TSTP Solution File: LDA002-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LDA002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 05:06:27 EDT 2022
% Result : Unsatisfiable 2.04s 1.60s
% Output : Proof 2.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 30
% Syntax : Number of formulae : 117 ( 89 unt; 5 typ; 0 def)
% Number of atoms : 137 ( 135 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 50 ( 26 ~; 19 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 1 ( 1 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 84 ( 81 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
tff(f_type,type,
f: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(v_type,type,
v: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
<=> ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(f(n1,n1),f(n1,n1)),f(n1,f(f(n1,n1),n1))) = f(f(f(f(n1,n1),f(n1,n1)),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),n1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
f(f(f(n1,n1),f(n1,n1)),f(n1,f(f(n1,n1),n1))) = f(f(f(f(n1,n1),f(n1,n1)),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),n1))),
inference(unit_resolution,[status(thm)],[11,7]) ).
tff(13,plain,
f(f(f(f(n1,n1),f(n1,n1)),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),n1))) = f(f(f(n1,n1),f(n1,n1)),f(n1,f(f(n1,n1),n1))),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
f(f(f(f(f(n1,n1),f(n1,n1)),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),n1))),f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(f(n1,n1),f(n1,n1)),f(n1,f(f(n1,n1),n1))),f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(monotonicity,[status(thm)],[13,10]) ).
tff(15,plain,
f(f(f(f(n1,n1),f(n1,n1)),f(n1,f(f(n1,n1),n1))),f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(f(f(n1,n1),f(n1,n1)),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),n1))),f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(f(n1,n1),f(n1,n1)),f(f(n1,f(f(n1,n1),n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(f(n1,n1),f(n1,n1)),f(n1,f(f(n1,n1),n1))),f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(17,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(n1,f(f(n1,n1),n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(f(n1,n1),f(n1,n1)),f(n1,f(f(n1,n1),n1))),f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(unit_resolution,[status(thm)],[16,7]) ).
tff(18,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(n1,f(n1,n1)) = f(f(n1,n1),f(n1,n1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
f(n1,f(n1,n1)) = f(f(n1,n1),f(n1,n1)),
inference(unit_resolution,[status(thm)],[18,7]) ).
tff(20,plain,
f(f(n1,n1),f(n1,n1)) = f(n1,f(n1,n1)),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
f(f(f(n1,n1),f(n1,n1)),f(n1,n1)) = f(f(n1,f(n1,n1)),f(n1,n1)),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
f(f(n1,f(n1,n1)),f(n1,n1)) = f(f(f(n1,n1),f(n1,n1)),f(n1,n1)),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(n1,f(f(n1,n1),n1)) = f(f(n1,f(n1,n1)),f(n1,n1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
f(n1,f(f(n1,n1),n1)) = f(f(n1,f(n1,n1)),f(n1,n1)),
inference(unit_resolution,[status(thm)],[23,7]) ).
tff(25,plain,
f(n1,f(f(n1,n1),n1)) = f(f(f(n1,n1),f(n1,n1)),f(n1,n1)),
inference(transitivity,[status(thm)],[24,22]) ).
tff(26,plain,
f(f(n1,f(f(n1,n1),n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(f(f(n1,n1),f(n1,n1)),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
f(f(f(f(n1,n1),f(n1,n1)),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(n1,f(f(n1,n1),n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))) = f(f(f(f(n1,n1),f(n1,n1)),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))) = f(f(f(f(n1,n1),f(n1,n1)),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(unit_resolution,[status(thm)],[28,7]) ).
tff(30,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(n1,n1),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))) = f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
f(f(n1,n1),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))) = f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))),
inference(unit_resolution,[status(thm)],[30,7]) ).
tff(32,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(n1,n1),f(f(n1,n1),f(n1,n1))) = f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
f(f(n1,n1),f(f(n1,n1),f(n1,n1))) = f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),
inference(unit_resolution,[status(thm)],[32,7]) ).
tff(34,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))) = f(f(n1,n1),f(f(n1,n1),f(n1,n1))),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
f(f(n1,n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(n1,n1),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
f(f(n1,n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(n1,f(f(n1,n1),n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(transitivity,[status(thm)],[35,31,29,27]) ).
tff(37,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(n1,n1),f(n1,n1)),f(f(n1,f(f(n1,n1),n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(n1,n1),f(f(n1,n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
f(f(n1,n1),f(f(n1,n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(unit_resolution,[status(thm)],[38,7]) ).
tff(40,plain,
f(f(n1,n1),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))) = f(f(n1,n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(symmetry,[status(thm)],[35]) ).
tff(41,plain,
f(f(n1,n1),f(n1,f(n1,n1))) = f(f(n1,n1),f(f(n1,n1),f(n1,n1))),
inference(monotonicity,[status(thm)],[19]) ).
tff(42,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(n1,f(n1,f(n1,n1))) = f(f(n1,n1),f(n1,f(n1,n1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
f(n1,f(n1,f(n1,n1))) = f(f(n1,n1),f(n1,f(n1,n1))),
inference(unit_resolution,[status(thm)],[42,7]) ).
tff(44,plain,
f(n1,f(f(n1,n1),f(n1,n1))) = f(n1,f(n1,f(n1,n1))),
inference(monotonicity,[status(thm)],[20]) ).
tff(45,plain,
f(n1,f(f(n1,n1),f(n1,n1))) = f(f(n1,n1),f(f(n1,n1),f(n1,n1))),
inference(transitivity,[status(thm)],[44,43,41]) ).
tff(46,plain,
f(f(n1,n1),f(n1,f(f(n1,n1),f(n1,n1)))) = f(f(n1,n1),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(n1,f(n1,f(f(n1,n1),f(n1,n1)))) = f(f(n1,n1),f(n1,f(f(n1,n1),f(n1,n1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
f(n1,f(n1,f(f(n1,n1),f(n1,n1)))) = f(f(n1,n1),f(n1,f(f(n1,n1),f(n1,n1)))),
inference(unit_resolution,[status(thm)],[47,7]) ).
tff(49,plain,
f(n1,f(n1,f(n1,n1))) = f(n1,f(f(n1,n1),f(n1,n1))),
inference(symmetry,[status(thm)],[44]) ).
tff(50,plain,
f(f(n1,n1),f(n1,f(n1,n1))) = f(n1,f(n1,f(n1,n1))),
inference(symmetry,[status(thm)],[43]) ).
tff(51,plain,
f(f(n1,n1),f(f(n1,n1),f(n1,n1))) = f(f(n1,n1),f(n1,f(n1,n1))),
inference(symmetry,[status(thm)],[41]) ).
tff(52,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))) = f(n1,f(f(n1,n1),f(n1,n1))),
inference(transitivity,[status(thm)],[34,51,50,49]) ).
tff(53,plain,
f(n1,f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(n1,f(n1,f(f(n1,n1),f(n1,n1)))),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
f(n1,f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(n1,n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(transitivity,[status(thm)],[53,48,46,40]) ).
tff(55,plain,
f(f(n1,n1),f(n1,f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(n1,n1),f(f(n1,n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(n1,n1),f(n1,f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(n1,n1),n1),f(f(n1,n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
f(f(n1,n1),f(n1,f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(n1,n1),n1),f(f(n1,n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(unit_resolution,[status(thm)],[56,7]) ).
tff(58,plain,
f(f(f(n1,n1),n1),f(f(n1,n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(n1,n1),f(n1,f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))) = f(f(n1,n1),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))),
inference(symmetry,[status(thm)],[31]) ).
tff(60,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))) = f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(monotonicity,[status(thm)],[33]) ).
tff(61,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(n1,n1),f(n1,f(n1,n1))) = f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
f(f(n1,n1),f(n1,f(n1,n1))) = f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))),
inference(unit_resolution,[status(thm)],[62,7]) ).
tff(64,plain,
f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))) = f(f(n1,n1),f(n1,f(n1,n1))),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))) = f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),
inference(transitivity,[status(thm)],[64,41,33]) ).
tff(66,plain,
f(f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1)))) = f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(monotonicity,[status(thm)],[65,65]) ).
tff(67,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(f(n1,n1),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
f(f(f(n1,n1),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1)))),
inference(unit_resolution,[status(thm)],[67,7]) ).
tff(69,plain,
f(f(f(n1,n1),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(n1,n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(transitivity,[status(thm)],[68,66,10,61,59,40]) ).
tff(70,plain,
f(f(f(n1,n1),n1),f(f(f(n1,n1),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(n1,n1),n1),f(f(n1,n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
f(f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1)))) = f(f(f(n1,n1),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(symmetry,[status(thm)],[68]) ).
tff(72,plain,
f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1)))),
inference(symmetry,[status(thm)],[66]) ).
tff(73,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(f(n1,n1),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(transitivity,[status(thm)],[9,72,71]) ).
tff(74,plain,
f(f(f(n1,n1),n1),f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(n1,n1),n1),f(f(f(n1,n1),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(f(n1,n1),n1),f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
f(f(f(n1,n1),n1),f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(unit_resolution,[status(thm)],[75,7]) ).
tff(77,plain,
f(f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(n1,n1),n1),f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))) = f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(79,plain,
f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))) = f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1))),
inference(unit_resolution,[status(thm)],[78,7]) ).
tff(80,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1))) = f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1))) = f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),
inference(transitivity,[status(thm)],[80,64,41,33]) ).
tff(82,plain,
f(f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1))),f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1)))) = f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(monotonicity,[status(thm)],[81,81]) ).
tff(83,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1)))) = f(f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1))),f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1)))) = f(f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1))),f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1)))),
inference(unit_resolution,[status(thm)],[83,7]) ).
tff(85,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))) = f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1))),
inference(transitivity,[status(thm)],[34,51,63,79]) ).
tff(86,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1)))),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(f(n1,n1),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(transitivity,[status(thm)],[86,84,82,72,71]) ).
tff(88,plain,
f(f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1))),f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(monotonicity,[status(thm)],[80,87]) ).
tff(89,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1))),f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1))),f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(unit_resolution,[status(thm)],[89,7]) ).
tff(91,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1)))) = f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(symmetry,[status(thm)],[86]) ).
tff(92,plain,
f(f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1))),f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1)))) = f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1)))),
inference(symmetry,[status(thm)],[84]) ).
tff(93,plain,
f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1))),f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(n1,n1)))),
inference(symmetry,[status(thm)],[82]) ).
tff(94,plain,
f(f(f(f(n1,n1),f(n1,n1)),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))),
inference(symmetry,[status(thm)],[29]) ).
tff(95,plain,
f(f(n1,f(n1,n1)),f(n1,n1)) = f(n1,f(f(n1,n1),n1)),
inference(symmetry,[status(thm)],[24]) ).
tff(96,plain,
f(f(f(n1,f(n1,n1)),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(n1,f(f(n1,n1),n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
f(f(f(n1,f(n1,n1)),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(transitivity,[status(thm)],[96,26,94,60,9,93,92,91]) ).
tff(98,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,f(n1,n1)),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,f(n1,n1)),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(n1,f(n1,n1)),f(n1,n1))),f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,f(n1,n1)),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(n1,f(n1,n1)),f(n1,n1))),f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(unit_resolution,[status(thm)],[99,7]) ).
tff(101,plain,
f(f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(n1,f(n1,n1)),f(n1,n1))),f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,f(n1,n1)),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(transitivity,[status(thm)],[93,92,91]) ).
tff(103,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(n1,f(n1,n1)),f(n1,n1))) = f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(n1,n1))),
inference(monotonicity,[status(thm)],[22]) ).
tff(104,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(n1,n1))) = f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(n1,f(n1,n1)),f(n1,n1))),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
f(f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(n1,n1))),f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(n1,f(n1,n1)),f(n1,n1))),f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(monotonicity,[status(thm)],[104,102]) ).
tff(106,plain,
f(f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(n1,n1))),f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(f(f(n1,n1),f(n1,n1)),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),n1))),f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(transitivity,[status(thm)],[105,101,98,90,88,77,74,70,58,55,39,37,17,15]) ).
tff(107,plain,
( ( f(a,v) != f(b,v) )
<=> ( f(f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(n1,n1))),f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) != f(f(f(f(f(n1,n1),f(n1,n1)),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),n1))),f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
( ( f(a,v) != f(b,v) )
<=> ( f(a,v) != f(b,v) ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,axiom,
f(a,v) != f(b,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
tff(110,plain,
f(a,v) != f(b,v),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
f(f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(n1,n1))),f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) != f(f(f(f(f(n1,n1),f(n1,n1)),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),n1))),f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(modus_ponens,[status(thm)],[110,107]) ).
tff(112,plain,
$false,
inference(unit_resolution,[status(thm)],[111,106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LDA002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 02:15:19 EDT 2022
% 0.12/0.34 % 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.
% 2.04/1.60 % SZS status Unsatisfiable
% 2.04/1.60 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------