TSTP Solution File: RNG014-6 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG014-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 20 03:17:41 EDT 2022
% Result : Unsatisfiable 5.74s 3.93s
% Output : Proof 5.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 37
% Syntax : Number of formulae : 87 ( 58 unt; 6 typ; 0 def)
% Number of atoms : 118 ( 110 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 42 ( 12 ~; 8 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 121 ( 109 !; 0 ?; 121 :)
% Comments :
%------------------------------------------------------------------------------
tff(additive_inverse_type,type,
additive_inverse: $i > $i ).
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(additive_identity_type,type,
additive_identity: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( add(X,additive_identity) = X )
<=> ( add(X,additive_identity) = X ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( add(X,additive_identity) = X )
<=> ! [X: $i] : ( add(X,additive_identity) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( add(X,additive_identity) = X )
<=> ! [X: $i] : ( add(X,additive_identity) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( add(X,additive_identity) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_additive_identity) ).
tff(5,plain,
! [X: $i] : ( add(X,additive_identity) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( add(X,additive_identity) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( add(X,additive_identity) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( add(X,additive_identity) = X )
| ( add(additive_inverse(multiply(a,b)),additive_identity) = additive_inverse(multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
add(additive_inverse(multiply(a,b)),additive_identity) = additive_inverse(multiply(a,b)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',distribute1) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(a,add(b,additive_inverse(b))) = add(multiply(a,b),multiply(a,additive_inverse(b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
multiply(a,add(b,additive_inverse(b))) = add(multiply(a,b),multiply(a,additive_inverse(b))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [X: $i] :
refl(
( ( add(X,additive_inverse(X)) = additive_identity )
<=> ( add(X,additive_inverse(X)) = additive_identity ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
<=> ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
<=> ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_additive_inverse) ).
tff(23,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [X: $i] : ( add(X,additive_inverse(X)) = additive_identity )
| ( add(b,additive_inverse(b)) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
add(b,additive_inverse(b)) = additive_identity,
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
multiply(a,add(b,additive_inverse(b))) = multiply(a,additive_identity),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
multiply(a,additive_identity) = multiply(a,add(b,additive_inverse(b))),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
^ [X: $i] :
refl(
( ( multiply(X,additive_identity) = additive_identity )
<=> ( multiply(X,additive_identity) = additive_identity ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [X: $i] : ( multiply(X,additive_identity) = additive_identity )
<=> ! [X: $i] : ( multiply(X,additive_identity) = additive_identity ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [X: $i] : ( multiply(X,additive_identity) = additive_identity )
<=> ! [X: $i] : ( multiply(X,additive_identity) = additive_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
! [X: $i] : ( multiply(X,additive_identity) = additive_identity ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_multiplicative_zero) ).
tff(34,plain,
! [X: $i] : ( multiply(X,additive_identity) = additive_identity ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [X: $i] : ( multiply(X,additive_identity) = additive_identity ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [X: $i] : ( multiply(X,additive_identity) = additive_identity ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [X: $i] : ( multiply(X,additive_identity) = additive_identity )
| ( multiply(a,additive_identity) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
multiply(a,additive_identity) = additive_identity,
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
additive_identity = multiply(a,additive_identity),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
additive_identity = add(multiply(a,b),multiply(a,additive_inverse(b))),
inference(transitivity,[status(thm)],[39,29,18]) ).
tff(41,plain,
add(additive_inverse(multiply(a,b)),additive_identity) = add(additive_inverse(multiply(a,b)),add(multiply(a,b),multiply(a,additive_inverse(b)))),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
add(additive_inverse(multiply(a,b)),add(multiply(a,b),multiply(a,additive_inverse(b)))) = add(additive_inverse(multiply(a,b)),additive_identity),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
<=> ( add(X,add(Y,Z)) = add(add(X,Y),Z) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',associativity_for_addition) ).
tff(47,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) )
| ( add(additive_inverse(multiply(a,b)),add(multiply(a,b),multiply(a,additive_inverse(b)))) = add(add(additive_inverse(multiply(a,b)),multiply(a,b)),multiply(a,additive_inverse(b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
add(additive_inverse(multiply(a,b)),add(multiply(a,b),multiply(a,additive_inverse(b)))) = add(add(additive_inverse(multiply(a,b)),multiply(a,b)),multiply(a,additive_inverse(b))),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
add(add(additive_inverse(multiply(a,b)),multiply(a,b)),multiply(a,additive_inverse(b))) = add(additive_inverse(multiply(a,b)),add(multiply(a,b),multiply(a,additive_inverse(b)))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
^ [X: $i] :
refl(
( ( add(additive_inverse(X),X) = additive_identity )
<=> ( add(additive_inverse(X),X) = additive_identity ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
<=> ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
<=> ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,axiom,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_additive_inverse) ).
tff(57,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
( ~ ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
| ( add(additive_inverse(multiply(a,b)),multiply(a,b)) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
add(additive_inverse(multiply(a,b)),multiply(a,b)) = additive_identity,
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
add(add(additive_inverse(multiply(a,b)),multiply(a,b)),multiply(a,additive_inverse(b))) = add(additive_identity,multiply(a,additive_inverse(b))),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
add(additive_identity,multiply(a,additive_inverse(b))) = add(add(additive_inverse(multiply(a,b)),multiply(a,b)),multiply(a,additive_inverse(b))),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
^ [Y: $i,X: $i] :
refl(
( ( add(X,Y) = add(Y,X) )
<=> ( add(X,Y) = add(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
<=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
<=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).
tff(68,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(additive_identity,multiply(a,additive_inverse(b))) = add(multiply(a,additive_inverse(b)),additive_identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
add(additive_identity,multiply(a,additive_inverse(b))) = add(multiply(a,additive_inverse(b)),additive_identity),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
add(multiply(a,additive_inverse(b)),additive_identity) = add(additive_identity,multiply(a,additive_inverse(b))),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( ~ ! [X: $i] : ( add(X,additive_identity) = X )
| ( add(multiply(a,additive_inverse(b)),additive_identity) = multiply(a,additive_inverse(b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
add(multiply(a,additive_inverse(b)),additive_identity) = multiply(a,additive_inverse(b)),
inference(unit_resolution,[status(thm)],[74,7]) ).
tff(76,plain,
multiply(a,additive_inverse(b)) = add(multiply(a,additive_inverse(b)),additive_identity),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
multiply(a,additive_inverse(b)) = additive_inverse(multiply(a,b)),
inference(transitivity,[status(thm)],[76,73,63,52,42,9]) ).
tff(78,plain,
( ( multiply(a,additive_inverse(b)) != additive_inverse(multiply(a,b)) )
<=> ( multiply(a,additive_inverse(b)) != additive_inverse(multiply(a,b)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,axiom,
multiply(a,additive_inverse(b)) != additive_inverse(multiply(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
tff(80,plain,
multiply(a,additive_inverse(b)) != additive_inverse(multiply(a,b)),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
$false,
inference(unit_resolution,[status(thm)],[80,77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG014-6 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n001.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 : Fri Sep 2 21:46:39 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.
% 5.74/3.93 % SZS status Unsatisfiable
% 5.74/3.93 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------