TSTP Solution File: NUN133-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUN133-1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 13:28:06 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 56
% Syntax : Number of formulae : 141 ( 97 unt; 6 typ; 0 def)
% Number of atoms : 193 ( 182 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 68 ( 20 ~; 16 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 5 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 225 ( 204 !; 0 ?; 225 :)
% Comments :
%------------------------------------------------------------------------------
tff(cubes_type,type,
cubes: $i > $i ).
tff(s_type,type,
s: $i > $i ).
tff(a_type,type,
a: $i ).
tff(times_type,type,
times: ( $i * $i ) > $i ).
tff(sum_type,type,
sum: $i > $i ).
tff(tptp_fun_____type,type,
tptp_fun____: ( $i * $i ) > $i ).
tff(1,plain,
^ [N: $i] :
refl(
( ( cubes(s(N)) = tptp_fun____(times(s(N),times(s(N),s(N))),cubes(N)) )
<=> ( cubes(s(N)) = tptp_fun____(times(s(N),times(s(N),s(N))),cubes(N)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [N: $i] : ( cubes(s(N)) = tptp_fun____(times(s(N),times(s(N),s(N))),cubes(N)) )
<=> ! [N: $i] : ( cubes(s(N)) = tptp_fun____(times(s(N),times(s(N),s(N))),cubes(N)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [N: $i] : ( cubes(s(N)) = tptp_fun____(times(s(N),times(s(N),s(N))),cubes(N)) )
<=> ! [N: $i] : ( cubes(s(N)) = tptp_fun____(times(s(N),times(s(N),s(N))),cubes(N)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [N: $i] : ( cubes(s(N)) = tptp_fun____(times(s(N),times(s(N),s(N))),cubes(N)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cubes_s) ).
tff(5,plain,
! [N: $i] : ( cubes(s(N)) = tptp_fun____(times(s(N),times(s(N),s(N))),cubes(N)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [N: $i] : ( cubes(s(N)) = tptp_fun____(times(s(N),times(s(N),s(N))),cubes(N)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [N: $i] : ( cubes(s(N)) = tptp_fun____(times(s(N),times(s(N),s(N))),cubes(N)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [N: $i] : ( cubes(s(N)) = tptp_fun____(times(s(N),times(s(N),s(N))),cubes(N)) )
| ( cubes(s(a)) = tptp_fun____(times(s(a),times(s(a),s(a))),cubes(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
cubes(s(a)) = tptp_fun____(times(s(a),times(s(a),s(a))),cubes(a)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
tptp_fun____(times(s(a),times(s(a),s(a))),cubes(a)) = cubes(s(a)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [Y: $i,X: $i] :
refl(
( ( tptp_fun____(X,Y) = tptp_fun____(Y,X) )
<=> ( tptp_fun____(X,Y) = tptp_fun____(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( tptp_fun____(X,Y) = tptp_fun____(Y,X) )
<=> ! [Y: $i,X: $i] : ( tptp_fun____(X,Y) = tptp_fun____(Y,X) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [Y: $i,X: $i] : ( tptp_fun____(X,Y) = tptp_fun____(Y,X) )
<=> ! [Y: $i,X: $i] : ( tptp_fun____(X,Y) = tptp_fun____(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [Y: $i,X: $i] : ( tptp_fun____(X,Y) = tptp_fun____(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_comm) ).
tff(15,plain,
! [Y: $i,X: $i] : ( tptp_fun____(X,Y) = tptp_fun____(Y,X) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( tptp_fun____(X,Y) = tptp_fun____(Y,X) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Y: $i,X: $i] : ( tptp_fun____(X,Y) = tptp_fun____(Y,X) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [Y: $i,X: $i] : ( tptp_fun____(X,Y) = tptp_fun____(Y,X) )
| ( tptp_fun____(times(s(a),times(s(a),s(a))),cubes(a)) = tptp_fun____(cubes(a),times(s(a),times(s(a),s(a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
tptp_fun____(times(s(a),times(s(a),s(a))),cubes(a)) = tptp_fun____(cubes(a),times(s(a),times(s(a),s(a)))),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
tptp_fun____(cubes(a),times(s(a),times(s(a),s(a)))) = tptp_fun____(times(s(a),times(s(a),s(a))),cubes(a)),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( times(tptp_fun____(X,Y),Z) = tptp_fun____(times(X,Z),times(Y,Z)) )
<=> ( times(tptp_fun____(X,Y),Z) = tptp_fun____(times(X,Z),times(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [Z: $i,Y: $i,X: $i] : ( times(tptp_fun____(X,Y),Z) = tptp_fun____(times(X,Z),times(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( times(tptp_fun____(X,Y),Z) = tptp_fun____(times(X,Z),times(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Z: $i,Y: $i,X: $i] : ( times(tptp_fun____(X,Y),Z) = tptp_fun____(times(X,Z),times(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( times(tptp_fun____(X,Y),Z) = tptp_fun____(times(X,Z),times(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [Z: $i,Y: $i,X: $i] : ( times(tptp_fun____(X,Y),Z) = tptp_fun____(times(X,Z),times(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distr_001) ).
tff(25,plain,
! [Z: $i,Y: $i,X: $i] : ( times(tptp_fun____(X,Y),Z) = tptp_fun____(times(X,Z),times(Y,Z)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] : ( times(tptp_fun____(X,Y),Z) = tptp_fun____(times(X,Z),times(Y,Z)) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Z: $i,Y: $i,X: $i] : ( times(tptp_fun____(X,Y),Z) = tptp_fun____(times(X,Z),times(Y,Z)) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( times(tptp_fun____(X,Y),Z) = tptp_fun____(times(X,Z),times(Y,Z)) )
| ( times(tptp_fun____(s(a),sum(a)),s(a)) = tptp_fun____(times(s(a),s(a)),times(sum(a),s(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
times(tptp_fun____(s(a),sum(a)),s(a)) = tptp_fun____(times(s(a),s(a)),times(sum(a),s(a))),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
tptp_fun____(times(s(a),s(a)),times(sum(a),s(a))) = times(tptp_fun____(s(a),sum(a)),s(a)),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
tptp_fun____(times(sum(a),s(a)),tptp_fun____(times(s(a),s(a)),times(sum(a),s(a)))) = tptp_fun____(times(sum(a),s(a)),times(tptp_fun____(s(a),sum(a)),s(a))),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
tptp_fun____(times(sum(a),s(a)),times(tptp_fun____(s(a),sum(a)),s(a))) = tptp_fun____(times(sum(a),s(a)),tptp_fun____(times(s(a),s(a)),times(sum(a),s(a)))),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( times(tptp_fun____(X,Y),Z) = tptp_fun____(times(X,Z),times(Y,Z)) )
| ( times(tptp_fun____(sum(a),tptp_fun____(s(a),sum(a))),s(a)) = tptp_fun____(times(sum(a),s(a)),times(tptp_fun____(s(a),sum(a)),s(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
times(tptp_fun____(sum(a),tptp_fun____(s(a),sum(a))),s(a)) = tptp_fun____(times(sum(a),s(a)),times(tptp_fun____(s(a),sum(a)),s(a))),
inference(unit_resolution,[status(thm)],[33,27]) ).
tff(35,plain,
^ [Y: $i,X: $i] :
refl(
( ( times(s(X),Y) = tptp_fun____(Y,times(X,Y)) )
<=> ( times(s(X),Y) = tptp_fun____(Y,times(X,Y)) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [Y: $i,X: $i] : ( times(s(X),Y) = tptp_fun____(Y,times(X,Y)) )
<=> ! [Y: $i,X: $i] : ( times(s(X),Y) = tptp_fun____(Y,times(X,Y)) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [Y: $i,X: $i] : ( times(s(X),Y) = tptp_fun____(Y,times(X,Y)) )
<=> ! [Y: $i,X: $i] : ( times(s(X),Y) = tptp_fun____(Y,times(X,Y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
! [Y: $i,X: $i] : ( times(s(X),Y) = tptp_fun____(Y,times(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_s) ).
tff(39,plain,
! [Y: $i,X: $i] : ( times(s(X),Y) = tptp_fun____(Y,times(X,Y)) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [Y: $i,X: $i] : ( times(s(X),Y) = tptp_fun____(Y,times(X,Y)) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [Y: $i,X: $i] : ( times(s(X),Y) = tptp_fun____(Y,times(X,Y)) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ~ ! [Y: $i,X: $i] : ( times(s(X),Y) = tptp_fun____(Y,times(X,Y)) )
| ( times(s(a),s(a)) = tptp_fun____(s(a),times(a,s(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
times(s(a),s(a)) = tptp_fun____(s(a),times(a,s(a))),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
tptp_fun____(s(a),times(a,s(a))) = times(s(a),s(a)),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
^ [N: $i] :
refl(
( ( tptp_fun____(sum(N),sum(N)) = times(N,s(N)) )
<=> ( tptp_fun____(sum(N),sum(N)) = times(N,s(N)) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [N: $i] : ( tptp_fun____(sum(N),sum(N)) = times(N,s(N)) )
<=> ! [N: $i] : ( tptp_fun____(sum(N),sum(N)) = times(N,s(N)) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [N: $i] : ( tptp_fun____(sum(N),sum(N)) = times(N,s(N)) )
<=> ! [N: $i] : ( tptp_fun____(sum(N),sum(N)) = times(N,s(N)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
! [N: $i] : ( tptp_fun____(sum(N),sum(N)) = times(N,s(N)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_sum) ).
tff(49,plain,
! [N: $i] : ( tptp_fun____(sum(N),sum(N)) = times(N,s(N)) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [N: $i] : ( tptp_fun____(sum(N),sum(N)) = times(N,s(N)) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [N: $i] : ( tptp_fun____(sum(N),sum(N)) = times(N,s(N)) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ~ ! [N: $i] : ( tptp_fun____(sum(N),sum(N)) = times(N,s(N)) )
| ( tptp_fun____(sum(a),sum(a)) = times(a,s(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
tptp_fun____(sum(a),sum(a)) = times(a,s(a)),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
tptp_fun____(s(a),tptp_fun____(sum(a),sum(a))) = tptp_fun____(s(a),times(a,s(a))),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( tptp_fun____(X,tptp_fun____(Y,Z)) = tptp_fun____(tptp_fun____(X,Y),Z) )
<=> ( tptp_fun____(X,tptp_fun____(Y,Z)) = tptp_fun____(tptp_fun____(X,Y),Z) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [Z: $i,Y: $i,X: $i] : ( tptp_fun____(X,tptp_fun____(Y,Z)) = tptp_fun____(tptp_fun____(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( tptp_fun____(X,tptp_fun____(Y,Z)) = tptp_fun____(tptp_fun____(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [Z: $i,Y: $i,X: $i] : ( tptp_fun____(X,tptp_fun____(Y,Z)) = tptp_fun____(tptp_fun____(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( tptp_fun____(X,tptp_fun____(Y,Z)) = tptp_fun____(tptp_fun____(X,Y),Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,axiom,
! [Z: $i,Y: $i,X: $i] : ( tptp_fun____(X,tptp_fun____(Y,Z)) = tptp_fun____(tptp_fun____(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_assoc) ).
tff(59,plain,
! [Z: $i,Y: $i,X: $i] : ( tptp_fun____(X,tptp_fun____(Y,Z)) = tptp_fun____(tptp_fun____(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [Z: $i,Y: $i,X: $i] : ( tptp_fun____(X,tptp_fun____(Y,Z)) = tptp_fun____(tptp_fun____(X,Y),Z) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [Z: $i,Y: $i,X: $i] : ( tptp_fun____(X,tptp_fun____(Y,Z)) = tptp_fun____(tptp_fun____(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( tptp_fun____(X,tptp_fun____(Y,Z)) = tptp_fun____(tptp_fun____(X,Y),Z) )
| ( tptp_fun____(s(a),tptp_fun____(sum(a),sum(a))) = tptp_fun____(tptp_fun____(s(a),sum(a)),sum(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
tptp_fun____(s(a),tptp_fun____(sum(a),sum(a))) = tptp_fun____(tptp_fun____(s(a),sum(a)),sum(a)),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
tptp_fun____(tptp_fun____(s(a),sum(a)),sum(a)) = tptp_fun____(s(a),tptp_fun____(sum(a),sum(a))),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( ~ ! [Y: $i,X: $i] : ( tptp_fun____(X,Y) = tptp_fun____(Y,X) )
| ( tptp_fun____(sum(a),tptp_fun____(s(a),sum(a))) = tptp_fun____(tptp_fun____(s(a),sum(a)),sum(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
tptp_fun____(sum(a),tptp_fun____(s(a),sum(a))) = tptp_fun____(tptp_fun____(s(a),sum(a)),sum(a)),
inference(unit_resolution,[status(thm)],[65,17]) ).
tff(67,plain,
tptp_fun____(sum(a),tptp_fun____(s(a),sum(a))) = times(s(a),s(a)),
inference(transitivity,[status(thm)],[66,64,54,44]) ).
tff(68,plain,
times(tptp_fun____(sum(a),tptp_fun____(s(a),sum(a))),s(a)) = times(times(s(a),s(a)),s(a)),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
times(times(s(a),s(a)),s(a)) = times(tptp_fun____(sum(a),tptp_fun____(s(a),sum(a))),s(a)),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( times(X,times(Y,Z)) = times(times(X,Y),Z) )
<=> ( times(X,times(Y,Z)) = times(times(X,Y),Z) ) )),
inference(bind,[status(th)],]) ).
tff(71,plain,
( ! [Z: $i,Y: $i,X: $i] : ( times(X,times(Y,Z)) = times(times(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( times(X,times(Y,Z)) = times(times(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [Z: $i,Y: $i,X: $i] : ( times(X,times(Y,Z)) = times(times(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( times(X,times(Y,Z)) = times(times(X,Y),Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,axiom,
! [Z: $i,Y: $i,X: $i] : ( times(X,times(Y,Z)) = times(times(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_assoc) ).
tff(74,plain,
! [Z: $i,Y: $i,X: $i] : ( times(X,times(Y,Z)) = times(times(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [Z: $i,Y: $i,X: $i] : ( times(X,times(Y,Z)) = times(times(X,Y),Z) ),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [Z: $i,Y: $i,X: $i] : ( times(X,times(Y,Z)) = times(times(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( times(X,times(Y,Z)) = times(times(X,Y),Z) )
| ( times(s(a),times(s(a),s(a))) = times(times(s(a),s(a)),s(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
times(s(a),times(s(a),s(a))) = times(times(s(a),s(a)),s(a)),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
times(s(a),times(s(a),s(a))) = tptp_fun____(times(sum(a),s(a)),tptp_fun____(times(s(a),s(a)),times(sum(a),s(a)))),
inference(transitivity,[status(thm)],[78,69,34,32]) ).
tff(80,plain,
tptp_fun____(cubes(a),times(s(a),times(s(a),s(a)))) = tptp_fun____(cubes(a),tptp_fun____(times(sum(a),s(a)),tptp_fun____(times(s(a),s(a)),times(sum(a),s(a))))),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
tptp_fun____(cubes(a),tptp_fun____(times(sum(a),s(a)),tptp_fun____(times(s(a),s(a)),times(sum(a),s(a))))) = tptp_fun____(cubes(a),times(s(a),times(s(a),s(a)))),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( tptp_fun____(X,tptp_fun____(Y,Z)) = tptp_fun____(tptp_fun____(X,Y),Z) )
| ( tptp_fun____(cubes(a),tptp_fun____(times(sum(a),s(a)),tptp_fun____(times(s(a),s(a)),times(sum(a),s(a))))) = tptp_fun____(tptp_fun____(cubes(a),times(sum(a),s(a))),tptp_fun____(times(s(a),s(a)),times(sum(a),s(a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
tptp_fun____(cubes(a),tptp_fun____(times(sum(a),s(a)),tptp_fun____(times(s(a),s(a)),times(sum(a),s(a))))) = tptp_fun____(tptp_fun____(cubes(a),times(sum(a),s(a))),tptp_fun____(times(s(a),s(a)),times(sum(a),s(a)))),
inference(unit_resolution,[status(thm)],[82,61]) ).
tff(84,plain,
tptp_fun____(tptp_fun____(cubes(a),times(sum(a),s(a))),tptp_fun____(times(s(a),s(a)),times(sum(a),s(a)))) = tptp_fun____(cubes(a),tptp_fun____(times(sum(a),s(a)),tptp_fun____(times(s(a),s(a)),times(sum(a),s(a))))),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
^ [Y: $i,X: $i] :
refl(
( ( times(X,Y) = times(Y,X) )
<=> ( times(X,Y) = times(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [Y: $i,X: $i] : ( times(X,Y) = times(Y,X) )
<=> ! [Y: $i,X: $i] : ( times(X,Y) = times(Y,X) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
( ! [Y: $i,X: $i] : ( times(X,Y) = times(Y,X) )
<=> ! [Y: $i,X: $i] : ( times(X,Y) = times(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,axiom,
! [Y: $i,X: $i] : ( times(X,Y) = times(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_comm) ).
tff(89,plain,
! [Y: $i,X: $i] : ( times(X,Y) = times(Y,X) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [Y: $i,X: $i] : ( times(X,Y) = times(Y,X) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [Y: $i,X: $i] : ( times(X,Y) = times(Y,X) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
( ~ ! [Y: $i,X: $i] : ( times(X,Y) = times(Y,X) )
| ( times(tptp_fun____(s(a),sum(a)),sum(a)) = times(sum(a),tptp_fun____(s(a),sum(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
times(tptp_fun____(s(a),sum(a)),sum(a)) = times(sum(a),tptp_fun____(s(a),sum(a))),
inference(unit_resolution,[status(thm)],[92,91]) ).
tff(94,plain,
times(sum(a),tptp_fun____(s(a),sum(a))) = times(tptp_fun____(s(a),sum(a)),sum(a)),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
( ~ ! [Y: $i,X: $i] : ( tptp_fun____(X,Y) = tptp_fun____(Y,X) )
| ( tptp_fun____(s(a),sum(a)) = tptp_fun____(sum(a),s(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
tptp_fun____(s(a),sum(a)) = tptp_fun____(sum(a),s(a)),
inference(unit_resolution,[status(thm)],[95,17]) ).
tff(97,plain,
tptp_fun____(sum(a),s(a)) = tptp_fun____(s(a),sum(a)),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
times(sum(a),tptp_fun____(sum(a),s(a))) = times(sum(a),tptp_fun____(s(a),sum(a))),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( times(X,tptp_fun____(Y,Z)) = tptp_fun____(times(X,Y),times(X,Z)) )
<=> ( times(X,tptp_fun____(Y,Z)) = tptp_fun____(times(X,Y),times(X,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [Z: $i,Y: $i,X: $i] : ( times(X,tptp_fun____(Y,Z)) = tptp_fun____(times(X,Y),times(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( times(X,tptp_fun____(Y,Z)) = tptp_fun____(times(X,Y),times(X,Z)) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
( ! [Z: $i,Y: $i,X: $i] : ( times(X,tptp_fun____(Y,Z)) = tptp_fun____(times(X,Y),times(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( times(X,tptp_fun____(Y,Z)) = tptp_fun____(times(X,Y),times(X,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,axiom,
! [Z: $i,Y: $i,X: $i] : ( times(X,tptp_fun____(Y,Z)) = tptp_fun____(times(X,Y),times(X,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distr) ).
tff(103,plain,
! [Z: $i,Y: $i,X: $i] : ( times(X,tptp_fun____(Y,Z)) = tptp_fun____(times(X,Y),times(X,Z)) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
! [Z: $i,Y: $i,X: $i] : ( times(X,tptp_fun____(Y,Z)) = tptp_fun____(times(X,Y),times(X,Z)) ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [Z: $i,Y: $i,X: $i] : ( times(X,tptp_fun____(Y,Z)) = tptp_fun____(times(X,Y),times(X,Z)) ),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( times(X,tptp_fun____(Y,Z)) = tptp_fun____(times(X,Y),times(X,Z)) )
| ( times(sum(a),tptp_fun____(sum(a),s(a))) = tptp_fun____(times(sum(a),sum(a)),times(sum(a),s(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
times(sum(a),tptp_fun____(sum(a),s(a))) = tptp_fun____(times(sum(a),sum(a)),times(sum(a),s(a))),
inference(unit_resolution,[status(thm)],[106,105]) ).
tff(108,plain,
tptp_fun____(times(sum(a),sum(a)),times(sum(a),s(a))) = times(sum(a),tptp_fun____(sum(a),s(a))),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
( ( times(sum(a),sum(a)) = cubes(a) )
<=> ( times(sum(a),sum(a)) = cubes(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,axiom,
times(sum(a),sum(a)) = cubes(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction_hypothesis) ).
tff(111,plain,
times(sum(a),sum(a)) = cubes(a),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
cubes(a) = times(sum(a),sum(a)),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
tptp_fun____(cubes(a),times(sum(a),s(a))) = tptp_fun____(times(sum(a),sum(a)),times(sum(a),s(a))),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
tptp_fun____(cubes(a),times(sum(a),s(a))) = times(tptp_fun____(s(a),sum(a)),sum(a)),
inference(transitivity,[status(thm)],[113,108,98,94]) ).
tff(115,plain,
tptp_fun____(tptp_fun____(cubes(a),times(sum(a),s(a))),tptp_fun____(times(s(a),s(a)),times(sum(a),s(a)))) = tptp_fun____(times(tptp_fun____(s(a),sum(a)),sum(a)),times(tptp_fun____(s(a),sum(a)),s(a))),
inference(monotonicity,[status(thm)],[114,30]) ).
tff(116,plain,
tptp_fun____(times(tptp_fun____(s(a),sum(a)),sum(a)),times(tptp_fun____(s(a),sum(a)),s(a))) = tptp_fun____(tptp_fun____(cubes(a),times(sum(a),s(a))),tptp_fun____(times(s(a),s(a)),times(sum(a),s(a)))),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
( ~ ! [Y: $i,X: $i] : ( tptp_fun____(X,Y) = tptp_fun____(Y,X) )
| ( tptp_fun____(times(tptp_fun____(s(a),sum(a)),s(a)),times(tptp_fun____(s(a),sum(a)),sum(a))) = tptp_fun____(times(tptp_fun____(s(a),sum(a)),sum(a)),times(tptp_fun____(s(a),sum(a)),s(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(118,plain,
tptp_fun____(times(tptp_fun____(s(a),sum(a)),s(a)),times(tptp_fun____(s(a),sum(a)),sum(a))) = tptp_fun____(times(tptp_fun____(s(a),sum(a)),sum(a)),times(tptp_fun____(s(a),sum(a)),s(a))),
inference(unit_resolution,[status(thm)],[117,17]) ).
tff(119,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( times(X,tptp_fun____(Y,Z)) = tptp_fun____(times(X,Y),times(X,Z)) )
| ( times(tptp_fun____(s(a),sum(a)),tptp_fun____(s(a),sum(a))) = tptp_fun____(times(tptp_fun____(s(a),sum(a)),s(a)),times(tptp_fun____(s(a),sum(a)),sum(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
times(tptp_fun____(s(a),sum(a)),tptp_fun____(s(a),sum(a))) = tptp_fun____(times(tptp_fun____(s(a),sum(a)),s(a)),times(tptp_fun____(s(a),sum(a)),sum(a))),
inference(unit_resolution,[status(thm)],[119,105]) ).
tff(121,plain,
^ [N: $i] :
refl(
( ( sum(s(N)) = tptp_fun____(s(N),sum(N)) )
<=> ( sum(s(N)) = tptp_fun____(s(N),sum(N)) ) )),
inference(bind,[status(th)],]) ).
tff(122,plain,
( ! [N: $i] : ( sum(s(N)) = tptp_fun____(s(N),sum(N)) )
<=> ! [N: $i] : ( sum(s(N)) = tptp_fun____(s(N),sum(N)) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,plain,
( ! [N: $i] : ( sum(s(N)) = tptp_fun____(s(N),sum(N)) )
<=> ! [N: $i] : ( sum(s(N)) = tptp_fun____(s(N),sum(N)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,axiom,
! [N: $i] : ( sum(s(N)) = tptp_fun____(s(N),sum(N)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_s) ).
tff(125,plain,
! [N: $i] : ( sum(s(N)) = tptp_fun____(s(N),sum(N)) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
! [N: $i] : ( sum(s(N)) = tptp_fun____(s(N),sum(N)) ),
inference(skolemize,[status(sab)],[125]) ).
tff(127,plain,
! [N: $i] : ( sum(s(N)) = tptp_fun____(s(N),sum(N)) ),
inference(modus_ponens,[status(thm)],[126,122]) ).
tff(128,plain,
( ~ ! [N: $i] : ( sum(s(N)) = tptp_fun____(s(N),sum(N)) )
| ( sum(s(a)) = tptp_fun____(s(a),sum(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
sum(s(a)) = tptp_fun____(s(a),sum(a)),
inference(unit_resolution,[status(thm)],[128,127]) ).
tff(130,plain,
times(sum(s(a)),sum(s(a))) = times(tptp_fun____(s(a),sum(a)),tptp_fun____(s(a),sum(a))),
inference(monotonicity,[status(thm)],[129,129]) ).
tff(131,plain,
times(sum(s(a)),sum(s(a))) = cubes(s(a)),
inference(transitivity,[status(thm)],[130,120,118,116,84,81,20,10]) ).
tff(132,plain,
( ( times(sum(s(a)),sum(s(a))) != cubes(s(a)) )
<=> ( times(sum(s(a)),sum(s(a))) != cubes(s(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(133,axiom,
times(sum(s(a)),sum(s(a))) != cubes(s(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
tff(134,plain,
times(sum(s(a)),sum(s(a))) != cubes(s(a)),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
$false,
inference(unit_resolution,[status(thm)],[134,131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN133-1 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 16:52:33 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------