TSTP Solution File: GRP542-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP542-1 : TPTP v8.1.0. Released v2.6.0.
% 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 : Fri Sep 16 22:28:11 EDT 2022
% Result : Unsatisfiable 0.13s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 27
% Syntax : Number of formulae : 76 ( 54 unt; 6 typ; 0 def)
% Number of atoms : 94 ( 89 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 31 ( 11 ~; 7 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 4 ( 4 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 : 74 ( 67 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
tff(a2_type,type,
a2: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b2_type,type,
b2: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(1,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
<=> ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
tff(5,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(divide(inverse(b2),divide(identity,b2)),a2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))),divide(identity,a2)) = a2 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
divide(divide(identity,divide(divide(divide(divide(inverse(b2),divide(identity,b2)),a2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))),divide(identity,a2)) = a2,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [B: $i,A: $i] :
refl(
( ( multiply(A,B) = divide(A,divide(identity,B)) )
<=> ( multiply(A,B) = divide(A,divide(identity,B)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
<=> ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
<=> ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
tff(14,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
| ( multiply(inverse(b2),b2) = divide(inverse(b2),divide(identity,b2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
multiply(inverse(b2),b2) = divide(inverse(b2),divide(identity,b2)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
divide(inverse(b2),divide(identity,b2)) = multiply(inverse(b2),b2),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [A: $i] :
refl(
( ( inverse(A) = divide(identity,A) )
<=> ( inverse(A) = divide(identity,A) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [A: $i] : ( inverse(A) = divide(identity,A) )
<=> ! [A: $i] : ( inverse(A) = divide(identity,A) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [A: $i] : ( inverse(A) = divide(identity,A) )
<=> ! [A: $i] : ( inverse(A) = divide(identity,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
! [A: $i] : ( inverse(A) = divide(identity,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
tff(24,plain,
! [A: $i] : ( inverse(A) = divide(identity,A) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [A: $i] : ( inverse(A) = divide(identity,A) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [A: $i] : ( inverse(A) = divide(identity,A) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [A: $i] : ( inverse(A) = divide(identity,A) )
| ( inverse(b2) = divide(identity,b2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
inverse(b2) = divide(identity,b2),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
divide(identity,b2) = inverse(b2),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
divide(divide(identity,b2),divide(identity,b2)) = divide(inverse(b2),divide(identity,b2)),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
^ [A: $i] :
refl(
( ( identity = divide(A,A) )
<=> ( identity = divide(A,A) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [A: $i] : ( identity = divide(A,A) )
<=> ! [A: $i] : ( identity = divide(A,A) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [A: $i] : ( identity = divide(A,A) )
<=> ! [A: $i] : ( identity = divide(A,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
! [A: $i] : ( identity = divide(A,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
tff(35,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(divide(identity,b2),divide(identity,b2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
identity = divide(divide(identity,b2),divide(identity,b2)),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
identity = divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))),
inference(unit_resolution,[status(thm)],[40,37]) ).
tff(42,plain,
divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))) = identity,
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
divide(divide(identity,b2),divide(identity,b2)) = identity,
inference(symmetry,[status(thm)],[39]) ).
tff(44,plain,
divide(divide(divide(identity,b2),divide(identity,b2)),b2) = divide(identity,b2),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
divide(divide(divide(identity,b2),divide(identity,b2)),b2) = inverse(b2),
inference(transitivity,[status(thm)],[44,29]) ).
tff(46,plain,
divide(divide(divide(divide(identity,b2),divide(identity,b2)),b2),divide(identity,b2)) = divide(inverse(b2),divide(identity,b2)),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
identity = divide(inverse(b2),divide(identity,b2)),
inference(transitivity,[status(thm)],[39,30]) ).
tff(48,plain,
divide(identity,divide(divide(divide(divide(identity,b2),divide(identity,b2)),b2),divide(identity,b2))) = divide(divide(inverse(b2),divide(identity,b2)),divide(inverse(b2),divide(identity,b2))),
inference(monotonicity,[status(thm)],[47,46]) ).
tff(49,plain,
divide(inverse(b2),divide(identity,b2)) = divide(divide(divide(divide(identity,b2),divide(identity,b2)),b2),divide(identity,b2)),
inference(symmetry,[status(thm)],[46]) ).
tff(50,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(divide(identity,a2),divide(identity,a2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
identity = divide(divide(identity,a2),divide(identity,a2)),
inference(unit_resolution,[status(thm)],[50,37]) ).
tff(52,plain,
divide(divide(identity,a2),divide(identity,a2)) = identity,
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
divide(inverse(b2),divide(identity,b2)) = divide(divide(identity,b2),divide(identity,b2)),
inference(symmetry,[status(thm)],[30]) ).
tff(54,plain,
divide(inverse(b2),divide(identity,b2)) = identity,
inference(transitivity,[status(thm)],[53,43]) ).
tff(55,plain,
divide(divide(inverse(b2),divide(identity,b2)),a2) = divide(identity,a2),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
divide(divide(divide(inverse(b2),divide(identity,b2)),a2),divide(identity,a2)) = divide(divide(identity,a2),divide(identity,a2)),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
divide(divide(divide(inverse(b2),divide(identity,b2)),a2),divide(identity,a2)) = identity,
inference(transitivity,[status(thm)],[56,52]) ).
tff(58,plain,
divide(divide(divide(divide(inverse(b2),divide(identity,b2)),a2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2))) = divide(identity,divide(divide(divide(divide(identity,b2),divide(identity,b2)),b2),divide(identity,b2))),
inference(monotonicity,[status(thm)],[57,49]) ).
tff(59,plain,
divide(divide(divide(divide(inverse(b2),divide(identity,b2)),a2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2))) = divide(divide(divide(divide(identity,b2),divide(identity,b2)),b2),divide(identity,b2)),
inference(transitivity,[status(thm)],[58,48,42,39,30,49]) ).
tff(60,plain,
divide(identity,divide(divide(divide(divide(inverse(b2),divide(identity,b2)),a2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))) = divide(identity,divide(divide(divide(divide(identity,b2),divide(identity,b2)),b2),divide(identity,b2))),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
divide(identity,divide(divide(divide(divide(inverse(b2),divide(identity,b2)),a2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))) = multiply(inverse(b2),b2),
inference(transitivity,[status(thm)],[60,48,42,39,30,19]) ).
tff(62,plain,
divide(divide(identity,divide(divide(divide(divide(inverse(b2),divide(identity,b2)),a2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))),divide(identity,a2)) = divide(multiply(inverse(b2),b2),divide(identity,a2)),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
divide(multiply(inverse(b2),b2),divide(identity,a2)) = divide(divide(identity,divide(divide(divide(divide(inverse(b2),divide(identity,b2)),a2),divide(identity,a2)),divide(inverse(b2),divide(identity,b2)))),divide(identity,a2)),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
| ( multiply(multiply(inverse(b2),b2),a2) = divide(multiply(inverse(b2),b2),divide(identity,a2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
multiply(multiply(inverse(b2),b2),a2) = divide(multiply(inverse(b2),b2),divide(identity,a2)),
inference(unit_resolution,[status(thm)],[64,16]) ).
tff(66,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(transitivity,[status(thm)],[65,63,9]) ).
tff(67,plain,
( ( multiply(multiply(inverse(b2),b2),a2) != a2 )
<=> ( multiply(multiply(inverse(b2),b2),a2) != a2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
tff(69,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
$false,
inference(unit_resolution,[status(thm)],[69,66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP542-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 17:47:37 EDT 2022
% 0.13/0.33 % 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.
% 0.13/0.40 % SZS status Unsatisfiable
% 0.13/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------