TSTP Solution File: RNG010-2 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG010-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 03:17:40 EDT 2022
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 30
% Syntax : Number of formulae : 65 ( 41 unt; 8 typ; 0 def)
% Number of atoms : 83 ( 77 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 39 ( 18 ~; 5 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 4 >; 4 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 110 ( 99 !; 0 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
tff(additive_inverse_type,type,
additive_inverse: $i > $i ).
tff(associator_type,type,
associator: ( $i * $i * $i ) > $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(cz_type,type,
cz: $i ).
tff(cy_type,type,
cy: $i ).
tff(cx_type,type,
cx: $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( add(additive_inverse(X),X) = additive_identity )
<=> ( add(additive_inverse(X),X) = additive_identity ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
<=> ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
<=> ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',add_inverse) ).
tff(5,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
| ( add(additive_inverse(multiply(multiply(cx,cx),multiply(cy,cz))),multiply(multiply(cx,cx),multiply(cy,cz))) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
add(additive_inverse(multiply(multiply(cx,cx),multiply(cy,cz))),multiply(multiply(cx,cx),multiply(cy,cz))) = additive_identity,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(
( ( add(X,Y) = add(Y,X) )
<=> ( add(X,Y) = add(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(11,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)],[10]) ).
tff(12,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(13,axiom,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',commutativity_for_addition) ).
tff(14,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(multiply(multiply(cx,cx),multiply(cy,cz)),additive_inverse(multiply(multiply(cx,cx),multiply(cy,cz)))) = add(additive_inverse(multiply(multiply(cx,cx),multiply(cy,cz))),multiply(multiply(cx,cx),multiply(cy,cz))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
add(multiply(multiply(cx,cx),multiply(cy,cz)),additive_inverse(multiply(multiply(cx,cx),multiply(cy,cz)))) = add(additive_inverse(multiply(multiply(cx,cx),multiply(cy,cz))),multiply(multiply(cx,cx),multiply(cy,cz))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [Y: $i,X: $i] :
refl(
( ( multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)) )
<=> ( multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [Y: $i,X: $i] : ( multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)) )
<=> ! [Y: $i,X: $i] : ( multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [Y: $i,X: $i] : ( multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)) )
<=> ! [Y: $i,X: $i] : ( multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
! [Y: $i,X: $i] : ( multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',left_alternative) ).
tff(23,plain,
! [Y: $i,X: $i] : ( multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [Y: $i,X: $i] : ( multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)) )
| ( multiply(multiply(cx,cx),multiply(cy,cz)) = multiply(cx,multiply(cx,multiply(cy,cz))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
multiply(multiply(cx,cx),multiply(cy,cz)) = multiply(cx,multiply(cx,multiply(cy,cz))),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
multiply(cx,multiply(cx,multiply(cy,cz))) = multiply(multiply(cx,cx),multiply(cy,cz)),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
additive_inverse(multiply(cx,multiply(cx,multiply(cy,cz)))) = additive_inverse(multiply(multiply(cx,cx),multiply(cy,cz))),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
add(multiply(multiply(cx,cx),multiply(cy,cz)),additive_inverse(multiply(cx,multiply(cx,multiply(cy,cz))))) = add(multiply(multiply(cx,cx),multiply(cy,cz)),additive_inverse(multiply(multiply(cx,cx),multiply(cy,cz)))),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
<=> ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associator) ).
tff(35,plain,
! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) )
| ( associator(cx,cx,multiply(cy,cz)) = add(multiply(multiply(cx,cx),multiply(cy,cz)),additive_inverse(multiply(cx,multiply(cx,multiply(cy,cz))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
associator(cx,cx,multiply(cy,cz)) = add(multiply(multiply(cx,cx),multiply(cy,cz)),additive_inverse(multiply(cx,multiply(cx,multiply(cy,cz))))),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
associator(cx,cx,multiply(cy,cz)) = additive_identity,
inference(transitivity,[status(thm)],[39,30,18,9]) ).
tff(41,plain,
additive_inverse(associator(cx,cx,multiply(cy,cz))) = additive_inverse(additive_identity),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
additive_inverse(additive_identity) = additive_inverse(associator(cx,cx,multiply(cy,cz))),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
( ( additive_inverse(additive_identity) = additive_identity )
<=> ( additive_inverse(additive_identity) = additive_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,axiom,
additive_inverse(additive_identity) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',inverse_additive_identity) ).
tff(45,plain,
additive_inverse(additive_identity) = additive_identity,
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
additive_identity = additive_inverse(additive_identity),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
associator(cx,cx,multiply(cy,cz)) = additive_inverse(associator(cx,cx,multiply(cy,cz))),
inference(transitivity,[status(thm)],[39,30,18,9,46,42]) ).
tff(48,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( associator(Y,X,Z) != additive_inverse(associator(X,Y,Z)) )
<=> ( associator(Y,X,Z) != additive_inverse(associator(X,Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [Z: $i,Y: $i,X: $i] : ( associator(Y,X,Z) != additive_inverse(associator(X,Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( associator(Y,X,Z) != additive_inverse(associator(X,Y,Z)) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [Z: $i,Y: $i,X: $i] : ( associator(Y,X,Z) != additive_inverse(associator(X,Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( associator(Y,X,Z) != additive_inverse(associator(X,Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,axiom,
! [Z: $i,Y: $i,X: $i] : ( associator(Y,X,Z) != additive_inverse(associator(X,Y,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associator_skew_symmetry1) ).
tff(52,plain,
! [Z: $i,Y: $i,X: $i] : ( associator(Y,X,Z) != additive_inverse(associator(X,Y,Z)) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [Z: $i,Y: $i,X: $i] : ( associator(Y,X,Z) != additive_inverse(associator(X,Y,Z)) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [Z: $i,Y: $i,X: $i] : ( associator(Y,X,Z) != additive_inverse(associator(X,Y,Z)) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( associator(Y,X,Z) != additive_inverse(associator(X,Y,Z)) )
| ( associator(cx,cx,multiply(cy,cz)) != additive_inverse(associator(cx,cx,multiply(cy,cz))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
associator(cx,cx,multiply(cy,cz)) != additive_inverse(associator(cx,cx,multiply(cy,cz))),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
$false,
inference(unit_resolution,[status(thm)],[56,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG010-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 21:36:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------