TSTP Solution File: LCL109-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL109-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 04:54:58 EDT 2022
% Result : Unsatisfiable 8.25s 5.55s
% Output : Proof 8.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 44
% Syntax : Number of formulae : 128 ( 71 unt; 4 typ; 0 def)
% Number of atoms : 225 ( 218 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 167 ( 72 ~; 61 |; 0 &)
% ( 34 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 194 ( 180 !; 0 ?; 194 :)
% Comments :
%------------------------------------------------------------------------------
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(truth_type,type,
truth: $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) )
<=> ( implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_7) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) )
| ( implies(a,implies(implies(a,implies(a,b)),b)) = implies(implies(a,implies(a,b)),implies(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
implies(a,implies(implies(a,implies(a,b)),b)) = implies(implies(a,implies(a,b)),implies(a,b)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
implies(implies(a,implies(a,b)),implies(a,b)) = implies(a,implies(implies(a,implies(a,b)),b)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [Y: $i,X: $i] :
refl(
( ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
<=> ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
<=> ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
<=> ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).
tff(15,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(implies(a,b),a),a) = implies(implies(a,implies(a,b)),implies(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
implies(implies(implies(a,b),a),a) = implies(implies(a,implies(a,b)),implies(a,b)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
implies(implies(implies(a,b),a),a) = implies(a,implies(implies(a,implies(a,b)),b)),
inference(transitivity,[status(thm)],[19,10]) ).
tff(21,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) )
<=> ( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [Z: $i,Y: $i,X: $i] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_5) ).
tff(25,plain,
! [Z: $i,Y: $i,X: $i] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Z: $i,Y: $i,X: $i] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) )
| ( implies(implies(implies(a,b),a),a) != implies(a,implies(implies(a,implies(a,b)),b)) )
| ( implies(implies(implies(a,b),a),implies(implies(a,implies(a,b)),b)) = truth ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) )
| ( implies(implies(implies(a,b),a),a) != implies(a,implies(implies(a,implies(a,b)),b)) )
| ( implies(implies(implies(a,b),a),implies(implies(a,implies(a,b)),b)) = truth ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) )
| ( implies(implies(implies(a,b),a),a) != implies(a,implies(implies(a,implies(a,b)),b)) )
| ( implies(implies(implies(a,b),a),implies(implies(a,implies(a,b)),b)) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) )
| ( implies(implies(implies(a,b),a),a) != implies(a,implies(implies(a,implies(a,b)),b)) )
| ( implies(implies(implies(a,b),a),implies(implies(a,implies(a,b)),b)) = truth ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
implies(implies(implies(a,b),a),implies(implies(a,implies(a,b)),b)) = truth,
inference(unit_resolution,[status(thm)],[30,27,20]) ).
tff(32,plain,
( ( implies(a,implies(implies(a,b),a)) = implies(implies(implies(a,b),a),implies(implies(a,implies(a,b)),b)) )
<=> ( implies(a,implies(implies(a,b),a)) = truth ) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ( implies(a,implies(implies(a,b),a)) = truth )
<=> ( implies(a,implies(implies(a,b),a)) = implies(implies(implies(a,b),a),implies(implies(a,implies(a,b)),b)) ) ),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
^ [Y: $i,X: $i] :
refl(
( ( implies(X,implies(Y,X)) = truth )
<=> ( implies(X,implies(Y,X)) = truth ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [Y: $i,X: $i] : ( implies(X,implies(Y,X)) = truth )
<=> ! [Y: $i,X: $i] : ( implies(X,implies(Y,X)) = truth ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [Y: $i,X: $i] : ( implies(X,implies(Y,X)) = truth )
<=> ! [Y: $i,X: $i] : ( implies(X,implies(Y,X)) = truth ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
! [Y: $i,X: $i] : ( implies(X,implies(Y,X)) = truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_4) ).
tff(38,plain,
! [Y: $i,X: $i] : ( implies(X,implies(Y,X)) = truth ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [Y: $i,X: $i] : ( implies(X,implies(Y,X)) = truth ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [Y: $i,X: $i] : ( implies(X,implies(Y,X)) = truth ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,implies(Y,X)) = truth )
| ( implies(a,implies(implies(a,b),a)) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
implies(a,implies(implies(a,b),a)) = truth,
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
implies(a,implies(implies(a,b),a)) = implies(implies(implies(a,b),a),implies(implies(a,implies(a,b)),b)),
inference(modus_ponens,[status(thm)],[42,33]) ).
tff(44,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) )
| ( implies(a,implies(implies(implies(implies(a,b),a),a),implies(implies(implies(b,a),implies(a,b)),b))) = implies(implies(implies(implies(a,b),a),a),implies(a,implies(implies(implies(b,a),implies(a,b)),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
implies(a,implies(implies(implies(implies(a,b),a),a),implies(implies(implies(b,a),implies(a,b)),b))) = implies(implies(implies(implies(a,b),a),a),implies(a,implies(implies(implies(b,a),implies(a,b)),b))),
inference(unit_resolution,[status(thm)],[44,7]) ).
tff(46,plain,
implies(implies(implies(implies(a,b),a),a),implies(a,implies(implies(implies(b,a),implies(a,b)),b))) = implies(a,implies(implies(implies(implies(a,b),a),a),implies(implies(implies(b,a),implies(a,b)),b))),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) )
| ( implies(b,implies(implies(a,b),a)) = implies(implies(a,b),implies(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
implies(b,implies(implies(a,b),a)) = implies(implies(a,b),implies(b,a)),
inference(unit_resolution,[status(thm)],[47,7]) ).
tff(49,plain,
implies(implies(b,implies(implies(a,b),a)),implies(b,a)) = implies(implies(implies(a,b),implies(b,a)),implies(b,a)),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = implies(implies(b,implies(implies(a,b),a)),implies(b,a)),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = implies(implies(implies(b,a),implies(a,b)),implies(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = implies(implies(implies(b,a),implies(a,b)),implies(a,b)),
inference(unit_resolution,[status(thm)],[51,17]) ).
tff(53,plain,
implies(implies(implies(b,a),implies(a,b)),implies(a,b)) = implies(implies(implies(a,b),implies(b,a)),implies(b,a)),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) )
| ( implies(a,implies(implies(implies(b,a),implies(a,b)),b)) = implies(implies(implies(b,a),implies(a,b)),implies(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
implies(a,implies(implies(implies(b,a),implies(a,b)),b)) = implies(implies(implies(b,a),implies(a,b)),implies(a,b)),
inference(unit_resolution,[status(thm)],[54,7]) ).
tff(56,plain,
implies(a,implies(implies(implies(b,a),implies(a,b)),b)) = implies(implies(b,implies(implies(a,b),a)),implies(b,a)),
inference(transitivity,[status(thm)],[55,53,50]) ).
tff(57,plain,
implies(implies(implies(implies(a,b),a),a),implies(a,implies(implies(implies(b,a),implies(a,b)),b))) = implies(implies(implies(implies(a,b),a),a),implies(implies(b,implies(implies(a,b),a)),implies(b,a))),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
implies(implies(implies(implies(a,b),a),a),implies(implies(b,implies(implies(a,b),a)),implies(b,a))) = implies(implies(implies(implies(a,b),a),a),implies(a,implies(implies(implies(b,a),implies(a,b)),b))),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) = truth )
<=> ( implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) = truth ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) = truth )
<=> ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) = truth ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) = truth )
<=> ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) = truth ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,axiom,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) = truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_6) ).
tff(63,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) = truth ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) = truth ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) = truth ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) = truth )
| ( implies(implies(implies(implies(a,b),a),a),implies(implies(b,implies(implies(a,b),a)),implies(b,a))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
implies(implies(implies(implies(a,b),a),a),implies(implies(b,implies(implies(a,b),a)),implies(b,a))) = truth,
inference(unit_resolution,[status(thm)],[66,65]) ).
tff(68,plain,
truth = implies(implies(implies(implies(a,b),a),a),implies(implies(b,implies(implies(a,b),a)),implies(b,a))),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
truth = implies(a,implies(implies(implies(implies(a,b),a),a),implies(implies(implies(b,a),implies(a,b)),b))),
inference(transitivity,[status(thm)],[68,58,46]) ).
tff(70,plain,
implies(implies(a,implies(a,b)),implies(a,b)) = implies(implies(implies(a,b),a),a),
inference(symmetry,[status(thm)],[19]) ).
tff(71,plain,
implies(a,implies(implies(a,implies(a,b)),b)) = implies(implies(implies(a,b),a),a),
inference(transitivity,[status(thm)],[9,70]) ).
tff(72,plain,
( ( implies(a,implies(implies(a,implies(a,b)),b)) = truth )
<=> ( implies(implies(implies(a,b),a),a) = implies(a,implies(implies(implies(implies(a,b),a),a),implies(implies(implies(b,a),implies(a,b)),b))) ) ),
inference(monotonicity,[status(thm)],[71,69]) ).
tff(73,plain,
( ( implies(implies(implies(a,b),a),a) = implies(a,implies(implies(implies(implies(a,b),a),a),implies(implies(implies(b,a),implies(a,b)),b))) )
<=> ( implies(a,implies(implies(a,implies(a,b)),b)) = truth ) ),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( ( implies(a,implies(implies(implies(implies(a,b),a),a),implies(implies(implies(b,a),implies(a,b)),b))) = implies(implies(implies(a,b),a),a) )
<=> ( implies(implies(implies(a,b),a),a) = implies(a,implies(implies(implies(implies(a,b),a),a),implies(implies(implies(b,a),implies(a,b)),b))) ) ),
inference(commutativity,[status(thm)],]) ).
tff(75,plain,
implies(implies(implies(b,a),implies(a,b)),implies(a,b)) = implies(implies(b,implies(implies(a,b),a)),implies(b,a)),
inference(transitivity,[status(thm)],[53,50]) ).
tff(76,plain,
implies(implies(implies(implies(a,b),a),a),implies(implies(implies(b,a),implies(a,b)),implies(a,b))) = implies(implies(implies(implies(a,b),a),a),implies(implies(b,implies(implies(a,b),a)),implies(b,a))),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) )
| ( implies(implies(implies(b,a),implies(a,b)),implies(implies(implies(implies(a,b),a),a),implies(a,b))) = implies(implies(implies(implies(a,b),a),a),implies(implies(implies(b,a),implies(a,b)),implies(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
implies(implies(implies(b,a),implies(a,b)),implies(implies(implies(implies(a,b),a),a),implies(a,b))) = implies(implies(implies(implies(a,b),a),a),implies(implies(implies(b,a),implies(a,b)),implies(a,b))),
inference(unit_resolution,[status(thm)],[77,7]) ).
tff(79,plain,
implies(implies(implies(implies(a,b),a),a),implies(a,b)) = implies(implies(implies(a,implies(a,b)),implies(a,b)),implies(a,b)),
inference(monotonicity,[status(thm)],[19]) ).
tff(80,plain,
implies(implies(implies(a,implies(a,b)),implies(a,b)),implies(a,b)) = implies(implies(implies(implies(a,b),a),a),implies(a,b)),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
implies(implies(implies(b,a),implies(a,b)),implies(implies(implies(a,implies(a,b)),implies(a,b)),implies(a,b))) = implies(implies(implies(b,a),implies(a,b)),implies(implies(implies(implies(a,b),a),a),implies(a,b))),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(implies(a,implies(a,b)),implies(a,b)),implies(a,b)) = implies(implies(implies(a,b),implies(a,implies(a,b))),implies(a,implies(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
implies(implies(implies(a,implies(a,b)),implies(a,b)),implies(a,b)) = implies(implies(implies(a,b),implies(a,implies(a,b))),implies(a,implies(a,b))),
inference(unit_resolution,[status(thm)],[82,17]) ).
tff(84,plain,
implies(implies(implies(a,b),implies(a,implies(a,b))),implies(a,implies(a,b))) = implies(implies(implies(a,implies(a,b)),implies(a,b)),implies(a,b)),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
implies(implies(implies(b,a),implies(a,b)),implies(implies(implies(a,b),implies(a,implies(a,b))),implies(a,implies(a,b)))) = implies(implies(implies(b,a),implies(a,b)),implies(implies(implies(a,implies(a,b)),implies(a,b)),implies(a,b))),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) )
| ( implies(implies(implies(a,b),implies(a,implies(a,b))),implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b)))) = implies(implies(implies(b,a),implies(a,b)),implies(implies(implies(a,b),implies(a,implies(a,b))),implies(a,implies(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
implies(implies(implies(a,b),implies(a,implies(a,b))),implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b)))) = implies(implies(implies(b,a),implies(a,b)),implies(implies(implies(a,b),implies(a,implies(a,b))),implies(a,implies(a,b)))),
inference(unit_resolution,[status(thm)],[86,7]) ).
tff(88,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,implies(Y,X)) = truth )
| ( implies(implies(a,b),implies(a,implies(a,b))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(89,plain,
implies(implies(a,b),implies(a,implies(a,b))) = truth,
inference(unit_resolution,[status(thm)],[88,40]) ).
tff(90,plain,
truth = implies(implies(a,b),implies(a,implies(a,b))),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
implies(truth,implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b)))) = implies(implies(implies(a,b),implies(a,implies(a,b))),implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b)))),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
^ [X: $i] :
refl(
( ( implies(truth,X) = X )
<=> ( implies(truth,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [X: $i] : ( implies(truth,X) = X )
<=> ! [X: $i] : ( implies(truth,X) = X ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
( ! [X: $i] : ( implies(truth,X) = X )
<=> ! [X: $i] : ( implies(truth,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,axiom,
! [X: $i] : ( implies(truth,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
tff(96,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(modus_ponens,[status(thm)],[97,93]) ).
tff(99,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b)))) = implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
implies(truth,implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b)))) = implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b))),
inference(unit_resolution,[status(thm)],[99,98]) ).
tff(101,plain,
implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b))) = implies(truth,implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b)))),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b))) = implies(a,implies(implies(implies(implies(a,b),a),a),implies(implies(implies(b,a),implies(a,b)),b))),
inference(transitivity,[status(thm)],[101,91,87,85,81,78,76,58,46]) ).
tff(103,plain,
( ( implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b))) = implies(implies(a,implies(a,b)),implies(a,b)) )
<=> ( implies(a,implies(implies(implies(implies(a,b),a),a),implies(implies(implies(b,a),implies(a,b)),b))) = implies(implies(implies(a,b),a),a) ) ),
inference(monotonicity,[status(thm)],[102,70]) ).
tff(104,plain,
( ( implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b))) = implies(implies(a,implies(a,b)),implies(a,b)) )
<=> ( implies(implies(implies(a,b),a),a) = implies(a,implies(implies(implies(implies(a,b),a),a),implies(implies(implies(b,a),implies(a,b)),b))) ) ),
inference(transitivity,[status(thm)],[103,74]) ).
tff(105,plain,
( ( implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b))) = implies(implies(a,implies(a,b)),implies(a,b)) )
<=> ( implies(a,implies(implies(a,implies(a,b)),b)) = truth ) ),
inference(transitivity,[status(thm)],[104,73]) ).
tff(106,plain,
( ( implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b))) != implies(implies(a,implies(a,b)),implies(a,b)) )
<=> ( implies(a,implies(implies(a,implies(a,b)),b)) != truth ) ),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
( ( implies(implies(implies(b,a),implies(a,b)),implies(a,b)) = truth )
<=> ( implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = truth ) ),
inference(monotonicity,[status(thm)],[53]) ).
tff(108,plain,
( ( implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = truth )
<=> ( implies(implies(implies(b,a),implies(a,b)),implies(a,b)) = truth ) ),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
( ( implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth )
<=> ( implies(implies(implies(b,a),implies(a,b)),implies(a,b)) != truth ) ),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
( ( implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth )
<=> ( implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,axiom,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_mv_4) ).
tff(112,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
implies(implies(implies(b,a),implies(a,b)),implies(a,b)) != truth,
inference(modus_ponens,[status(thm)],[112,109]) ).
tff(114,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) )
| ( implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b))) != implies(implies(a,implies(a,b)),implies(a,b)) )
| ( implies(implies(implies(b,a),implies(a,b)),implies(a,b)) = truth ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) )
| ( implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b))) != implies(implies(a,implies(a,b)),implies(a,b)) )
| ( implies(implies(implies(b,a),implies(a,b)),implies(a,b)) = truth ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(115,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) )
| ( implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b))) != implies(implies(a,implies(a,b)),implies(a,b)) )
| ( implies(implies(implies(b,a),implies(a,b)),implies(a,b)) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) )
| ( implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b))) != implies(implies(a,implies(a,b)),implies(a,b)) )
| ( implies(implies(implies(b,a),implies(a,b)),implies(a,b)) = truth ) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
( ( implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b))) != implies(implies(a,implies(a,b)),implies(a,b)) )
| ( implies(implies(implies(b,a),implies(a,b)),implies(a,b)) = truth ) ),
inference(unit_resolution,[status(thm)],[116,27]) ).
tff(118,plain,
implies(implies(implies(b,a),implies(a,b)),implies(a,implies(a,b))) != implies(implies(a,implies(a,b)),implies(a,b)),
inference(unit_resolution,[status(thm)],[117,113]) ).
tff(119,plain,
implies(a,implies(implies(a,implies(a,b)),b)) != truth,
inference(modus_ponens,[status(thm)],[118,106]) ).
tff(120,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) )
| ( implies(a,implies(implies(a,b),a)) != implies(implies(implies(a,b),a),implies(implies(a,implies(a,b)),b)) )
| ( implies(a,implies(implies(a,implies(a,b)),b)) = truth ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) )
| ( implies(a,implies(implies(a,b),a)) != implies(implies(implies(a,b),a),implies(implies(a,implies(a,b)),b)) )
| ( implies(a,implies(implies(a,implies(a,b)),b)) = truth ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) )
| ( implies(a,implies(implies(a,b),a)) != implies(implies(implies(a,b),a),implies(implies(a,implies(a,b)),b)) )
| ( implies(a,implies(implies(a,implies(a,b)),b)) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( implies(X,Y) != implies(Y,Z) )
| ( implies(X,Z) = truth ) )
| ( implies(a,implies(implies(a,b),a)) != implies(implies(implies(a,b),a),implies(implies(a,implies(a,b)),b)) )
| ( implies(a,implies(implies(a,implies(a,b)),b)) = truth ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
( ( implies(a,implies(implies(a,b),a)) != implies(implies(implies(a,b),a),implies(implies(a,implies(a,b)),b)) )
| ( implies(a,implies(implies(a,implies(a,b)),b)) = truth ) ),
inference(unit_resolution,[status(thm)],[122,27]) ).
tff(124,plain,
$false,
inference(unit_resolution,[status(thm)],[123,119,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL109-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 18:07:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 8.25/5.55 % SZS status Unsatisfiable
% 8.25/5.55 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------