TSTP Solution File: BOO021-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : BOO021-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 : Tue Sep 6 17:18:46 EDT 2022
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 23
% Syntax : Number of formulae : 68 ( 49 unt; 4 typ; 0 def)
% Number of atoms : 85 ( 81 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 30 ( 12 ~; 8 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 74 !; 0 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( ( add(multiply(X,Y),Y) = Y )
<=> ( add(multiply(X,Y),Y) = Y ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
<=> ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
<=> ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_multiply) ).
tff(5,plain,
! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(a,b),b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
add(multiply(a,b),b) = b,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
b = add(multiply(a,b),b),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
multiply(a,b) = multiply(a,add(multiply(a,b),b)),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
multiply(a,add(multiply(a,b),b)) = multiply(a,b),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
<=> ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add_property) ).
tff(17,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(a,add(multiply(a,b),b)) = add(multiply(multiply(a,b),a),multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
multiply(a,add(multiply(a,b),b)) = add(multiply(multiply(a,b),a),multiply(b,a)),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
add(multiply(multiply(a,b),a),multiply(b,a)) = multiply(a,add(multiply(a,b),b)),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(add(multiply(multiply(b,a),b),multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a))),add(multiply(multiply(a,b),a),multiply(b,a))) = add(multiply(multiply(a,b),a),multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
add(multiply(add(multiply(multiply(b,a),b),multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a))),add(multiply(multiply(a,b),a),multiply(b,a))) = add(multiply(multiply(a,b),a),multiply(b,a)),
inference(unit_resolution,[status(thm)],[23,7]) ).
tff(25,plain,
^ [Y: $i,X: $i] :
refl(
( ( multiply(add(X,Y),Y) = Y )
<=> ( multiply(add(X,Y),Y) = Y ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
<=> ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
<=> ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add) ).
tff(29,plain,
! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
| ( multiply(add(multiply(multiply(b,a),b),add(multiply(multiply(a,b),a),multiply(b,a))),add(multiply(multiply(a,b),a),multiply(b,a))) = add(multiply(multiply(a,b),a),multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
multiply(add(multiply(multiply(b,a),b),add(multiply(multiply(a,b),a),multiply(b,a))),add(multiply(multiply(a,b),a),multiply(b,a))) = add(multiply(multiply(a,b),a),multiply(b,a)),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
add(multiply(multiply(a,b),a),multiply(b,a)) = multiply(a,b),
inference(transitivity,[status(thm)],[22,12]) ).
tff(35,plain,
add(multiply(multiply(b,a),b),add(multiply(multiply(a,b),a),multiply(b,a))) = add(multiply(multiply(b,a),b),multiply(a,b)),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
add(multiply(multiply(b,a),b),multiply(a,b)) = add(multiply(multiply(b,a),b),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
multiply(add(multiply(multiply(b,a),b),multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a))) = multiply(add(multiply(multiply(b,a),b),add(multiply(multiply(a,b),a),multiply(b,a))),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
multiply(add(multiply(multiply(b,a),b),multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a))) = add(multiply(multiply(a,b),a),multiply(b,a)),
inference(transitivity,[status(thm)],[37,33]) ).
tff(39,plain,
add(multiply(add(multiply(multiply(b,a),b),multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a))),add(multiply(multiply(a,b),a),multiply(b,a))) = add(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
add(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))) = add(multiply(add(multiply(multiply(b,a),b),multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a))),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
add(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))) = add(multiply(a,b),multiply(a,b)),
inference(monotonicity,[status(thm)],[34,34]) ).
tff(42,plain,
add(multiply(a,b),multiply(a,b)) = add(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(b,add(a,a)) = add(multiply(a,b),multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
multiply(b,add(a,a)) = add(multiply(a,b),multiply(a,b)),
inference(unit_resolution,[status(thm)],[43,19]) ).
tff(45,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(a,a),a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
add(multiply(a,a),a) = a,
inference(unit_resolution,[status(thm)],[45,7]) ).
tff(47,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(b,a),a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
add(multiply(b,a),a) = a,
inference(unit_resolution,[status(thm)],[47,7]) ).
tff(49,plain,
a = add(multiply(b,a),a),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
multiply(a,a) = multiply(add(multiply(b,a),a),a),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
multiply(add(multiply(b,a),a),a) = multiply(a,a),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
| ( multiply(add(multiply(b,a),a),a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
multiply(add(multiply(b,a),a),a) = a,
inference(unit_resolution,[status(thm)],[52,31]) ).
tff(54,plain,
a = multiply(add(multiply(b,a),a),a),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
a = multiply(a,a),
inference(transitivity,[status(thm)],[54,51]) ).
tff(56,plain,
add(a,a) = add(multiply(a,a),a),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
add(a,a) = a,
inference(transitivity,[status(thm)],[56,46]) ).
tff(58,plain,
multiply(b,add(a,a)) = multiply(b,a),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
multiply(b,a) = multiply(b,add(a,a)),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
multiply(b,a) = multiply(a,b),
inference(transitivity,[status(thm)],[59,44,42,40,24,22,12]) ).
tff(61,plain,
( ( multiply(b,a) != multiply(a,b) )
<=> ( multiply(b,a) != multiply(a,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,axiom,
multiply(b,a) != multiply(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity_of_multiply) ).
tff(63,plain,
multiply(b,a) != multiply(a,b),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
$false,
inference(unit_resolution,[status(thm)],[63,60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : BOO021-1 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n016.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 : Tue Aug 30 03:33:15 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.
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------