TSTP Solution File: LCL161-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL161-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 04:55:08 EDT 2022
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 39
% Syntax : Number of formulae : 88 ( 57 unt; 7 typ; 0 def)
% Number of atoms : 121 ( 112 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 44 ( 12 ~; 8 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 116 ( 104 !; 0 ?; 116 :)
% Comments :
%------------------------------------------------------------------------------
tff(x_type,type,
x: $i ).
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(truth_type,type,
truth: $i ).
tff(xor_type,type,
xor: ( $i * $i ) > $i ).
tff(not_type,type,
not: $i > $i ).
tff(falsehood_type,type,
falsehood: $i ).
tff(and_star_type,type,
and_star: ( $i * $i ) > $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( xor(X,not(truth)) = X )
<=> ( xor(X,not(truth)) = X ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( xor(X,not(truth)) = X )
<=> ! [X: $i] : ( xor(X,not(truth)) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
rewrite(
( ( xor(X,falsehood) = X )
<=> ( xor(X,not(truth)) = X ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i] : ( xor(X,falsehood) = X )
<=> ! [X: $i] : ( xor(X,not(truth)) = X ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] : ( xor(X,falsehood) = X )
<=> ! [X: $i] : ( xor(X,falsehood) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
! [X: $i] : ( xor(X,falsehood) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_2) ).
tff(7,plain,
! [X: $i] : ( xor(X,falsehood) = X ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i] : ( xor(X,not(truth)) = X ),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
! [X: $i] : ( xor(X,not(truth)) = X ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i] : ( xor(X,not(truth)) = X ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [X: $i] : ( xor(X,not(truth)) = X )
| ( xor(x,not(truth)) = x ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
xor(x,not(truth)) = x,
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
^ [X: $i] :
refl(
( ( not(X) = xor(X,truth) )
<=> ( not(X) = xor(X,truth) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X: $i] : ( not(X) = xor(X,truth) )
<=> ! [X: $i] : ( not(X) = xor(X,truth) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [X: $i] : ( not(X) = xor(X,truth) )
<=> ! [X: $i] : ( not(X) = xor(X,truth) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
! [X: $i] : ( not(X) = xor(X,truth) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_1) ).
tff(17,plain,
! [X: $i] : ( not(X) = xor(X,truth) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [X: $i] : ( not(X) = xor(X,truth) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X: $i] : ( not(X) = xor(X,truth) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ~ ! [X: $i] : ( not(X) = xor(X,truth) )
| ( not(truth) = xor(truth,truth) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
not(truth) = xor(truth,truth),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
xor(x,not(truth)) = xor(x,xor(truth,truth)),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
xor(x,xor(truth,truth)) = xor(x,not(truth)),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
^ [Y: $i,X: $i] :
refl(
( ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) )
<=> ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) )
<=> ! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) )
<=> ! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_7) ).
tff(28,plain,
! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) )
| ( xor(x,xor(truth,truth)) = xor(xor(x,truth),truth) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
xor(x,xor(truth,truth)) = xor(xor(x,truth),truth),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
xor(xor(x,truth),truth) = xor(x,xor(truth,truth)),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
^ [Y: $i,X: $i] :
refl(
( ( and_star(X,Y) = and_star(Y,X) )
<=> ( and_star(X,Y) = and_star(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) )
<=> ! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) )
<=> ! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_commutativity) ).
tff(38,plain,
! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) )
| ( and_star(xor(truth,x),truth) = and_star(truth,xor(truth,x)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
and_star(xor(truth,x),truth) = and_star(truth,xor(truth,x)),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
^ [X: $i] :
refl(
( ( and_star(X,truth) = X )
<=> ( and_star(X,truth) = X ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [X: $i] : ( and_star(X,truth) = X )
<=> ! [X: $i] : ( and_star(X,truth) = X ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [X: $i] : ( and_star(X,truth) = X )
<=> ! [X: $i] : ( and_star(X,truth) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
! [X: $i] : ( and_star(X,truth) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_4) ).
tff(47,plain,
! [X: $i] : ( and_star(X,truth) = X ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [X: $i] : ( and_star(X,truth) = X ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [X: $i] : ( and_star(X,truth) = X ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ~ ! [X: $i] : ( and_star(X,truth) = X )
| ( and_star(xor(truth,x),truth) = xor(truth,x) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
and_star(xor(truth,x),truth) = xor(truth,x),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
xor(truth,x) = and_star(xor(truth,x),truth),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
^ [Y: $i,X: $i] :
refl(
( ( xor(X,Y) = xor(Y,X) )
<=> ( xor(X,Y) = xor(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
<=> ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
<=> ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,axiom,
! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutativity) ).
tff(57,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
| ( xor(x,truth) = xor(truth,x) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
xor(x,truth) = xor(truth,x),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
xor(x,truth) = and_star(truth,xor(truth,x)),
inference(transitivity,[status(thm)],[61,52,42]) ).
tff(63,plain,
xor(xor(x,truth),truth) = xor(and_star(truth,xor(truth,x)),truth),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
xor(and_star(truth,xor(truth,x)),truth) = xor(xor(x,truth),truth),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
| ( xor(and_star(truth,xor(truth,x)),truth) = xor(truth,and_star(truth,xor(truth,x))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
xor(and_star(truth,xor(truth,x)),truth) = xor(truth,and_star(truth,xor(truth,x))),
inference(unit_resolution,[status(thm)],[65,59]) ).
tff(67,plain,
xor(truth,and_star(truth,xor(truth,x))) = xor(and_star(truth,xor(truth,x)),truth),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
^ [Y: $i,X: $i] :
refl(
( ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
<=> ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
<=> ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
<=> ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,axiom,
! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
tff(72,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ),
inference(modus_ponens,[status(thm)],[73,69]) ).
tff(75,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
| ( implies(truth,x) = xor(truth,and_star(truth,xor(truth,x))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
implies(truth,x) = xor(truth,and_star(truth,xor(truth,x))),
inference(unit_resolution,[status(thm)],[75,74]) ).
tff(77,plain,
implies(truth,x) = x,
inference(transitivity,[status(thm)],[76,67,64,33,23,12]) ).
tff(78,plain,
( ( implies(truth,x) != x )
<=> ( implies(truth,x) != x ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,axiom,
implies(truth,x) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_axiom) ).
tff(80,plain,
implies(truth,x) != x,
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
$false,
inference(unit_resolution,[status(thm)],[80,77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LCL161-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n018.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 18:27:27 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.
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------