TSTP Solution File: GRP010-4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP010-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 22:25:24 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 28
% Syntax : Number of formulae : 87 ( 63 unt; 5 typ; 0 def)
% Number of atoms : 111 ( 105 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 40 ( 16 ~; 9 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 67 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(c_type,type,
c: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(identity_type,type,
identity: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( multiply(inverse(X),X) = multiply(c,b) )
<=> ( multiply(inverse(X),X) = multiply(c,b) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = multiply(c,b) )
<=> ! [X: $i] : ( multiply(inverse(X),X) = multiply(c,b) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
rewrite(
( ( multiply(inverse(X),X) = identity )
<=> ( multiply(inverse(X),X) = multiply(c,b) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = multiply(c,b) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
tff(7,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i] : ( multiply(inverse(X),X) = multiply(c,b) ),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
! [X: $i] : ( multiply(inverse(X),X) = multiply(c,b) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i] : ( multiply(inverse(X),X) = multiply(c,b) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = multiply(c,b) )
| ( multiply(inverse(multiply(b,c)),multiply(b,c)) = multiply(c,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
multiply(inverse(multiply(b,c)),multiply(b,c)) = multiply(c,b),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
^ [X: $i] :
refl(
( ( multiply(multiply(c,b),X) = X )
<=> ( multiply(multiply(c,b),X) = X ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X: $i] : ( multiply(multiply(c,b),X) = X )
<=> ! [X: $i] : ( multiply(multiply(c,b),X) = X ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
^ [X: $i] :
rewrite(
( ( multiply(identity,X) = X )
<=> ( multiply(multiply(c,b),X) = X ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(multiply(c,b),X) = X ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
tff(19,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [X: $i] : ( multiply(multiply(c,b),X) = X ),
inference(modus_ponens,[status(thm)],[19,16]) ).
tff(21,plain,
! [X: $i] : ( multiply(multiply(c,b),X) = X ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [X: $i] : ( multiply(multiply(c,b),X) = X ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ~ ! [X: $i] : ( multiply(multiply(c,b),X) = X )
| ( multiply(multiply(c,b),c) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
multiply(multiply(c,b),c) = c,
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
tff(29,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(c,b),c) = multiply(c,multiply(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
multiply(multiply(c,b),c) = multiply(c,multiply(b,c)),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
multiply(c,multiply(b,c)) = multiply(multiply(c,b),c),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
multiply(c,multiply(b,c)) = c,
inference(transitivity,[status(thm)],[34,24]) ).
tff(36,plain,
multiply(multiply(c,multiply(b,c)),multiply(b,c)) = multiply(c,multiply(b,c)),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
multiply(c,multiply(b,c)) = multiply(multiply(c,multiply(b,c)),multiply(b,c)),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
c = multiply(multiply(c,b),c),
inference(symmetry,[status(thm)],[24]) ).
tff(39,plain,
c = multiply(multiply(c,multiply(b,c)),multiply(b,c)),
inference(transitivity,[status(thm)],[38,33,37]) ).
tff(40,plain,
multiply(b,c) = multiply(b,multiply(multiply(c,multiply(b,c)),multiply(b,c))),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
multiply(b,multiply(multiply(c,multiply(b,c)),multiply(b,c))) = multiply(b,c),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,multiply(c,multiply(b,c))),multiply(b,c)) = multiply(b,multiply(multiply(c,multiply(b,c)),multiply(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
multiply(multiply(b,multiply(c,multiply(b,c))),multiply(b,c)) = multiply(b,multiply(multiply(c,multiply(b,c)),multiply(b,c))),
inference(unit_resolution,[status(thm)],[42,31]) ).
tff(44,plain,
multiply(b,multiply(c,multiply(b,c))) = multiply(b,c),
inference(monotonicity,[status(thm)],[35]) ).
tff(45,plain,
multiply(multiply(b,multiply(c,multiply(b,c))),multiply(b,c)) = multiply(multiply(b,c),multiply(b,c)),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
multiply(multiply(b,c),multiply(b,c)) = multiply(multiply(b,multiply(c,multiply(b,c))),multiply(b,c)),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
multiply(multiply(b,c),multiply(b,c)) = multiply(b,c),
inference(transitivity,[status(thm)],[46,43,41]) ).
tff(48,plain,
multiply(inverse(multiply(b,c)),multiply(multiply(b,c),multiply(b,c))) = multiply(inverse(multiply(b,c)),multiply(b,c)),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(multiply(b,c)),multiply(b,c)),multiply(b,c)) = multiply(inverse(multiply(b,c)),multiply(multiply(b,c),multiply(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
multiply(multiply(inverse(multiply(b,c)),multiply(b,c)),multiply(b,c)) = multiply(inverse(multiply(b,c)),multiply(multiply(b,c),multiply(b,c))),
inference(unit_resolution,[status(thm)],[49,31]) ).
tff(51,plain,
multiply(c,b) = multiply(inverse(multiply(b,c)),multiply(b,c)),
inference(symmetry,[status(thm)],[12]) ).
tff(52,plain,
multiply(multiply(c,b),multiply(b,c)) = multiply(multiply(inverse(multiply(b,c)),multiply(b,c)),multiply(b,c)),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
multiply(b,c) = multiply(b,multiply(c,multiply(b,c))),
inference(symmetry,[status(thm)],[44]) ).
tff(54,plain,
multiply(multiply(b,c),multiply(b,c)) = multiply(multiply(b,c),multiply(b,multiply(c,multiply(b,c)))),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
multiply(multiply(b,c),multiply(b,multiply(c,multiply(b,c)))) = multiply(multiply(b,c),multiply(b,c)),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,c),b),multiply(c,multiply(b,c))) = multiply(multiply(b,c),multiply(b,multiply(c,multiply(b,c)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
multiply(multiply(multiply(b,c),b),multiply(c,multiply(b,c))) = multiply(multiply(b,c),multiply(b,multiply(c,multiply(b,c)))),
inference(unit_resolution,[status(thm)],[56,31]) ).
tff(58,plain,
multiply(multiply(b,c),b) = multiply(multiply(b,multiply(c,multiply(b,c))),b),
inference(monotonicity,[status(thm)],[53]) ).
tff(59,plain,
multiply(multiply(b,multiply(c,multiply(b,c))),b) = multiply(multiply(b,c),b),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,multiply(c,multiply(b,c))),b) = multiply(b,multiply(multiply(c,multiply(b,c)),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
multiply(multiply(b,multiply(c,multiply(b,c))),b) = multiply(b,multiply(multiply(c,multiply(b,c)),b)),
inference(unit_resolution,[status(thm)],[60,31]) ).
tff(62,plain,
multiply(b,multiply(multiply(c,multiply(b,c)),b)) = multiply(multiply(b,multiply(c,multiply(b,c))),b),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
multiply(b,multiply(multiply(c,multiply(b,c)),b)) = multiply(multiply(b,c),b),
inference(transitivity,[status(thm)],[62,59]) ).
tff(64,plain,
multiply(multiply(b,multiply(multiply(c,multiply(b,c)),b)),multiply(c,multiply(b,c))) = multiply(multiply(multiply(b,c),b),multiply(c,multiply(b,c))),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
multiply(multiply(b,multiply(multiply(c,multiply(b,c)),b)),multiply(c,multiply(b,c))) = multiply(b,c),
inference(transitivity,[status(thm)],[64,57,55,46,43,41]) ).
tff(66,plain,
multiply(multiply(c,b),multiply(multiply(b,multiply(multiply(c,multiply(b,c)),b)),multiply(c,multiply(b,c)))) = multiply(multiply(c,b),multiply(b,c)),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(c,b),multiply(b,multiply(multiply(c,multiply(b,c)),b))),multiply(c,multiply(b,c))) = multiply(multiply(c,b),multiply(multiply(b,multiply(multiply(c,multiply(b,c)),b)),multiply(c,multiply(b,c)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
multiply(multiply(multiply(c,b),multiply(b,multiply(multiply(c,multiply(b,c)),b))),multiply(c,multiply(b,c))) = multiply(multiply(c,b),multiply(multiply(b,multiply(multiply(c,multiply(b,c)),b)),multiply(c,multiply(b,c)))),
inference(unit_resolution,[status(thm)],[67,31]) ).
tff(69,plain,
( ~ ! [X: $i] : ( multiply(multiply(c,b),X) = X )
| ( multiply(multiply(c,b),multiply(b,multiply(multiply(c,multiply(b,c)),b))) = multiply(b,multiply(multiply(c,multiply(b,c)),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
multiply(multiply(c,b),multiply(b,multiply(multiply(c,multiply(b,c)),b))) = multiply(b,multiply(multiply(c,multiply(b,c)),b)),
inference(unit_resolution,[status(thm)],[69,22]) ).
tff(71,plain,
multiply(b,multiply(multiply(c,multiply(b,c)),b)) = multiply(multiply(c,b),multiply(b,multiply(multiply(c,multiply(b,c)),b))),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
multiply(multiply(b,c),b) = multiply(multiply(c,b),multiply(b,multiply(multiply(c,multiply(b,c)),b))),
inference(transitivity,[status(thm)],[58,61,71]) ).
tff(73,plain,
multiply(multiply(multiply(b,c),b),multiply(c,multiply(b,c))) = multiply(multiply(multiply(c,b),multiply(b,multiply(multiply(c,multiply(b,c)),b))),multiply(c,multiply(b,c))),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
multiply(multiply(b,c),multiply(b,multiply(c,multiply(b,c)))) = multiply(multiply(multiply(b,c),b),multiply(c,multiply(b,c))),
inference(symmetry,[status(thm)],[57]) ).
tff(75,plain,
multiply(b,multiply(multiply(c,multiply(b,c)),multiply(b,c))) = multiply(multiply(b,multiply(c,multiply(b,c))),multiply(b,c)),
inference(symmetry,[status(thm)],[43]) ).
tff(76,plain,
multiply(b,c) = multiply(c,b),
inference(transitivity,[status(thm)],[40,75,45,54,74,73,68,66,52,50,48,12]) ).
tff(77,plain,
( ( multiply(b,c) != identity )
<=> ( multiply(b,c) != multiply(c,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
( ( multiply(b,c) != identity )
<=> ( multiply(b,c) != identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,axiom,
multiply(b,c) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_times_c_is_e) ).
tff(80,plain,
multiply(b,c) != identity,
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
multiply(b,c) != multiply(c,b),
inference(modus_ponens,[status(thm)],[80,77]) ).
tff(82,plain,
$false,
inference(unit_resolution,[status(thm)],[81,76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP010-4 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.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 : Wed Aug 31 13:28:06 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.
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------