TSTP Solution File: SYO038-1.003.003 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO038-1.003.003 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 : Fri Sep 30 01:39:22 EDT 2022
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 66
% Syntax : Number of formulae : 223 ( 109 unt; 4 typ; 0 def)
% Number of atoms : 499 ( 122 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 521 ( 246 ~; 223 |; 0 &)
% ( 52 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 3 >; 1 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 129 ( 123 !; 0 ?; 129 :)
% Comments :
%------------------------------------------------------------------------------
tff(d_type,type,
d: $i > $o ).
tff(s_type,type,
s: $i > $i ).
tff(f_type,type,
f: ( $i * $i ) > $i ).
tff(one_type,type,
one: $i ).
tff(1,plain,
^ [N: $i] :
refl(
( ( f(N,one) = s(one) )
<=> ( f(N,one) = s(one) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [N: $i] : ( f(N,one) = s(one) )
<=> ! [N: $i] : ( f(N,one) = s(one) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [N: $i] : ( f(N,one) = s(one) )
<=> ! [N: $i] : ( f(N,one) = s(one) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [N: $i] : ( f(N,one) = s(one) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
tff(5,plain,
! [N: $i] : ( f(N,one) = s(one) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [N: $i] : ( f(N,one) = s(one) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [N: $i] : ( f(N,one) = s(one) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [N: $i] : ( f(N,one) = s(one) )
| ( f(s(s(one)),one) = s(one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
f(s(s(one)),one) = s(one),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
s(one) = f(s(s(one)),one),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
f(s(one),s(one)) = f(s(one),f(s(s(one)),one)),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
f(s(one),f(s(s(one)),one)) = f(s(one),s(one)),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
f(one,f(s(one),f(s(s(one)),one))) = f(one,f(s(one),s(one))),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
f(one,f(s(one),s(one))) = f(one,f(s(one),f(s(s(one)),one))),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
s(f(one,f(s(one),s(one)))) = s(f(one,f(s(one),f(s(s(one)),one)))),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( d(s(f(one,f(s(one),s(one)))))
<=> d(s(f(one,f(s(one),f(s(s(one)),one))))) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
^ [X: $i] :
refl(
( ( f(one,s(X)) = s(s(f(one,X))) )
<=> ( f(one,s(X)) = s(s(f(one,X))) ) )),
inference(bind,[status(th)],]) ).
tff(18,plain,
( ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
<=> ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
<=> ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
tff(21,plain,
! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
| ( f(one,s(s(s(one)))) = s(s(f(one,s(s(one))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
f(one,s(s(s(one)))) = s(s(f(one,s(s(one))))),
inference(unit_resolution,[status(thm)],[24,23]) ).
tff(26,plain,
^ [N: $i,X: $i] :
refl(
( ( f(s(N),s(X)) = f(N,f(s(N),X)) )
<=> ( f(s(N),s(X)) = f(N,f(s(N),X)) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
<=> ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
<=> ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(30,plain,
! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ~ ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
| ( f(s(one),s(one)) = f(one,f(s(one),one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
f(s(one),s(one)) = f(one,f(s(one),one)),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
f(one,f(s(one),one)) = f(s(one),s(one)),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
( ~ ! [N: $i] : ( f(N,one) = s(one) )
| ( f(s(one),one) = s(one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
f(s(one),one) = s(one),
inference(unit_resolution,[status(thm)],[36,7]) ).
tff(38,plain,
s(one) = f(s(one),one),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
f(one,s(one)) = f(one,f(s(one),one)),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
| ( f(one,s(one)) = s(s(f(one,one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
f(one,s(one)) = s(s(f(one,one))),
inference(unit_resolution,[status(thm)],[40,23]) ).
tff(42,plain,
s(s(f(one,one))) = f(one,s(one)),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
( ~ ! [N: $i] : ( f(N,one) = s(one) )
| ( f(one,one) = s(one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
f(one,one) = s(one),
inference(unit_resolution,[status(thm)],[43,7]) ).
tff(45,plain,
s(f(one,one)) = s(s(one)),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
s(s(one)) = s(f(one,one)),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
s(s(s(one))) = s(s(f(one,one))),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
s(s(s(one))) = f(s(one),s(one)),
inference(transitivity,[status(thm)],[47,42,39,35]) ).
tff(49,plain,
f(one,s(s(s(one)))) = f(one,f(s(one),s(one))),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
f(one,f(s(one),s(one))) = f(one,s(s(s(one)))),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
f(one,f(s(one),s(one))) = s(s(f(one,s(s(one))))),
inference(transitivity,[status(thm)],[50,25]) ).
tff(52,plain,
( d(f(one,f(s(one),s(one))))
<=> d(s(s(f(one,s(s(one)))))) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( d(s(s(f(one,s(s(one))))))
<=> d(f(one,f(s(one),s(one)))) ),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
| ( f(one,s(s(one))) = s(s(f(one,s(one)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
f(one,s(s(one))) = s(s(f(one,s(one)))),
inference(unit_resolution,[status(thm)],[54,23]) ).
tff(56,plain,
s(s(f(one,s(one)))) = f(one,s(s(one))),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
( d(s(s(f(one,s(one)))))
<=> d(f(one,s(s(one)))) ),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
f(one,f(s(one),one)) = f(one,s(one)),
inference(symmetry,[status(thm)],[39]) ).
tff(59,plain,
f(s(one),f(s(s(one)),one)) = f(one,s(one)),
inference(transitivity,[status(thm)],[12,34,58]) ).
tff(60,plain,
s(f(s(one),f(s(s(one)),one))) = s(f(one,s(one))),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( d(s(f(s(one),f(s(s(one)),one))))
<=> d(s(f(one,s(one)))) ),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
f(s(one),f(s(s(one)),one)) = s(s(f(one,one))),
inference(transitivity,[status(thm)],[12,34,58,41]) ).
tff(63,plain,
( d(f(s(one),f(s(s(one)),one)))
<=> d(s(s(f(one,one)))) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( d(s(s(f(one,one))))
<=> d(f(s(one),f(s(s(one)),one))) ),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( d(s(f(one,one)))
<=> d(s(s(one))) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(66,plain,
( d(s(s(one)))
<=> d(s(f(one,one))) ),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
^ [X: $i] :
refl(
( ( d(s(X))
| ~ d(X) )
<=> ( d(s(X))
| ~ d(X) ) )),
inference(bind,[status(th)],]) ).
tff(68,plain,
( ! [X: $i] :
( d(s(X))
| ~ d(X) )
<=> ! [X: $i] :
( d(s(X))
| ~ d(X) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,plain,
( ! [X: $i] :
( d(s(X))
| ~ d(X) )
<=> ! [X: $i] :
( d(s(X))
| ~ d(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
^ [X: $i] :
rewrite(
( ( ~ d(X)
| d(s(X)) )
<=> ( d(s(X))
| ~ d(X) ) )),
inference(bind,[status(th)],]) ).
tff(71,plain,
( ! [X: $i] :
( ~ d(X)
| d(s(X)) )
<=> ! [X: $i] :
( d(s(X))
| ~ d(X) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,axiom,
! [X: $i] :
( ~ d(X)
| d(s(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
tff(73,plain,
! [X: $i] :
( d(s(X))
| ~ d(X) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
! [X: $i] :
( d(s(X))
| ~ d(X) ),
inference(modus_ponens,[status(thm)],[73,69]) ).
tff(75,plain,
! [X: $i] :
( d(s(X))
| ~ d(X) ),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [X: $i] :
( d(s(X))
| ~ d(X) ),
inference(modus_ponens,[status(thm)],[75,68]) ).
tff(77,plain,
( d(one)
<=> d(one) ),
inference(rewrite,[status(thm)],]) ).
tff(78,axiom,
d(one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
tff(79,plain,
d(one),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(one))
| ~ d(one) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(one))
| ~ d(one) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(one))
| ~ d(one) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(one))
| ~ d(one) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
d(s(one)),
inference(unit_resolution,[status(thm)],[82,79,76]) ).
tff(84,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(one)))
| ~ d(s(one)) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(one)))
| ~ d(s(one)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(one)))
| ~ d(s(one)) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(one)))
| ~ d(s(one)) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
d(s(s(one))),
inference(unit_resolution,[status(thm)],[86,76,83]) ).
tff(88,plain,
d(s(f(one,one))),
inference(modus_ponens,[status(thm)],[87,66]) ).
tff(89,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,one))))
| ~ d(s(f(one,one))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,one))))
| ~ d(s(f(one,one))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,one))))
| ~ d(s(f(one,one))) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,one))))
| ~ d(s(f(one,one))) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
( d(s(s(f(one,one))))
| ~ d(s(f(one,one))) ),
inference(unit_resolution,[status(thm)],[91,76]) ).
tff(93,plain,
d(s(s(f(one,one)))),
inference(unit_resolution,[status(thm)],[92,88]) ).
tff(94,plain,
d(f(s(one),f(s(s(one)),one))),
inference(modus_ponens,[status(thm)],[93,64]) ).
tff(95,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(s(one),f(s(s(one)),one))))
| ~ d(f(s(one),f(s(s(one)),one))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(s(one),f(s(s(one)),one))))
| ~ d(f(s(one),f(s(s(one)),one))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(s(one),f(s(s(one)),one))))
| ~ d(f(s(one),f(s(s(one)),one))) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(s(one),f(s(s(one)),one))))
| ~ d(f(s(one),f(s(s(one)),one))) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
( d(s(f(s(one),f(s(s(one)),one))))
| ~ d(f(s(one),f(s(s(one)),one))) ),
inference(unit_resolution,[status(thm)],[97,76]) ).
tff(99,plain,
d(s(f(s(one),f(s(s(one)),one)))),
inference(unit_resolution,[status(thm)],[98,94]) ).
tff(100,plain,
d(s(f(one,s(one)))),
inference(modus_ponens,[status(thm)],[99,61]) ).
tff(101,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(one)))))
| ~ d(s(f(one,s(one)))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(one)))))
| ~ d(s(f(one,s(one)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(one)))))
| ~ d(s(f(one,s(one)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(one)))))
| ~ d(s(f(one,s(one)))) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
( d(s(s(f(one,s(one)))))
| ~ d(s(f(one,s(one)))) ),
inference(unit_resolution,[status(thm)],[103,76]) ).
tff(105,plain,
d(s(s(f(one,s(one))))),
inference(unit_resolution,[status(thm)],[104,100]) ).
tff(106,plain,
d(f(one,s(s(one)))),
inference(modus_ponens,[status(thm)],[105,57]) ).
tff(107,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(one,s(s(one)))))
| ~ d(f(one,s(s(one)))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(one,s(s(one)))))
| ~ d(f(one,s(s(one)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(one,s(s(one)))))
| ~ d(f(one,s(s(one)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(109,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(one,s(s(one)))))
| ~ d(f(one,s(s(one)))) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
( d(s(f(one,s(s(one)))))
| ~ d(f(one,s(s(one)))) ),
inference(unit_resolution,[status(thm)],[109,76]) ).
tff(111,plain,
d(s(f(one,s(s(one))))),
inference(unit_resolution,[status(thm)],[110,106]) ).
tff(112,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(s(one))))))
| ~ d(s(f(one,s(s(one))))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(s(one))))))
| ~ d(s(f(one,s(s(one))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(s(one))))))
| ~ d(s(f(one,s(s(one))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(s(one))))))
| ~ d(s(f(one,s(s(one))))) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
( d(s(s(f(one,s(s(one))))))
| ~ d(s(f(one,s(s(one))))) ),
inference(unit_resolution,[status(thm)],[114,76]) ).
tff(116,plain,
d(s(s(f(one,s(s(one)))))),
inference(unit_resolution,[status(thm)],[115,111]) ).
tff(117,plain,
d(f(one,f(s(one),s(one)))),
inference(modus_ponens,[status(thm)],[116,53]) ).
tff(118,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(one,f(s(one),s(one)))))
| ~ d(f(one,f(s(one),s(one)))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(one,f(s(one),s(one)))))
| ~ d(f(one,f(s(one),s(one)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(one,f(s(one),s(one)))))
| ~ d(f(one,f(s(one),s(one)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(one,f(s(one),s(one)))))
| ~ d(f(one,f(s(one),s(one)))) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
( d(s(f(one,f(s(one),s(one)))))
| ~ d(f(one,f(s(one),s(one)))) ),
inference(unit_resolution,[status(thm)],[120,76]) ).
tff(122,plain,
d(s(f(one,f(s(one),s(one))))),
inference(unit_resolution,[status(thm)],[121,117]) ).
tff(123,plain,
d(s(f(one,f(s(one),f(s(s(one)),one))))),
inference(modus_ponens,[status(thm)],[122,16]) ).
tff(124,plain,
s(f(one,s(one))) = s(f(s(one),f(s(s(one)),one))),
inference(symmetry,[status(thm)],[60]) ).
tff(125,plain,
f(one,s(f(one,s(one)))) = f(one,s(f(s(one),f(s(s(one)),one)))),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
f(one,s(f(s(one),f(s(s(one)),one)))) = f(one,s(f(one,s(one)))),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
| ( f(one,s(f(s(one),f(s(s(one)),one)))) = s(s(f(one,f(s(one),f(s(s(one)),one))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(128,plain,
f(one,s(f(s(one),f(s(s(one)),one)))) = s(s(f(one,f(s(one),f(s(s(one)),one))))),
inference(unit_resolution,[status(thm)],[127,23]) ).
tff(129,plain,
s(s(f(one,f(s(one),f(s(s(one)),one))))) = f(one,s(f(s(one),f(s(s(one)),one)))),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
s(s(f(one,f(s(one),f(s(s(one)),one))))) = f(one,s(f(one,s(one)))),
inference(transitivity,[status(thm)],[129,126]) ).
tff(131,plain,
( d(s(s(f(one,f(s(one),f(s(s(one)),one))))))
<=> d(f(one,s(f(one,s(one))))) ),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
( d(f(one,s(f(one,s(one)))))
<=> d(s(s(f(one,f(s(one),f(s(s(one)),one)))))) ),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
( ~ d(f(one,s(f(one,s(one)))))
<=> ~ d(s(s(f(one,f(s(one),f(s(s(one)),one)))))) ),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
| ( f(one,s(s(f(one,s(one))))) = s(s(f(one,s(f(one,s(one)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(135,plain,
f(one,s(s(f(one,s(one))))) = s(s(f(one,s(f(one,s(one)))))),
inference(unit_resolution,[status(thm)],[134,23]) ).
tff(136,plain,
s(s(f(one,s(f(one,s(one)))))) = f(one,s(s(f(one,s(one))))),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
( d(s(s(f(one,s(f(one,s(one)))))))
<=> d(f(one,s(s(f(one,s(one)))))) ),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
( d(f(one,s(s(f(one,s(one))))))
<=> d(s(s(f(one,s(f(one,s(one))))))) ),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
( ~ d(f(one,s(s(f(one,s(one))))))
<=> ~ d(s(s(f(one,s(f(one,s(one))))))) ),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
s(s(s(f(one,s(one))))) = s(f(one,s(s(one)))),
inference(monotonicity,[status(thm)],[56]) ).
tff(141,plain,
s(f(one,s(s(one)))) = s(s(s(f(one,s(one))))),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
f(one,s(f(one,s(s(one))))) = f(one,s(s(s(f(one,s(one)))))),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
f(one,s(s(s(f(one,s(one)))))) = f(one,s(f(one,s(s(one))))),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
| ( f(one,s(s(s(f(one,s(one)))))) = s(s(f(one,s(s(f(one,s(one))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(145,plain,
f(one,s(s(s(f(one,s(one)))))) = s(s(f(one,s(s(f(one,s(one))))))),
inference(unit_resolution,[status(thm)],[144,23]) ).
tff(146,plain,
s(s(f(one,s(s(f(one,s(one))))))) = f(one,s(s(s(f(one,s(one)))))),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
s(s(f(one,s(s(f(one,s(one))))))) = f(one,s(f(one,s(s(one))))),
inference(transitivity,[status(thm)],[146,143]) ).
tff(148,plain,
( d(s(s(f(one,s(s(f(one,s(one))))))))
<=> d(f(one,s(f(one,s(s(one)))))) ),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
( d(f(one,s(f(one,s(s(one))))))
<=> d(s(s(f(one,s(s(f(one,s(one)))))))) ),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
( ~ d(f(one,s(f(one,s(s(one))))))
<=> ~ d(s(s(f(one,s(s(f(one,s(one)))))))) ),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
( ~ ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
| ( f(s(s(one)),s(s(one))) = f(s(one),f(s(s(one)),s(one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(152,plain,
f(s(s(one)),s(s(one))) = f(s(one),f(s(s(one)),s(one))),
inference(unit_resolution,[status(thm)],[151,32]) ).
tff(153,plain,
f(s(one),f(s(s(one)),s(one))) = f(s(s(one)),s(s(one))),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
( ~ ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
| ( f(s(s(one)),s(one)) = f(s(one),f(s(s(one)),one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(155,plain,
f(s(s(one)),s(one)) = f(s(one),f(s(s(one)),one)),
inference(unit_resolution,[status(thm)],[154,32]) ).
tff(156,plain,
f(s(one),f(s(s(one)),one)) = f(s(s(one)),s(one)),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
s(s(f(one,one))) = f(s(s(one)),s(one)),
inference(transitivity,[status(thm)],[42,39,35,11,156]) ).
tff(158,plain,
f(s(one),s(s(f(one,one)))) = f(s(one),f(s(s(one)),s(one))),
inference(monotonicity,[status(thm)],[157]) ).
tff(159,plain,
( ~ ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
| ( f(s(one),s(s(f(one,one)))) = f(one,f(s(one),s(f(one,one)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(160,plain,
f(s(one),s(s(f(one,one)))) = f(one,f(s(one),s(f(one,one)))),
inference(unit_resolution,[status(thm)],[159,32]) ).
tff(161,plain,
f(one,f(s(one),s(f(one,one)))) = f(s(one),s(s(f(one,one)))),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
f(s(one),s(f(one,one))) = f(s(one),s(s(one))),
inference(monotonicity,[status(thm)],[45]) ).
tff(163,plain,
f(s(one),s(s(one))) = f(s(one),s(f(one,one))),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
( ~ ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
| ( f(s(one),s(s(one))) = f(one,f(s(one),s(one))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(165,plain,
f(s(one),s(s(one))) = f(one,f(s(one),s(one))),
inference(unit_resolution,[status(thm)],[164,32]) ).
tff(166,plain,
f(one,f(s(one),s(one))) = f(s(one),s(s(one))),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
s(s(f(one,s(s(one))))) = f(one,s(s(s(one)))),
inference(symmetry,[status(thm)],[25]) ).
tff(168,plain,
s(s(f(one,s(s(one))))) = f(s(one),s(f(one,one))),
inference(transitivity,[status(thm)],[167,49,166,163]) ).
tff(169,plain,
f(one,s(s(f(one,s(s(one)))))) = f(one,f(s(one),s(f(one,one)))),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,plain,
( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
| ( f(one,s(s(f(one,s(s(one)))))) = s(s(f(one,s(f(one,s(s(one))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(171,plain,
f(one,s(s(f(one,s(s(one)))))) = s(s(f(one,s(f(one,s(s(one))))))),
inference(unit_resolution,[status(thm)],[170,23]) ).
tff(172,plain,
s(s(f(one,s(f(one,s(s(one))))))) = f(one,s(s(f(one,s(s(one)))))),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
s(s(f(one,s(f(one,s(s(one))))))) = f(s(s(one)),s(s(one))),
inference(transitivity,[status(thm)],[172,169,161,158,153]) ).
tff(174,plain,
( d(s(s(f(one,s(f(one,s(s(one))))))))
<=> d(f(s(s(one)),s(s(one)))) ),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,plain,
( d(f(s(s(one)),s(s(one))))
<=> d(s(s(f(one,s(f(one,s(s(one)))))))) ),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
( ~ d(f(s(s(one)),s(s(one))))
<=> ~ d(s(s(f(one,s(f(one,s(s(one)))))))) ),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
( ~ d(f(s(s(one)),s(s(one))))
<=> ~ d(f(s(s(one)),s(s(one)))) ),
inference(rewrite,[status(thm)],]) ).
tff(178,axiom,
~ d(f(s(s(one)),s(s(one)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(179,plain,
~ d(f(s(s(one)),s(s(one)))),
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
~ d(s(s(f(one,s(f(one,s(s(one)))))))),
inference(modus_ponens,[status(thm)],[179,176]) ).
tff(181,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(f(one,s(s(one))))))))
| ~ d(s(f(one,s(f(one,s(s(one))))))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(f(one,s(s(one))))))))
| ~ d(s(f(one,s(f(one,s(s(one))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(182,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(f(one,s(s(one))))))))
| ~ d(s(f(one,s(f(one,s(s(one))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(183,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(f(one,s(s(one))))))))
| ~ d(s(f(one,s(f(one,s(s(one))))))) ),
inference(modus_ponens,[status(thm)],[182,181]) ).
tff(184,plain,
( d(s(s(f(one,s(f(one,s(s(one))))))))
| ~ d(s(f(one,s(f(one,s(s(one))))))) ),
inference(unit_resolution,[status(thm)],[183,76]) ).
tff(185,plain,
~ d(s(f(one,s(f(one,s(s(one))))))),
inference(unit_resolution,[status(thm)],[184,180]) ).
tff(186,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(one,s(f(one,s(s(one)))))))
| ~ d(f(one,s(f(one,s(s(one)))))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(one,s(f(one,s(s(one)))))))
| ~ d(f(one,s(f(one,s(s(one)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(187,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(one,s(f(one,s(s(one)))))))
| ~ d(f(one,s(f(one,s(s(one)))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(188,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(one,s(f(one,s(s(one)))))))
| ~ d(f(one,s(f(one,s(s(one)))))) ),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
( d(s(f(one,s(f(one,s(s(one)))))))
| ~ d(f(one,s(f(one,s(s(one)))))) ),
inference(unit_resolution,[status(thm)],[188,76]) ).
tff(190,plain,
~ d(f(one,s(f(one,s(s(one)))))),
inference(unit_resolution,[status(thm)],[189,185]) ).
tff(191,plain,
~ d(s(s(f(one,s(s(f(one,s(one)))))))),
inference(modus_ponens,[status(thm)],[190,150]) ).
tff(192,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(s(f(one,s(one))))))))
| ~ d(s(f(one,s(s(f(one,s(one))))))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(s(f(one,s(one))))))))
| ~ d(s(f(one,s(s(f(one,s(one))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(193,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(s(f(one,s(one))))))))
| ~ d(s(f(one,s(s(f(one,s(one))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(194,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(s(f(one,s(one))))))))
| ~ d(s(f(one,s(s(f(one,s(one))))))) ),
inference(modus_ponens,[status(thm)],[193,192]) ).
tff(195,plain,
( d(s(s(f(one,s(s(f(one,s(one))))))))
| ~ d(s(f(one,s(s(f(one,s(one))))))) ),
inference(unit_resolution,[status(thm)],[194,76]) ).
tff(196,plain,
~ d(s(f(one,s(s(f(one,s(one))))))),
inference(unit_resolution,[status(thm)],[195,191]) ).
tff(197,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(one,s(s(f(one,s(one)))))))
| ~ d(f(one,s(s(f(one,s(one)))))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(one,s(s(f(one,s(one)))))))
| ~ d(f(one,s(s(f(one,s(one)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(198,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(one,s(s(f(one,s(one)))))))
| ~ d(f(one,s(s(f(one,s(one)))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(199,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(one,s(s(f(one,s(one)))))))
| ~ d(f(one,s(s(f(one,s(one)))))) ),
inference(modus_ponens,[status(thm)],[198,197]) ).
tff(200,plain,
( d(s(f(one,s(s(f(one,s(one)))))))
| ~ d(f(one,s(s(f(one,s(one)))))) ),
inference(unit_resolution,[status(thm)],[199,76]) ).
tff(201,plain,
~ d(f(one,s(s(f(one,s(one)))))),
inference(unit_resolution,[status(thm)],[200,196]) ).
tff(202,plain,
~ d(s(s(f(one,s(f(one,s(one))))))),
inference(modus_ponens,[status(thm)],[201,139]) ).
tff(203,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(f(one,s(one)))))))
| ~ d(s(f(one,s(f(one,s(one)))))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(f(one,s(one)))))))
| ~ d(s(f(one,s(f(one,s(one)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(204,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(f(one,s(one)))))))
| ~ d(s(f(one,s(f(one,s(one)))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(205,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,s(f(one,s(one)))))))
| ~ d(s(f(one,s(f(one,s(one)))))) ),
inference(modus_ponens,[status(thm)],[204,203]) ).
tff(206,plain,
( d(s(s(f(one,s(f(one,s(one)))))))
| ~ d(s(f(one,s(f(one,s(one)))))) ),
inference(unit_resolution,[status(thm)],[205,76]) ).
tff(207,plain,
~ d(s(f(one,s(f(one,s(one)))))),
inference(unit_resolution,[status(thm)],[206,202]) ).
tff(208,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(one,s(f(one,s(one))))))
| ~ d(f(one,s(f(one,s(one))))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(one,s(f(one,s(one))))))
| ~ d(f(one,s(f(one,s(one))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(209,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(one,s(f(one,s(one))))))
| ~ d(f(one,s(f(one,s(one))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(210,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(f(one,s(f(one,s(one))))))
| ~ d(f(one,s(f(one,s(one))))) ),
inference(modus_ponens,[status(thm)],[209,208]) ).
tff(211,plain,
( d(s(f(one,s(f(one,s(one))))))
| ~ d(f(one,s(f(one,s(one))))) ),
inference(unit_resolution,[status(thm)],[210,76]) ).
tff(212,plain,
~ d(f(one,s(f(one,s(one))))),
inference(unit_resolution,[status(thm)],[211,207]) ).
tff(213,plain,
~ d(s(s(f(one,f(s(one),f(s(s(one)),one)))))),
inference(modus_ponens,[status(thm)],[212,133]) ).
tff(214,plain,
( ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,f(s(one),f(s(s(one)),one))))))
| ~ d(s(f(one,f(s(one),f(s(s(one)),one))))) )
<=> ( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,f(s(one),f(s(s(one)),one))))))
| ~ d(s(f(one,f(s(one),f(s(s(one)),one))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(215,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,f(s(one),f(s(s(one)),one))))))
| ~ d(s(f(one,f(s(one),f(s(s(one)),one))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(216,plain,
( ~ ! [X: $i] :
( d(s(X))
| ~ d(X) )
| d(s(s(f(one,f(s(one),f(s(s(one)),one))))))
| ~ d(s(f(one,f(s(one),f(s(s(one)),one))))) ),
inference(modus_ponens,[status(thm)],[215,214]) ).
tff(217,plain,
( d(s(s(f(one,f(s(one),f(s(s(one)),one))))))
| ~ d(s(f(one,f(s(one),f(s(s(one)),one))))) ),
inference(unit_resolution,[status(thm)],[216,76]) ).
tff(218,plain,
~ d(s(f(one,f(s(one),f(s(s(one)),one))))),
inference(unit_resolution,[status(thm)],[217,213]) ).
tff(219,plain,
$false,
inference(unit_resolution,[status(thm)],[218,123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYO038-1.003.003 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n004.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 10:14:04 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------