TSTP Solution File: LDA001-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LDA001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 44 ( 28 unt; 5 typ; 0 def)
% Number of atoms : 52 ( 50 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 7 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 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 : 48 ( 45 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
tff(f_type,type,
f: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(u_type,type,
u: $i ).
tff(n2_type,type,
n2: $i ).
tff(n3_type,type,
n3: $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/sandbox2/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(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(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(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)],[9]) ).
tff(11,plain,
f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(n1,n1),f(n1,n1))) = f(f(f(n1,n1),f(f(n1,n1),f(n1,n1))),f(f(n1,n1),f(n1,n1))),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
f(f(f(n1,n1),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(n1,n1),f(n1,n1))),
inference(symmetry,[status(thm)],[11]) ).
tff(13,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(f(n1,n1),f(n1,n1)),f(n1,n1))) = f(f(f(n1,n1),f(f(n1,n1),f(n1,n1))),f(f(n1,n1),f(n1,n1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(14,plain,
f(f(n1,n1),f(f(f(n1,n1),f(n1,n1)),f(n1,n1))) = f(f(f(n1,n1),f(f(n1,n1),f(n1,n1))),f(f(n1,n1),f(n1,n1))),
inference(unit_resolution,[status(thm)],[13,7]) ).
tff(15,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(16,plain,
f(n1,f(n1,n1)) = f(f(n1,n1),f(n1,n1)),
inference(unit_resolution,[status(thm)],[15,7]) ).
tff(17,plain,
f(f(n1,n1),f(n1,n1)) = f(n1,f(n1,n1)),
inference(symmetry,[status(thm)],[16]) ).
tff(18,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)],[17]) ).
tff(19,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)],[18]) ).
tff(20,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(21,plain,
f(n1,f(f(n1,n1),n1)) = f(f(n1,f(n1,n1)),f(n1,n1)),
inference(unit_resolution,[status(thm)],[20,7]) ).
tff(22,plain,
f(n1,f(f(n1,n1),n1)) = f(f(f(n1,n1),f(n1,n1)),f(n1,n1)),
inference(transitivity,[status(thm)],[21,19]) ).
tff(23,plain,
f(f(n1,n1),f(n1,f(f(n1,n1),n1))) = f(f(n1,n1),f(f(f(n1,n1),f(n1,n1)),f(n1,n1))),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,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(n1,n1),n1))) = f(f(f(n1,n1),n1),f(f(n1,n1),f(f(n1,n1),n1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
f(f(n1,n1),f(n1,f(f(n1,n1),n1))) = f(f(f(n1,n1),n1),f(f(n1,n1),f(f(n1,n1),n1))),
inference(unit_resolution,[status(thm)],[24,7]) ).
tff(26,plain,
f(f(f(n1,n1),n1),f(f(n1,n1),f(f(n1,n1),n1))) = f(f(n1,n1),f(n1,f(f(n1,n1),n1))),
inference(symmetry,[status(thm)],[25]) ).
tff(27,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(f(n1,n1),n1))) = f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(f(n1,n1),n1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
f(f(f(n1,n1),n1),f(f(n1,n1),f(f(n1,n1),n1))) = f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(f(n1,n1),n1))),
inference(unit_resolution,[status(thm)],[27,7]) ).
tff(29,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),n1),f(f(n1,n1),n1))) = f(f(f(n1,n1),n1),f(f(n1,n1),f(f(n1,n1),n1))),
inference(symmetry,[status(thm)],[28]) ).
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(n1,n1)) = f(f(f(n1,n1),n1),f(f(n1,n1),n1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
f(f(n1,n1),f(n1,n1)) = f(f(f(n1,n1),n1),f(f(n1,n1),n1)),
inference(unit_resolution,[status(thm)],[30,7]) ).
tff(32,plain,
f(f(f(f(n1,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(f(n1,n1),n1))),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
f(f(f(f(n1,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(n1,n1),f(n1,n1))),
inference(transitivity,[status(thm)],[32,29,26,23,14,12]) ).
tff(34,plain,
( ( f(f(n3,n2),u) != f(f(u,u),u) )
<=> ( f(f(f(f(n1,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(n1,n1),f(n1,n1))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( f(f(n3,n2),u) != f(f(u,u),u) )
<=> ( f(f(n3,n2),u) != f(f(u,u),u) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,axiom,
f(f(n3,n2),u) != f(f(u,u),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
tff(37,plain,
f(f(n3,n2),u) != f(f(u,u),u),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
f(f(f(f(n1,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(n1,n1),f(n1,n1))),
inference(modus_ponens,[status(thm)],[37,34]) ).
tff(39,plain,
$false,
inference(unit_resolution,[status(thm)],[38,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LDA001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n021.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 01:56:13 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.
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------