TSTP Solution File: GRP175-4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP175-4 : 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 22:26:34 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 39
% Syntax : Number of formulae : 92 ( 62 unt; 7 typ; 0 def)
% Number of atoms : 122 ( 114 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 41 ( 11 ~; 7 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 7 ( 7 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 : 140 ( 126 !; 0 ?; 140 :)
% Comments :
%------------------------------------------------------------------------------
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(identity_type,type,
identity: $i ).
tff(greatest_lower_bound_type,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
<=> ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
<=> ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
<=> ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
tff(5,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
| ( least_upper_bound(multiply(b,a),a) = least_upper_bound(a,multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
least_upper_bound(multiply(b,a),a) = least_upper_bound(a,multiply(b,a)),
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,
least_upper_bound(multiply(b,a),multiply(identity,a)) = least_upper_bound(multiply(b,a),a),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,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(21,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)],[20]) ).
tff(22,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(23,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(24,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)],[23,22]) ).
tff(25,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)],[24]) ).
tff(26,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)],[25,21]) ).
tff(27,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(b,identity),a) = least_upper_bound(multiply(b,a),multiply(identity,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
multiply(least_upper_bound(b,identity),a) = least_upper_bound(multiply(b,a),multiply(identity,a)),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
^ [Y: $i,X: $i] :
refl(
( ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
<=> ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
<=> ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
<=> ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
tff(33,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
| ( greatest_lower_bound(identity,b) = greatest_lower_bound(b,identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
greatest_lower_bound(identity,b) = greatest_lower_bound(b,identity),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
( ( greatest_lower_bound(identity,b) = identity )
<=> ( greatest_lower_bound(identity,b) = identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
greatest_lower_bound(identity,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p06d_1) ).
tff(40,plain,
greatest_lower_bound(identity,b) = identity,
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
identity = greatest_lower_bound(identity,b),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
identity = greatest_lower_bound(b,identity),
inference(transitivity,[status(thm)],[41,37]) ).
tff(43,plain,
least_upper_bound(b,identity) = least_upper_bound(b,greatest_lower_bound(b,identity)),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
least_upper_bound(b,greatest_lower_bound(b,identity)) = least_upper_bound(b,identity),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
^ [Y: $i,X: $i] :
refl(
( ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
<=> ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
tff(49,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
| ( least_upper_bound(b,greatest_lower_bound(b,identity)) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
least_upper_bound(b,greatest_lower_bound(b,identity)) = b,
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
b = least_upper_bound(b,greatest_lower_bound(b,identity)),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
b = least_upper_bound(b,identity),
inference(transitivity,[status(thm)],[54,44]) ).
tff(56,plain,
multiply(b,a) = multiply(least_upper_bound(b,identity),a),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
multiply(b,a) = least_upper_bound(a,multiply(b,a)),
inference(transitivity,[status(thm)],[56,28,19,9]) ).
tff(58,plain,
multiply(inverse(a),multiply(b,a)) = multiply(inverse(a),least_upper_bound(a,multiply(b,a))),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
multiply(inverse(a),least_upper_bound(a,multiply(b,a))) = multiply(inverse(a),multiply(b,a)),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) )
<=> ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(61,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
tff(64,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) )
| ( multiply(inverse(a),least_upper_bound(a,multiply(b,a))) = least_upper_bound(multiply(inverse(a),a),multiply(inverse(a),multiply(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
multiply(inverse(a),least_upper_bound(a,multiply(b,a))) = least_upper_bound(multiply(inverse(a),a),multiply(inverse(a),multiply(b,a))),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
least_upper_bound(multiply(inverse(a),a),multiply(inverse(a),multiply(b,a))) = multiply(inverse(a),least_upper_bound(a,multiply(b,a))),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
^ [X: $i] :
refl(
( ( multiply(inverse(X),X) = identity )
<=> ( multiply(inverse(X),X) = identity ) )),
inference(bind,[status(th)],]) ).
tff(71,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,axiom,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
tff(74,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(a),a) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
multiply(inverse(a),a) = identity,
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
least_upper_bound(multiply(inverse(a),a),multiply(inverse(a),multiply(b,a))) = least_upper_bound(identity,multiply(inverse(a),multiply(b,a))),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) = least_upper_bound(multiply(inverse(a),a),multiply(inverse(a),multiply(b,a))),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) = multiply(inverse(a),multiply(b,a)),
inference(transitivity,[status(thm)],[80,69,59]) ).
tff(82,plain,
( ( least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(b,a)) )
<=> ( least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(b,a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,axiom,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(b,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p06d) ).
tff(84,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(b,a)),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
$false,
inference(unit_resolution,[status(thm)],[84,81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP175-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n002.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Aug 31 15:36:15 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.34 Usage: tptp [options] [-file:]file
% 0.11/0.34 -h, -? prints this message.
% 0.11/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.34 -m, -model generate model.
% 0.11/0.34 -p, -proof generate proof.
% 0.11/0.34 -c, -core generate unsat core of named formulas.
% 0.11/0.34 -st, -statistics display statistics.
% 0.11/0.34 -t:timeout set timeout (in second).
% 0.11/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.34 -<param>:<value> configuration parameter and value.
% 0.11/0.34 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------