TSTP Solution File: GRP175-3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP175-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 : Fri Sep 16 22:26:33 EDT 2022
% Result : Unsatisfiable 0.22s 0.42s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 31
% Syntax : Number of formulae : 79 ( 55 unt; 7 typ; 0 def)
% Number of atoms : 99 ( 93 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 31 ( 9 ~; 5 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 100 ( 90 !; 0 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
tff(identity_type,type,
identity: $i ).
tff(greatest_lower_bound_type,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(least_upper_bound_type,type,
least_upper_bound: ( $i * $i ) > $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( multiply(inverse(X),X) = identity )
<=> ( multiply(inverse(X),X) = identity ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
tff(5,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(a),a) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
multiply(inverse(a),a) = identity,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(
( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
tff(14,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
multiply(identity,a) = a,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
multiply(inverse(a),multiply(identity,a)) = multiply(inverse(a),a),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
^ [Y: $i,X: $i] :
refl(
( ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
<=> ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
tff(24,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
| ( greatest_lower_bound(multiply(identity,a),least_upper_bound(multiply(identity,a),least_upper_bound(multiply(identity,a),multiply(b,a)))) = multiply(identity,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
greatest_lower_bound(multiply(identity,a),least_upper_bound(multiply(identity,a),least_upper_bound(multiply(identity,a),multiply(b,a)))) = multiply(identity,a),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
( ( least_upper_bound(identity,b) = b )
<=> ( least_upper_bound(identity,b) = b ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
least_upper_bound(identity,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p06c_1) ).
tff(31,plain,
least_upper_bound(identity,b) = b,
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
b = least_upper_bound(identity,b),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
multiply(b,a) = multiply(least_upper_bound(identity,b),a),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
multiply(least_upper_bound(identity,b),a) = multiply(b,a),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) )
<=> ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
tff(39,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) )
| ( multiply(least_upper_bound(identity,b),a) = least_upper_bound(multiply(identity,a),multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
multiply(least_upper_bound(identity,b),a) = least_upper_bound(multiply(identity,a),multiply(b,a)),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
least_upper_bound(multiply(identity,a),multiply(b,a)) = multiply(least_upper_bound(identity,b),a),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
least_upper_bound(multiply(identity,a),multiply(b,a)) = multiply(b,a),
inference(transitivity,[status(thm)],[44,34]) ).
tff(46,plain,
least_upper_bound(multiply(identity,a),least_upper_bound(multiply(identity,a),multiply(b,a))) = least_upper_bound(multiply(identity,a),multiply(b,a)),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
least_upper_bound(multiply(identity,a),multiply(b,a)) = least_upper_bound(multiply(identity,a),least_upper_bound(multiply(identity,a),multiply(b,a))),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
multiply(b,a) = least_upper_bound(multiply(identity,a),least_upper_bound(multiply(identity,a),multiply(b,a))),
inference(transitivity,[status(thm)],[33,43,47]) ).
tff(49,plain,
greatest_lower_bound(multiply(identity,a),multiply(b,a)) = greatest_lower_bound(multiply(identity,a),least_upper_bound(multiply(identity,a),least_upper_bound(multiply(identity,a),multiply(b,a)))),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
a = multiply(identity,a),
inference(symmetry,[status(thm)],[18]) ).
tff(51,plain,
greatest_lower_bound(a,least_upper_bound(multiply(identity,a),multiply(b,a))) = greatest_lower_bound(multiply(identity,a),multiply(b,a)),
inference(monotonicity,[status(thm)],[50,45]) ).
tff(52,plain,
greatest_lower_bound(a,least_upper_bound(multiply(identity,a),multiply(b,a))) = multiply(identity,a),
inference(transitivity,[status(thm)],[51,49,28]) ).
tff(53,plain,
multiply(inverse(a),greatest_lower_bound(a,least_upper_bound(multiply(identity,a),multiply(b,a)))) = multiply(inverse(a),multiply(identity,a)),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) )
<=> ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
tff(58,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) )
| ( multiply(inverse(a),greatest_lower_bound(a,least_upper_bound(multiply(identity,a),multiply(b,a)))) = greatest_lower_bound(multiply(inverse(a),a),multiply(inverse(a),least_upper_bound(multiply(identity,a),multiply(b,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
multiply(inverse(a),greatest_lower_bound(a,least_upper_bound(multiply(identity,a),multiply(b,a)))) = greatest_lower_bound(multiply(inverse(a),a),multiply(inverse(a),least_upper_bound(multiply(identity,a),multiply(b,a)))),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
greatest_lower_bound(multiply(inverse(a),a),multiply(inverse(a),least_upper_bound(multiply(identity,a),multiply(b,a)))) = multiply(inverse(a),greatest_lower_bound(a,least_upper_bound(multiply(identity,a),multiply(b,a)))),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
multiply(inverse(a),least_upper_bound(multiply(identity,a),multiply(b,a))) = multiply(inverse(a),multiply(b,a)),
inference(monotonicity,[status(thm)],[45]) ).
tff(65,plain,
multiply(inverse(a),multiply(b,a)) = multiply(inverse(a),least_upper_bound(multiply(identity,a),multiply(b,a))),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
identity = multiply(inverse(a),a),
inference(symmetry,[status(thm)],[9]) ).
tff(67,plain,
greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) = greatest_lower_bound(multiply(inverse(a),a),multiply(inverse(a),least_upper_bound(multiply(identity,a),multiply(b,a)))),
inference(monotonicity,[status(thm)],[66,65]) ).
tff(68,plain,
greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) = identity,
inference(transitivity,[status(thm)],[67,63,53,19,9]) ).
tff(69,plain,
( ( greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != identity )
<=> ( greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,axiom,
greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p06c) ).
tff(71,plain,
greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != identity,
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
$false,
inference(unit_resolution,[status(thm)],[71,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP175-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 31 15:36:00 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.22/0.42 % SZS status Unsatisfiable
% 0.22/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------