64,X65)
| p3(X65,X66) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,axiom,
! [X64: $i,X66: $i,X65: $i] :
( p3(X65,X66)
| ~ p3(X64,X65)
| ~ p3(X64,X66) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_22) ).
tff(54,plain,
! [X64: $i,X66: $i,X65: $i] :
( ~ p3(X64,X66)
| ~ p3(X64,X65)
| p3(X65,X66) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [X64: $i,X66: $i,X65: $i] :
( ~ p3(X64,X66)
| ~ p3(X64,X65)
| p3(X65,X66) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
! [X64: $i,X66: $i,X65: $i] :
( ~ p3(X64,X66)
| ~ p3(X64,X65)
| p3(X65,X66) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [X64: $i,X66: $i,X65: $i] :
( ~ p3(X64,X66)
| ~ p3(X64,X65)
| p3(X65,X66) ),
inference(modus_ponens,[status(thm)],[56,49]) ).
tff(58,plain,
( ( ~ ! [X64: $i,X66: $i,X65: $i] :
( ~ p3(X64,X66)
| ~ p3(X64,X65)
| p3(X65,X66) )
| ~ p3(f13(c31,c34),f13(c31,c34))
| ~ p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),c35)))
| p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)) )
<=> ( ~ ! [X64: $i,X66: $i,X65: $i] :
( ~ p3(X64,X66)
| ~ p3(X64,X65)
| p3(X65,X66) )
| ~ p3(f13(c31,c34),f13(c31,c34))
| ~ p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),c35)))
| p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ~ ! [X64: $i,X66: $i,X65: $i] :
( ~ p3(X64,X66)
| ~ p3(X64,X65)
| p3(X65,X66) )
| ~ p3(f13(c31,c34),f13(c31,c34))
| ~ p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),c35)))
| p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
( ~ ! [X64: $i,X66: $i,X65: $i] :
( ~ p3(X64,X66)
| ~ p3(X64,X65)
| p3(X65,X66) )
| ~ p3(f13(c31,c34),f13(c31,c34))
| ~ p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),c35)))
| p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)),
inference(unit_resolution,[status(thm)],[60,57,47,9]) ).
tff(62,plain,
^ [X57: $i,X56: $i,X55: $i] :
refl(
( ( ~ p25(f5(X55,X56),X57)
| p25(f5(f7(c28,X55),X56),X57) )
<=> ( ~ p25(f5(X55,X56),X57)
| p25(f5(f7(c28,X55),X56),X57) ) )),
inference(bind,[status(th)],]) ).
tff(63,plain,
( ! [X57: $i,X56: $i,X55: $i] :
( ~ p25(f5(X55,X56),X57)
| p25(f5(f7(c28,X55),X56),X57) )
<=> ! [X57: $i,X56: $i,X55: $i] :
( ~ p25(f5(X55,X56),X57)
| p25(f5(f7(c28,X55),X56),X57) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [X57: $i,X56: $i,X55: $i] :
( ~ p25(f5(X55,X56),X57)
| p25(f5(f7(c28,X55),X56),X57) )
<=> ! [X57: $i,X56: $i,X55: $i] :
( ~ p25(f5(X55,X56),X57)
| p25(f5(f7(c28,X55),X56),X57) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
^ [X57: $i,X56: $i,X55: $i] :
rewrite(
( ( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(X55,X56),X57) )
<=> ( ~ p25(f5(X55,X56),X57)
| p25(f5(f7(c28,X55),X56),X57) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [X57: $i,X56: $i,X55: $i] :
( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(X55,X56),X57) )
<=> ! [X57: $i,X56: $i,X55: $i] :
( ~ p25(f5(X55,X56),X57)
| p25(f5(f7(c28,X55),X56),X57) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,axiom,
! [X57: $i,X56: $i,X55: $i] :
( p25(f5(f7(c28,X55),X56),X57)
| ~ p25(f5(X55,X56),X57) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25_32) ).
tff(68,plain,
! [X57: $i,X56: $i,X55: $i] :
( ~ p25(f5(X55,X56),X57)
| p25(f5(f7(c28,X55),X56),X57) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [X57: $i,X56: $i,X55: $i] :
( ~ p25(f5(X55,X56),X57)
| p25(f5(f7(c28,X55),X56),X57) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
! [X57: $i,X56: $i,X55: $i] :
( ~ p25(f5(X55,X56),X57)
| p25(f5(f7(c28,X55),X56),X57) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [X57: $i,X56: $i,X55: $i] :
( ~ p25(f5(X55,X56),X57)
| p25(f5(f7(c28,X55),X56),X57) ),
inference(modus_ponens,[status(thm)],[70,63]) ).
tff(72,plain,
( ( ~ ! [X57: $i,X56: $i,X55: $i] :
( ~ p25(f5(X55,X56),X57)
| p25(f5(f7(c28,X55),X56),X57) )
| ~ p25(f5(c29,f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
| p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))) )
<=> ( ~ ! [X57: $i,X56: $i,X55: $i] :
( ~ p25(f5(X55,X56),X57)
| p25(f5(f7(c28,X55),X56),X57) )
| ~ p25(f5(c29,f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
| p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( ~ ! [X57: $i,X56: $i,X55: $i] :
( ~ p25(f5(X55,X56),X57)
| p25(f5(f7(c28,X55),X56),X57) )
| ~ p25(f5(c29,f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
| p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
( ~ ! [X57: $i,X56: $i,X55: $i] :
( ~ p25(f5(X55,X56),X57)
| p25(f5(f7(c28,X55),X56),X57) )
| ~ p25(f5(c29,f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
| p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))),
inference(unit_resolution,[status(thm)],[74,71,18]) ).
tff(76,plain,
^ [X75: $i] :
refl(
( p4(X75,X75)
<=> p4(X75,X75) )),
inference(bind,[status(th)],]) ).
tff(77,plain,
( ! [X75: $i] : p4(X75,X75)
<=> ! [X75: $i] : p4(X75,X75) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
( ! [X75: $i] : p4(X75,X75)
<=> ! [X75: $i] : p4(X75,X75) ),
inference(rewrite,[status(thm)],]) ).
tff(79,axiom,
! [X75: $i] : p4(X75,X75),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_5) ).
tff(80,plain,
! [X75: $i] : p4(X75,X75),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [X75: $i] : p4(X75,X75),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [X75: $i] : p4(X75,X75),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
( ~ ! [X75: $i] : p4(X75,X75)
| p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35))))),
inference(unit_resolution,[status(thm)],[83,82]) ).
tff(85,plain,
^ [X53: $i,X52: $i,X51: $i,X54: $i] :
refl(
( ( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) )
<=> ( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [X53: $i,X52: $i,X51: $i,X54: $i] :
( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) )
<=> ! [X53: $i,X52: $i,X51: $i,X54: $i] :
( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
( ! [X53: $i,X52: $i,X51: $i,X54: $i] :
( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) )
<=> ! [X53: $i,X52: $i,X51: $i,X54: $i] :
( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
^ [X53: $i,X52: $i,X51: $i,X54: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p25(X51,X52)
| ~ p3(X54,X52) )
<=> ( ~ p3(X54,X52)
| p25(X51,X52) ) )),
( ( p25(X51,X52)
| ~ p3(X54,X52)
| ~ p4(X53,X51) )
<=> ( ~ p3(X54,X52)
| p25(X51,X52)
| ~ p4(X53,X51) ) )),
rewrite(
( ( ~ p3(X54,X52)
| p25(X51,X52)
| ~ p4(X53,X51) )
<=> ( ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) ) )),
( ( p25(X51,X52)
| ~ p3(X54,X52)
| ~ p4(X53,X51) )
<=> ( ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) ) )),
( ( p25(X51,X52)
| ~ p3(X54,X52)
| ~ p4(X53,X51)
| ~ p25(X53,X54) )
<=> ( ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52)
| ~ p25(X53,X54) ) )),
rewrite(
( ( ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52)
| ~ p25(X53,X54) )
<=> ( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) ) )),
( ( p25(X51,X52)
| ~ p3(X54,X52)
| ~ p4(X53,X51)
| ~ p25(X53,X54) )
<=> ( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) ) )),
inference(bind,[status(th)],]) ).
tff(89,plain,
( ! [X53: $i,X52: $i,X51: $i,X54: $i] :
( p25(X51,X52)
| ~ p3(X54,X52)
| ~ p4(X53,X51)
| ~ p25(X53,X54) )
<=> ! [X53: $i,X52: $i,X51: $i,X54: $i] :
( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,axiom,
! [X53: $i,X52: $i,X51: $i,X54: $i] :
( p25(X51,X52)
| ~ p3(X54,X52)
| ~ p4(X53,X51)
| ~ p25(X53,X54) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25_35) ).
tff(91,plain,
! [X53: $i,X52: $i,X51: $i,X54: $i] :
( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
! [X53: $i,X52: $i,X51: $i,X54: $i] :
( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) ),
inference(modus_ponens,[status(thm)],[91,87]) ).
tff(93,plain,
! [X53: $i,X52: $i,X51: $i,X54: $i] :
( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) ),
inference(skolemize,[status(sab)],[92]) ).
tff(94,plain,
! [X53: $i,X52: $i,X51: $i,X54: $i] :
( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) ),
inference(modus_ponens,[status(thm)],[93,86]) ).
tff(95,plain,
( ( ~ ! [X53: $i,X52: $i,X51: $i,X54: $i] :
( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) )
| p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
| ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
| ~ p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))))
| ~ p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)) )
<=> ( ~ ! [X53: $i,X52: $i,X51: $i,X54: $i] :
( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) )
| p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
| ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
| ~ p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))))
| ~ p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
( ( ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
| ~ p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))))
| ~ p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34))
| p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34)) )
<=> ( p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
| ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
| ~ p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))))
| ~ p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,plain,
( ( ~ ! [X53: $i,X52: $i,X51: $i,X54: $i] :
( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) )
| ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
| ~ p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))))
| ~ p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34))
| p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34)) )
<=> ( ~ ! [X53: $i,X52: $i,X51: $i,X54: $i] :
( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) )
| p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
| ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
| ~ p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))))
| ~ p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)) ) ),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
( ( ~ ! [X53: $i,X52: $i,X51: $i,X54: $i] :
( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) )
| ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
| ~ p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))))
| ~ p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34))
| p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34)) )
<=> ( ~ ! [X53: $i,X52: $i,X51: $i,X54: $i] :
( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) )
| p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
| ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
| ~ p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))))
| ~ p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)) ) ),
inference(transitivity,[status(thm)],[97,95]) ).
tff(99,plain,
( ~ ! [X53: $i,X52: $i,X51: $i,X54: $i] :
( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) )
| ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
| ~ p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))))
| ~ p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34))
| p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34)) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
( ~ ! [X53: $i,X52: $i,X51: $i,X54: $i] :
( ~ p25(X53,X54)
| ~ p4(X53,X51)
| ~ p3(X54,X52)
| p25(X51,X52) )
| p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
| ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
| ~ p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))))
| ~ p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
$false,
inference(unit_resolution,[status(thm)],[100,94,31,84,75,61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYN656-1 : TPTP v8.1.0. Released v2.5.0.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Sep 5 06:25:39 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.22/0.46 % SZS status Unsatisfiable
% 0.22/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------