TSTP Solution File: GRP665-12 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP665-12 : TPTP v8.1.0. Released v8.1.0.
% 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 22:29:20 EDT 2022
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 21
% Syntax : Number of formulae : 49 ( 32 unt; 5 typ; 0 def)
% Number of atoms : 62 ( 58 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 9 ~; 5 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 56 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(op_c_type,type,
op_c: $i ).
tff(x1_type,type,
x1: $i ).
tff(x0_type,type,
x0: $i ).
tff(rd_type,type,
rd: ( $i * $i ) > $i ).
tff(1,plain,
^ [A: $i] :
refl(
( ( mult(op_c,A) = mult(A,op_c) )
<=> ( mult(op_c,A) = mult(A,op_c) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
<=> ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
<=> ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
tff(5,plain,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,x1) = mult(x1,op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
mult(op_c,x1) = mult(x1,op_c),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
mult(x1,op_c) = mult(op_c,x1),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,x0) = mult(x0,op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
mult(op_c,x0) = mult(x0,op_c),
inference(unit_resolution,[status(thm)],[11,7]) ).
tff(13,plain,
rd(mult(op_c,x0),op_c) = rd(mult(x0,op_c),op_c),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
rd(mult(x0,op_c),op_c) = rd(mult(op_c,x0),op_c),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
^ [B: $i,A: $i] :
refl(
( ( rd(mult(A,B),B) = A )
<=> ( rd(mult(A,B),B) = A ) )),
inference(bind,[status(th)],]) ).
tff(16,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)],[15]) ).
tff(17,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(18,axiom,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
tff(19,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(x0,op_c),op_c) = x0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(23,plain,
rd(mult(x0,op_c),op_c) = x0,
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
x0 = rd(mult(x0,op_c),op_c),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
x0 = rd(mult(op_c,x0),op_c),
inference(transitivity,[status(thm)],[24,14]) ).
tff(26,plain,
mult(x0,mult(x1,op_c)) = mult(rd(mult(op_c,x0),op_c),mult(op_c,x1)),
inference(monotonicity,[status(thm)],[25,10]) ).
tff(27,plain,
mult(rd(mult(op_c,x0),op_c),mult(op_c,x1)) = mult(x0,mult(x1,op_c)),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) )
<=> ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
tff(32,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) )
| ( mult(op_c,mult(x0,x1)) = mult(rd(mult(op_c,x0),op_c),mult(op_c,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
mult(op_c,mult(x0,x1)) = mult(rd(mult(op_c,x0),op_c),mult(op_c,x1)),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,mult(x0,x1)) = mult(mult(x0,x1),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
mult(op_c,mult(x0,x1)) = mult(mult(x0,x1),op_c),
inference(unit_resolution,[status(thm)],[37,7]) ).
tff(39,plain,
mult(mult(x0,x1),op_c) = mult(op_c,mult(x0,x1)),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
mult(mult(x0,x1),op_c) = mult(x0,mult(x1,op_c)),
inference(transitivity,[status(thm)],[39,36,27]) ).
tff(41,plain,
( ( mult(mult(x0,x1),op_c) != mult(x0,mult(x1,op_c)) )
<=> ( mult(mult(x0,x1),op_c) != mult(x0,mult(x1,op_c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
mult(mult(x0,x1),op_c) != mult(x0,mult(x1,op_c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(43,plain,
mult(mult(x0,x1),op_c) != mult(x0,mult(x1,op_c)),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
$false,
inference(unit_resolution,[status(thm)],[43,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP665-12 : 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 : n017.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 19:06:06 EDT 2022
% 0.12/0.34 % 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.
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------