TSTP Solution File: PUZ056-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ056-1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 : Sun Sep 18 14:11:09 EDT 2022
% Result : Unsatisfiable 0.14s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 83
% Syntax : Number of formulae : 192 ( 102 unt; 11 typ; 0 def)
% Number of atoms : 472 ( 192 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 515 ( 239 ~; 232 |; 0 &)
% ( 44 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 280 ( 264 !; 0 ?; 280 :)
% Comments :
%------------------------------------------------------------------------------
tff(state_type,type,
state: $i > $o ).
tff(nextto_type,type,
nextto: ( $i * $i ) > $i ).
tff(pin_type,type,
pin: $i > $i ).
tff(n3_type,type,
n3: $i ).
tff(n2_type,type,
n2: $i ).
tff(on_type,type,
on: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(large_type,type,
large: $i ).
tff(medium_type,type,
medium: $i ).
tff(small_type,type,
small: $i ).
tff(fits_type,type,
fits: ( $i * $i ) > $o ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( ( nextto(X,Y) = nextto(Y,X) )
<=> ( nextto(X,Y) = nextto(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( nextto(X,Y) = nextto(Y,X) )
<=> ! [Y: $i,X: $i] : ( nextto(X,Y) = nextto(Y,X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( nextto(X,Y) = nextto(Y,X) )
<=> ! [Y: $i,X: $i] : ( nextto(X,Y) = nextto(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( nextto(X,Y) = nextto(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nextto_commutative) ).
tff(5,plain,
! [Y: $i,X: $i] : ( nextto(X,Y) = nextto(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( nextto(X,Y) = nextto(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( nextto(X,Y) = nextto(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( nextto(X,Y) = nextto(Y,X) )
| ( nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3)))))) = nextto(nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))),pin(n1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3)))))) = nextto(nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))),pin(n1)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
nextto(nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))),pin(n1)) = nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3)))))),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z) )
<=> ( nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] : ( nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [Z: $i,Y: $i,X: $i] : ( nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [Z: $i,Y: $i,X: $i] : ( nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nextto_associative) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] : ( nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : ( nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Z: $i,Y: $i,X: $i] : ( nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z) )
| ( nextto(pin(n2),nextto(on(small,on(medium,on(large,pin(n3)))),pin(n1))) = nextto(nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))),pin(n1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
nextto(pin(n2),nextto(on(small,on(medium,on(large,pin(n3)))),pin(n1))) = nextto(nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))),pin(n1)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
( ~ ! [Y: $i,X: $i] : ( nextto(X,Y) = nextto(Y,X) )
| ( nextto(pin(n2),nextto(on(small,on(medium,on(large,pin(n3)))),pin(n1))) = nextto(nextto(on(small,on(medium,on(large,pin(n3)))),pin(n1)),pin(n2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
nextto(pin(n2),nextto(on(small,on(medium,on(large,pin(n3)))),pin(n1))) = nextto(nextto(on(small,on(medium,on(large,pin(n3)))),pin(n1)),pin(n2)),
inference(unit_resolution,[status(thm)],[20,7]) ).
tff(22,plain,
nextto(nextto(on(small,on(medium,on(large,pin(n3)))),pin(n1)),pin(n2)) = nextto(pin(n2),nextto(on(small,on(medium,on(large,pin(n3)))),pin(n1))),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
( ~ ! [Y: $i,X: $i] : ( nextto(X,Y) = nextto(Y,X) )
| ( nextto(on(small,on(medium,on(large,pin(n3)))),pin(n1)) = nextto(pin(n1),on(small,on(medium,on(large,pin(n3))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
nextto(on(small,on(medium,on(large,pin(n3)))),pin(n1)) = nextto(pin(n1),on(small,on(medium,on(large,pin(n3))))),
inference(unit_resolution,[status(thm)],[23,7]) ).
tff(25,plain,
nextto(pin(n1),on(small,on(medium,on(large,pin(n3))))) = nextto(on(small,on(medium,on(large,pin(n3)))),pin(n1)),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
^ [N: $i] :
refl(
( fits(small,pin(N))
<=> fits(small,pin(N)) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [N: $i] : fits(small,pin(N))
<=> ! [N: $i] : fits(small,pin(N)) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [N: $i] : fits(small,pin(N))
<=> ! [N: $i] : fits(small,pin(N)) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
! [N: $i] : fits(small,pin(N)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fits_1) ).
tff(30,plain,
! [N: $i] : fits(small,pin(N)),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [N: $i] : fits(small,pin(N)),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [N: $i] : fits(small,pin(N)),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ~ ! [N: $i] : fits(small,pin(N))
| fits(small,pin(n1)) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
fits(small,pin(n1)),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
^ [A: $i] :
refl(
( fits(small,on(medium,A))
<=> fits(small,on(medium,A)) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [A: $i] : fits(small,on(medium,A))
<=> ! [A: $i] : fits(small,on(medium,A)) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [A: $i] : fits(small,on(medium,A))
<=> ! [A: $i] : fits(small,on(medium,A)) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
! [A: $i] : fits(small,on(medium,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fits_4) ).
tff(39,plain,
! [A: $i] : fits(small,on(medium,A)),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [A: $i] : fits(small,on(medium,A)),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [A: $i] : fits(small,on(medium,A)),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ~ ! [A: $i] : fits(small,on(medium,A))
| fits(small,on(medium,on(large,pin(n3)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
fits(small,on(medium,on(large,pin(n3)))),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
^ [B: $i,A: $i,X: $i] :
refl(
( ( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
<=> ( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
<=> ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
<=> ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
^ [B: $i,A: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ( nextto(on(X,A),B) = nextto(A,on(X,B)) )
| ~ fits(X,B) )
<=> ( ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) ) )),
( ( ( nextto(on(X,A),B) = nextto(A,on(X,B)) )
| ~ fits(X,B)
| ~ fits(X,A) )
<=> ( ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) )
| ~ fits(X,A) ) )),
rewrite(
( ( ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) )
| ~ fits(X,A) )
<=> ( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) ) )),
( ( ( nextto(on(X,A),B) = nextto(A,on(X,B)) )
| ~ fits(X,B)
| ~ fits(X,A) )
<=> ( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [B: $i,A: $i,X: $i] :
( ( nextto(on(X,A),B) = nextto(A,on(X,B)) )
| ~ fits(X,B)
| ~ fits(X,A) )
<=> ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,axiom,
! [B: $i,A: $i,X: $i] :
( ( nextto(on(X,A),B) = nextto(A,on(X,B)) )
| ~ fits(X,B)
| ~ fits(X,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_move) ).
tff(50,plain,
! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
( ( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(small,pin(n1))
| ~ fits(small,on(medium,on(large,pin(n3))))
| ( nextto(on(small,pin(n1)),on(medium,on(large,pin(n3)))) = nextto(pin(n1),on(small,on(medium,on(large,pin(n3))))) ) )
<=> ( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(small,pin(n1))
| ~ fits(small,on(medium,on(large,pin(n3))))
| ( nextto(on(small,pin(n1)),on(medium,on(large,pin(n3)))) = nextto(pin(n1),on(small,on(medium,on(large,pin(n3))))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(small,pin(n1))
| ~ fits(small,on(medium,on(large,pin(n3))))
| ( nextto(on(small,pin(n1)),on(medium,on(large,pin(n3)))) = nextto(pin(n1),on(small,on(medium,on(large,pin(n3))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(small,pin(n1))
| ~ fits(small,on(medium,on(large,pin(n3))))
| ( nextto(on(small,pin(n1)),on(medium,on(large,pin(n3)))) = nextto(pin(n1),on(small,on(medium,on(large,pin(n3))))) ) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
nextto(on(small,pin(n1)),on(medium,on(large,pin(n3)))) = nextto(pin(n1),on(small,on(medium,on(large,pin(n3))))),
inference(unit_resolution,[status(thm)],[56,53,43,34]) ).
tff(58,plain,
nextto(on(small,pin(n1)),on(medium,on(large,pin(n3)))) = nextto(on(small,on(medium,on(large,pin(n3)))),pin(n1)),
inference(transitivity,[status(thm)],[57,25]) ).
tff(59,plain,
nextto(nextto(on(small,pin(n1)),on(medium,on(large,pin(n3)))),pin(n2)) = nextto(nextto(on(small,on(medium,on(large,pin(n3)))),pin(n1)),pin(n2)),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z) )
| ( nextto(on(small,pin(n1)),nextto(on(medium,on(large,pin(n3))),pin(n2))) = nextto(nextto(on(small,pin(n1)),on(medium,on(large,pin(n3)))),pin(n2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
nextto(on(small,pin(n1)),nextto(on(medium,on(large,pin(n3))),pin(n2))) = nextto(nextto(on(small,pin(n1)),on(medium,on(large,pin(n3)))),pin(n2)),
inference(unit_resolution,[status(thm)],[60,17]) ).
tff(62,plain,
( ~ ! [Y: $i,X: $i] : ( nextto(X,Y) = nextto(Y,X) )
| ( nextto(on(small,pin(n1)),nextto(on(medium,on(large,pin(n3))),pin(n2))) = nextto(nextto(on(medium,on(large,pin(n3))),pin(n2)),on(small,pin(n1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
nextto(on(small,pin(n1)),nextto(on(medium,on(large,pin(n3))),pin(n2))) = nextto(nextto(on(medium,on(large,pin(n3))),pin(n2)),on(small,pin(n1))),
inference(unit_resolution,[status(thm)],[62,7]) ).
tff(64,plain,
nextto(nextto(on(medium,on(large,pin(n3))),pin(n2)),on(small,pin(n1))) = nextto(on(small,pin(n1)),nextto(on(medium,on(large,pin(n3))),pin(n2))),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
^ [A: $i] :
refl(
( fits(medium,on(large,A))
<=> fits(medium,on(large,A)) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [A: $i] : fits(medium,on(large,A))
<=> ! [A: $i] : fits(medium,on(large,A)) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [A: $i] : fits(medium,on(large,A))
<=> ! [A: $i] : fits(medium,on(large,A)) ),
inference(rewrite,[status(thm)],]) ).
tff(68,axiom,
! [A: $i] : fits(medium,on(large,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fits_5) ).
tff(69,plain,
! [A: $i] : fits(medium,on(large,A)),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [A: $i] : fits(medium,on(large,A)),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [A: $i] : fits(medium,on(large,A)),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
( ~ ! [A: $i] : fits(medium,on(large,A))
| fits(medium,on(large,pin(n3))) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
fits(medium,on(large,pin(n3))),
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
^ [N: $i] :
refl(
( fits(medium,pin(N))
<=> fits(medium,pin(N)) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [N: $i] : fits(medium,pin(N))
<=> ! [N: $i] : fits(medium,pin(N)) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [N: $i] : fits(medium,pin(N))
<=> ! [N: $i] : fits(medium,pin(N)) ),
inference(rewrite,[status(thm)],]) ).
tff(77,axiom,
! [N: $i] : fits(medium,pin(N)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fits_2) ).
tff(78,plain,
! [N: $i] : fits(medium,pin(N)),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [N: $i] : fits(medium,pin(N)),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [N: $i] : fits(medium,pin(N)),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
( ~ ! [N: $i] : fits(medium,pin(N))
| fits(medium,pin(n2)) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
fits(medium,pin(n2)),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,plain,
( ( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(medium,on(large,pin(n3)))
| ~ fits(medium,pin(n2))
| ( nextto(on(medium,on(large,pin(n3))),pin(n2)) = nextto(on(large,pin(n3)),on(medium,pin(n2))) ) )
<=> ( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(medium,on(large,pin(n3)))
| ~ fits(medium,pin(n2))
| ( nextto(on(medium,on(large,pin(n3))),pin(n2)) = nextto(on(large,pin(n3)),on(medium,pin(n2))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(medium,on(large,pin(n3)))
| ~ fits(medium,pin(n2))
| ( nextto(on(medium,on(large,pin(n3))),pin(n2)) = nextto(on(large,pin(n3)),on(medium,pin(n2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(medium,on(large,pin(n3)))
| ~ fits(medium,pin(n2))
| ( nextto(on(medium,on(large,pin(n3))),pin(n2)) = nextto(on(large,pin(n3)),on(medium,pin(n2))) ) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
nextto(on(medium,on(large,pin(n3))),pin(n2)) = nextto(on(large,pin(n3)),on(medium,pin(n2))),
inference(unit_resolution,[status(thm)],[85,53,82,73]) ).
tff(87,plain,
nextto(on(large,pin(n3)),on(medium,pin(n2))) = nextto(on(medium,on(large,pin(n3))),pin(n2)),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
nextto(nextto(on(large,pin(n3)),on(medium,pin(n2))),on(small,pin(n1))) = nextto(nextto(on(medium,on(large,pin(n3))),pin(n2)),on(small,pin(n1))),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z) )
| ( nextto(on(large,pin(n3)),nextto(on(medium,pin(n2)),on(small,pin(n1)))) = nextto(nextto(on(large,pin(n3)),on(medium,pin(n2))),on(small,pin(n1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
nextto(on(large,pin(n3)),nextto(on(medium,pin(n2)),on(small,pin(n1)))) = nextto(nextto(on(large,pin(n3)),on(medium,pin(n2))),on(small,pin(n1))),
inference(unit_resolution,[status(thm)],[89,17]) ).
tff(91,plain,
( ~ ! [Y: $i,X: $i] : ( nextto(X,Y) = nextto(Y,X) )
| ( nextto(on(medium,pin(n2)),on(small,pin(n1))) = nextto(on(small,pin(n1)),on(medium,pin(n2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
nextto(on(medium,pin(n2)),on(small,pin(n1))) = nextto(on(small,pin(n1)),on(medium,pin(n2))),
inference(unit_resolution,[status(thm)],[91,7]) ).
tff(93,plain,
nextto(on(small,pin(n1)),on(medium,pin(n2))) = nextto(on(medium,pin(n2)),on(small,pin(n1))),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
( ~ ! [A: $i] : fits(small,on(medium,A))
| fits(small,on(medium,pin(n2))) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
fits(small,on(medium,pin(n2))),
inference(unit_resolution,[status(thm)],[94,41]) ).
tff(96,plain,
( ( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(small,pin(n1))
| ~ fits(small,on(medium,pin(n2)))
| ( nextto(on(small,pin(n1)),on(medium,pin(n2))) = nextto(pin(n1),on(small,on(medium,pin(n2)))) ) )
<=> ( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(small,pin(n1))
| ~ fits(small,on(medium,pin(n2)))
| ( nextto(on(small,pin(n1)),on(medium,pin(n2))) = nextto(pin(n1),on(small,on(medium,pin(n2)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,plain,
( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(small,pin(n1))
| ~ fits(small,on(medium,pin(n2)))
| ( nextto(on(small,pin(n1)),on(medium,pin(n2))) = nextto(pin(n1),on(small,on(medium,pin(n2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(small,pin(n1))
| ~ fits(small,on(medium,pin(n2)))
| ( nextto(on(small,pin(n1)),on(medium,pin(n2))) = nextto(pin(n1),on(small,on(medium,pin(n2)))) ) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
nextto(on(small,pin(n1)),on(medium,pin(n2))) = nextto(pin(n1),on(small,on(medium,pin(n2)))),
inference(unit_resolution,[status(thm)],[98,53,34,95]) ).
tff(100,plain,
nextto(pin(n1),on(small,on(medium,pin(n2)))) = nextto(on(small,pin(n1)),on(medium,pin(n2))),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
nextto(pin(n1),on(small,on(medium,pin(n2)))) = nextto(on(medium,pin(n2)),on(small,pin(n1))),
inference(transitivity,[status(thm)],[100,93]) ).
tff(102,plain,
nextto(on(large,pin(n3)),nextto(pin(n1),on(small,on(medium,pin(n2))))) = nextto(on(large,pin(n3)),nextto(on(medium,pin(n2)),on(small,pin(n1)))),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z) )
| ( nextto(on(large,pin(n3)),nextto(pin(n1),on(small,on(medium,pin(n2))))) = nextto(nextto(on(large,pin(n3)),pin(n1)),on(small,on(medium,pin(n2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
nextto(on(large,pin(n3)),nextto(pin(n1),on(small,on(medium,pin(n2))))) = nextto(nextto(on(large,pin(n3)),pin(n1)),on(small,on(medium,pin(n2)))),
inference(unit_resolution,[status(thm)],[103,17]) ).
tff(105,plain,
nextto(nextto(on(large,pin(n3)),pin(n1)),on(small,on(medium,pin(n2)))) = nextto(on(large,pin(n3)),nextto(pin(n1),on(small,on(medium,pin(n2))))),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
^ [N: $i] :
refl(
( fits(large,pin(N))
<=> fits(large,pin(N)) )),
inference(bind,[status(th)],]) ).
tff(107,plain,
( ! [N: $i] : fits(large,pin(N))
<=> ! [N: $i] : fits(large,pin(N)) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,plain,
( ! [N: $i] : fits(large,pin(N))
<=> ! [N: $i] : fits(large,pin(N)) ),
inference(rewrite,[status(thm)],]) ).
tff(109,axiom,
! [N: $i] : fits(large,pin(N)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fits_3) ).
tff(110,plain,
! [N: $i] : fits(large,pin(N)),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
! [N: $i] : fits(large,pin(N)),
inference(skolemize,[status(sab)],[110]) ).
tff(112,plain,
! [N: $i] : fits(large,pin(N)),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
( ~ ! [N: $i] : fits(large,pin(N))
| fits(large,pin(n3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
fits(large,pin(n3)),
inference(unit_resolution,[status(thm)],[113,112]) ).
tff(115,plain,
( ~ ! [N: $i] : fits(large,pin(N))
| fits(large,pin(n1)) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
fits(large,pin(n1)),
inference(unit_resolution,[status(thm)],[115,112]) ).
tff(117,plain,
( ( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(large,pin(n3))
| ~ fits(large,pin(n1))
| ( nextto(on(large,pin(n3)),pin(n1)) = nextto(pin(n3),on(large,pin(n1))) ) )
<=> ( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(large,pin(n3))
| ~ fits(large,pin(n1))
| ( nextto(on(large,pin(n3)),pin(n1)) = nextto(pin(n3),on(large,pin(n1))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(large,pin(n3))
| ~ fits(large,pin(n1))
| ( nextto(on(large,pin(n3)),pin(n1)) = nextto(pin(n3),on(large,pin(n1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(119,plain,
( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(large,pin(n3))
| ~ fits(large,pin(n1))
| ( nextto(on(large,pin(n3)),pin(n1)) = nextto(pin(n3),on(large,pin(n1))) ) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
nextto(on(large,pin(n3)),pin(n1)) = nextto(pin(n3),on(large,pin(n1))),
inference(unit_resolution,[status(thm)],[119,53,116,114]) ).
tff(121,plain,
nextto(pin(n3),on(large,pin(n1))) = nextto(on(large,pin(n3)),pin(n1)),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
nextto(nextto(pin(n3),on(large,pin(n1))),on(small,on(medium,pin(n2)))) = nextto(nextto(on(large,pin(n3)),pin(n1)),on(small,on(medium,pin(n2)))),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
( ~ ! [Y: $i,X: $i] : ( nextto(X,Y) = nextto(Y,X) )
| ( nextto(on(small,on(medium,pin(n2))),nextto(pin(n3),on(large,pin(n1)))) = nextto(nextto(pin(n3),on(large,pin(n1))),on(small,on(medium,pin(n2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(124,plain,
nextto(on(small,on(medium,pin(n2))),nextto(pin(n3),on(large,pin(n1)))) = nextto(nextto(pin(n3),on(large,pin(n1))),on(small,on(medium,pin(n2)))),
inference(unit_resolution,[status(thm)],[123,7]) ).
tff(125,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z) )
| ( nextto(on(small,on(medium,pin(n2))),nextto(pin(n3),on(large,pin(n1)))) = nextto(nextto(on(small,on(medium,pin(n2))),pin(n3)),on(large,pin(n1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(126,plain,
nextto(on(small,on(medium,pin(n2))),nextto(pin(n3),on(large,pin(n1)))) = nextto(nextto(on(small,on(medium,pin(n2))),pin(n3)),on(large,pin(n1))),
inference(unit_resolution,[status(thm)],[125,17]) ).
tff(127,plain,
nextto(nextto(on(small,on(medium,pin(n2))),pin(n3)),on(large,pin(n1))) = nextto(on(small,on(medium,pin(n2))),nextto(pin(n3),on(large,pin(n1)))),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
( ~ ! [N: $i] : fits(small,pin(N))
| fits(small,pin(n3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
fits(small,pin(n3)),
inference(unit_resolution,[status(thm)],[128,32]) ).
tff(130,plain,
( ( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(small,pin(n3))
| ~ fits(small,on(medium,pin(n2)))
| ( nextto(on(small,on(medium,pin(n2))),pin(n3)) = nextto(on(medium,pin(n2)),on(small,pin(n3))) ) )
<=> ( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(small,pin(n3))
| ~ fits(small,on(medium,pin(n2)))
| ( nextto(on(small,on(medium,pin(n2))),pin(n3)) = nextto(on(medium,pin(n2)),on(small,pin(n3))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(131,plain,
( ( ~ fits(small,on(medium,pin(n2)))
| ~ fits(small,pin(n3))
| ( nextto(on(small,on(medium,pin(n2))),pin(n3)) = nextto(on(medium,pin(n2)),on(small,pin(n3))) ) )
<=> ( ~ fits(small,pin(n3))
| ~ fits(small,on(medium,pin(n2)))
| ( nextto(on(small,on(medium,pin(n2))),pin(n3)) = nextto(on(medium,pin(n2)),on(small,pin(n3))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(132,plain,
( ( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(small,on(medium,pin(n2)))
| ~ fits(small,pin(n3))
| ( nextto(on(small,on(medium,pin(n2))),pin(n3)) = nextto(on(medium,pin(n2)),on(small,pin(n3))) ) )
<=> ( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(small,pin(n3))
| ~ fits(small,on(medium,pin(n2)))
| ( nextto(on(small,on(medium,pin(n2))),pin(n3)) = nextto(on(medium,pin(n2)),on(small,pin(n3))) ) ) ),
inference(monotonicity,[status(thm)],[131]) ).
tff(133,plain,
( ( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(small,on(medium,pin(n2)))
| ~ fits(small,pin(n3))
| ( nextto(on(small,on(medium,pin(n2))),pin(n3)) = nextto(on(medium,pin(n2)),on(small,pin(n3))) ) )
<=> ( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(small,pin(n3))
| ~ fits(small,on(medium,pin(n2)))
| ( nextto(on(small,on(medium,pin(n2))),pin(n3)) = nextto(on(medium,pin(n2)),on(small,pin(n3))) ) ) ),
inference(transitivity,[status(thm)],[132,130]) ).
tff(134,plain,
( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(small,on(medium,pin(n2)))
| ~ fits(small,pin(n3))
| ( nextto(on(small,on(medium,pin(n2))),pin(n3)) = nextto(on(medium,pin(n2)),on(small,pin(n3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(135,plain,
( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(small,pin(n3))
| ~ fits(small,on(medium,pin(n2)))
| ( nextto(on(small,on(medium,pin(n2))),pin(n3)) = nextto(on(medium,pin(n2)),on(small,pin(n3))) ) ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
nextto(on(small,on(medium,pin(n2))),pin(n3)) = nextto(on(medium,pin(n2)),on(small,pin(n3))),
inference(unit_resolution,[status(thm)],[135,53,129,95]) ).
tff(137,plain,
nextto(on(medium,pin(n2)),on(small,pin(n3))) = nextto(on(small,on(medium,pin(n2))),pin(n3)),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
nextto(nextto(on(medium,pin(n2)),on(small,pin(n3))),on(large,pin(n1))) = nextto(nextto(on(small,on(medium,pin(n2))),pin(n3)),on(large,pin(n1))),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
( ~ ! [Y: $i,X: $i] : ( nextto(X,Y) = nextto(Y,X) )
| ( nextto(on(large,pin(n1)),nextto(on(medium,pin(n2)),on(small,pin(n3)))) = nextto(nextto(on(medium,pin(n2)),on(small,pin(n3))),on(large,pin(n1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
nextto(on(large,pin(n1)),nextto(on(medium,pin(n2)),on(small,pin(n3)))) = nextto(nextto(on(medium,pin(n2)),on(small,pin(n3))),on(large,pin(n1))),
inference(unit_resolution,[status(thm)],[139,7]) ).
tff(141,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z) )
| ( nextto(on(large,pin(n1)),nextto(on(medium,pin(n2)),on(small,pin(n3)))) = nextto(nextto(on(large,pin(n1)),on(medium,pin(n2))),on(small,pin(n3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(142,plain,
nextto(on(large,pin(n1)),nextto(on(medium,pin(n2)),on(small,pin(n3)))) = nextto(nextto(on(large,pin(n1)),on(medium,pin(n2))),on(small,pin(n3))),
inference(unit_resolution,[status(thm)],[141,17]) ).
tff(143,plain,
nextto(nextto(on(large,pin(n1)),on(medium,pin(n2))),on(small,pin(n3))) = nextto(on(large,pin(n1)),nextto(on(medium,pin(n2)),on(small,pin(n3)))),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
( ~ ! [A: $i] : fits(medium,on(large,A))
| fits(medium,on(large,pin(n1))) ),
inference(quant_inst,[status(thm)],]) ).
tff(145,plain,
fits(medium,on(large,pin(n1))),
inference(unit_resolution,[status(thm)],[144,71]) ).
tff(146,plain,
( ( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(medium,on(large,pin(n1)))
| ~ fits(medium,pin(n2))
| ( nextto(on(medium,on(large,pin(n1))),pin(n2)) = nextto(on(large,pin(n1)),on(medium,pin(n2))) ) )
<=> ( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(medium,on(large,pin(n1)))
| ~ fits(medium,pin(n2))
| ( nextto(on(medium,on(large,pin(n1))),pin(n2)) = nextto(on(large,pin(n1)),on(medium,pin(n2))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(147,plain,
( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(medium,on(large,pin(n1)))
| ~ fits(medium,pin(n2))
| ( nextto(on(medium,on(large,pin(n1))),pin(n2)) = nextto(on(large,pin(n1)),on(medium,pin(n2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(148,plain,
( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(medium,on(large,pin(n1)))
| ~ fits(medium,pin(n2))
| ( nextto(on(medium,on(large,pin(n1))),pin(n2)) = nextto(on(large,pin(n1)),on(medium,pin(n2))) ) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
nextto(on(medium,on(large,pin(n1))),pin(n2)) = nextto(on(large,pin(n1)),on(medium,pin(n2))),
inference(unit_resolution,[status(thm)],[148,53,82,145]) ).
tff(150,plain,
nextto(nextto(on(medium,on(large,pin(n1))),pin(n2)),on(small,pin(n3))) = nextto(nextto(on(large,pin(n1)),on(medium,pin(n2))),on(small,pin(n3))),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
( ~ ! [Y: $i,X: $i] : ( nextto(X,Y) = nextto(Y,X) )
| ( nextto(on(small,pin(n3)),nextto(on(medium,on(large,pin(n1))),pin(n2))) = nextto(nextto(on(medium,on(large,pin(n1))),pin(n2)),on(small,pin(n3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(152,plain,
nextto(on(small,pin(n3)),nextto(on(medium,on(large,pin(n1))),pin(n2))) = nextto(nextto(on(medium,on(large,pin(n1))),pin(n2)),on(small,pin(n3))),
inference(unit_resolution,[status(thm)],[151,7]) ).
tff(153,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z) )
| ( nextto(on(small,pin(n3)),nextto(on(medium,on(large,pin(n1))),pin(n2))) = nextto(nextto(on(small,pin(n3)),on(medium,on(large,pin(n1)))),pin(n2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(154,plain,
nextto(on(small,pin(n3)),nextto(on(medium,on(large,pin(n1))),pin(n2))) = nextto(nextto(on(small,pin(n3)),on(medium,on(large,pin(n1)))),pin(n2)),
inference(unit_resolution,[status(thm)],[153,17]) ).
tff(155,plain,
nextto(nextto(on(small,pin(n3)),on(medium,on(large,pin(n1)))),pin(n2)) = nextto(on(small,pin(n3)),nextto(on(medium,on(large,pin(n1))),pin(n2))),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
( ~ ! [A: $i] : fits(small,on(medium,A))
| fits(small,on(medium,on(large,pin(n1)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(157,plain,
fits(small,on(medium,on(large,pin(n1)))),
inference(unit_resolution,[status(thm)],[156,41]) ).
tff(158,plain,
( ( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(small,pin(n3))
| ~ fits(small,on(medium,on(large,pin(n1))))
| ( nextto(on(small,pin(n3)),on(medium,on(large,pin(n1)))) = nextto(pin(n3),on(small,on(medium,on(large,pin(n1))))) ) )
<=> ( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(small,pin(n3))
| ~ fits(small,on(medium,on(large,pin(n1))))
| ( nextto(on(small,pin(n3)),on(medium,on(large,pin(n1)))) = nextto(pin(n3),on(small,on(medium,on(large,pin(n1))))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(159,plain,
( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(small,pin(n3))
| ~ fits(small,on(medium,on(large,pin(n1))))
| ( nextto(on(small,pin(n3)),on(medium,on(large,pin(n1)))) = nextto(pin(n3),on(small,on(medium,on(large,pin(n1))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(160,plain,
( ~ ! [B: $i,A: $i,X: $i] :
( ~ fits(X,A)
| ~ fits(X,B)
| ( nextto(on(X,A),B) = nextto(A,on(X,B)) ) )
| ~ fits(small,pin(n3))
| ~ fits(small,on(medium,on(large,pin(n1))))
| ( nextto(on(small,pin(n3)),on(medium,on(large,pin(n1)))) = nextto(pin(n3),on(small,on(medium,on(large,pin(n1))))) ) ),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
nextto(on(small,pin(n3)),on(medium,on(large,pin(n1)))) = nextto(pin(n3),on(small,on(medium,on(large,pin(n1))))),
inference(unit_resolution,[status(thm)],[160,53,157,129]) ).
tff(162,plain,
nextto(pin(n3),on(small,on(medium,on(large,pin(n1))))) = nextto(on(small,pin(n3)),on(medium,on(large,pin(n1)))),
inference(symmetry,[status(thm)],[161]) ).
tff(163,plain,
nextto(nextto(pin(n3),on(small,on(medium,on(large,pin(n1))))),pin(n2)) = nextto(nextto(on(small,pin(n3)),on(medium,on(large,pin(n1)))),pin(n2)),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z) )
| ( nextto(pin(n3),nextto(on(small,on(medium,on(large,pin(n1)))),pin(n2))) = nextto(nextto(pin(n3),on(small,on(medium,on(large,pin(n1))))),pin(n2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(165,plain,
nextto(pin(n3),nextto(on(small,on(medium,on(large,pin(n1)))),pin(n2))) = nextto(nextto(pin(n3),on(small,on(medium,on(large,pin(n1))))),pin(n2)),
inference(unit_resolution,[status(thm)],[164,17]) ).
tff(166,plain,
( ~ ! [Y: $i,X: $i] : ( nextto(X,Y) = nextto(Y,X) )
| ( nextto(nextto(on(small,on(medium,on(large,pin(n1)))),pin(n2)),pin(n3)) = nextto(pin(n3),nextto(on(small,on(medium,on(large,pin(n1)))),pin(n2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(167,plain,
nextto(nextto(on(small,on(medium,on(large,pin(n1)))),pin(n2)),pin(n3)) = nextto(pin(n3),nextto(on(small,on(medium,on(large,pin(n1)))),pin(n2))),
inference(unit_resolution,[status(thm)],[166,7]) ).
tff(168,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z) )
| ( nextto(on(small,on(medium,on(large,pin(n1)))),nextto(pin(n2),pin(n3))) = nextto(nextto(on(small,on(medium,on(large,pin(n1)))),pin(n2)),pin(n3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(169,plain,
nextto(on(small,on(medium,on(large,pin(n1)))),nextto(pin(n2),pin(n3))) = nextto(nextto(on(small,on(medium,on(large,pin(n1)))),pin(n2)),pin(n3)),
inference(unit_resolution,[status(thm)],[168,17]) ).
tff(170,plain,
nextto(on(small,on(medium,on(large,pin(n1)))),nextto(pin(n2),pin(n3))) = nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3)))))),
inference(transitivity,[status(thm)],[169,167,165,163,155,152,150,143,140,138,127,124,122,105,102,90,88,64,61,59,22,19,10]) ).
tff(171,plain,
( state(nextto(on(small,on(medium,on(large,pin(n1)))),nextto(pin(n2),pin(n3))))
<=> state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))) ),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
( state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3)))))))
<=> state(nextto(on(small,on(medium,on(large,pin(n1)))),nextto(pin(n2),pin(n3)))) ),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
( ~ state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3)))))))
<=> ~ state(nextto(on(small,on(medium,on(large,pin(n1)))),nextto(pin(n2),pin(n3)))) ),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
( ~ state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3)))))))
<=> ~ state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))) ),
inference(rewrite,[status(thm)],]) ).
tff(175,axiom,
~ state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',final_state) ).
tff(176,plain,
~ state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))),
inference(modus_ponens,[status(thm)],[175,174]) ).
tff(177,plain,
~ state(nextto(on(small,on(medium,on(large,pin(n1)))),nextto(pin(n2),pin(n3)))),
inference(modus_ponens,[status(thm)],[176,173]) ).
tff(178,plain,
( state(nextto(on(small,on(medium,on(large,pin(n1)))),nextto(pin(n2),pin(n3))))
<=> state(nextto(on(small,on(medium,on(large,pin(n1)))),nextto(pin(n2),pin(n3)))) ),
inference(rewrite,[status(thm)],]) ).
tff(179,axiom,
state(nextto(on(small,on(medium,on(large,pin(n1)))),nextto(pin(n2),pin(n3)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_state) ).
tff(180,plain,
state(nextto(on(small,on(medium,on(large,pin(n1)))),nextto(pin(n2),pin(n3)))),
inference(modus_ponens,[status(thm)],[179,178]) ).
tff(181,plain,
$false,
inference(unit_resolution,[status(thm)],[180,177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ056-1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Sep 2 18:50:08 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.
% 0.14/0.41 % SZS status Unsatisfiable
% 0.14/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------