TSTP Solution File: GRP702-12 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP702-12 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 22:29:31 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 26
% Syntax : Number of formulae : 62 ( 41 unt; 7 typ; 0 def)
% Number of atoms : 77 ( 72 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 9 ~; 5 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 65 !; 0 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(x1_type,type,
x1: $i ).
tff(op_d_type,type,
op_d: $i ).
tff(x0_type,type,
x0: $i ).
tff(op_c_type,type,
op_c: $i ).
tff(rd_type,type,
rd: ( $i * $i ) > $i ).
tff(ld_type,type,
ld: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(
( ( rd(mult(A,B),B) = A )
<=> ( rd(mult(A,B),B) = A ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
tff(5,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(op_d,op_d),op_d) = op_d ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
rd(mult(op_d,op_d),op_d) = op_d,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [A: $i] :
refl(
( ( op_d = ld(A,mult(op_c,A)) )
<=> ( op_d = ld(A,mult(op_c,A)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [A: $i] : ( op_d = ld(A,mult(op_c,A)) )
<=> ! [A: $i] : ( op_d = ld(A,mult(op_c,A)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [A: $i] : ( op_d = ld(A,mult(op_c,A)) )
<=> ! [A: $i] : ( op_d = ld(A,mult(op_c,A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [A: $i] : ( op_d = ld(A,mult(op_c,A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f11) ).
tff(14,plain,
! [A: $i] : ( op_d = ld(A,mult(op_c,A)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [A: $i] : ( op_d = ld(A,mult(op_c,A)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [A: $i] : ( op_d = ld(A,mult(op_c,A)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [A: $i] : ( op_d = ld(A,mult(op_c,A)) )
| ( op_d = ld(op_d,mult(op_c,op_d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
op_d = ld(op_d,mult(op_c,op_d)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
mult(op_d,op_d) = mult(op_d,ld(op_d,mult(op_c,op_d))),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
mult(op_d,ld(op_d,mult(op_c,op_d))) = mult(op_d,op_d),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
^ [B: $i,A: $i] :
refl(
( ( mult(A,ld(A,B)) = B )
<=> ( mult(A,ld(A,B)) = B ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
<=> ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
<=> ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
tff(25,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
| ( mult(op_d,ld(op_d,mult(op_c,op_d))) = mult(op_c,op_d) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
mult(op_d,ld(op_d,mult(op_c,op_d))) = mult(op_c,op_d),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
mult(op_c,op_d) = mult(op_d,ld(op_d,mult(op_c,op_d))),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
mult(op_c,op_d) = mult(op_d,op_d),
inference(transitivity,[status(thm)],[30,20]) ).
tff(32,plain,
rd(mult(op_c,op_d),op_d) = rd(mult(op_d,op_d),op_d),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(op_c,op_d),op_d) = op_c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
rd(mult(op_c,op_d),op_d) = op_c,
inference(unit_resolution,[status(thm)],[33,7]) ).
tff(35,plain,
op_c = rd(mult(op_c,op_d),op_d),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
op_c = op_d,
inference(transitivity,[status(thm)],[35,32,9]) ).
tff(37,plain,
mult(x0,op_c) = mult(x0,op_d),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
mult(mult(x0,op_c),x1) = mult(mult(x0,op_d),x1),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
^ [B: $i,A: $i] :
refl(
( ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) )
<=> ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) )
<=> ! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) )
<=> ! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f10) ).
tff(43,plain,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) )
| ( mult(x0,mult(op_c,x1)) = mult(mult(x0,op_c),x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
mult(x0,mult(op_c,x1)) = mult(mult(x0,op_c),x1),
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
mult(op_c,x1) = mult(op_d,x1),
inference(monotonicity,[status(thm)],[36]) ).
tff(49,plain,
mult(op_d,x1) = mult(op_c,x1),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
mult(x0,mult(op_d,x1)) = mult(x0,mult(op_c,x1)),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
mult(x0,mult(op_d,x1)) = mult(mult(x0,op_d),x1),
inference(transitivity,[status(thm)],[50,47,38]) ).
tff(52,plain,
( ( mult(x0,mult(op_d,x1)) != mult(mult(x0,op_d),x1) )
<=> ( mult(x0,mult(op_d,x1)) != mult(mult(x0,op_d),x1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
mult(x0,mult(op_d,x1)) != mult(mult(x0,op_d),x1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
tff(54,plain,
mult(x0,mult(op_d,x1)) != mult(mult(x0,op_d),x1),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
$false,
inference(unit_resolution,[status(thm)],[54,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP702-12 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n028.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 : Wed Aug 31 20:24:20 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.
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------