TSTP Solution File: GRP671-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP671-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 22:29:23 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 45 ( 30 unt; 4 typ; 0 def)
% Number of atoms : 58 ( 54 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 8 ~; 4 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 46 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(unit_type,type,
unit: $i ).
tff(1,plain,
^ [A: $i] :
refl(
( ( mult(unit,A) = A )
<=> ( mult(unit,A) = A ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [A: $i] : ( mult(unit,A) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
tff(5,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
mult(unit,a) = a,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
mult(b,mult(unit,a)) = mult(b,a),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
mult(mult(unit,a),mult(b,mult(unit,a))) = mult(a,mult(b,a)),
inference(monotonicity,[status(thm)],[9,10]) ).
tff(12,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( mult(mult(A,B),mult(C,mult(A,B))) = mult(mult(mult(A,mult(B,C)),A),B) )
<=> ( mult(mult(A,B),mult(C,mult(A,B))) = mult(mult(mult(A,mult(B,C)),A),B) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,mult(A,B))) = mult(mult(mult(A,mult(B,C)),A),B) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,mult(A,B))) = mult(mult(mult(A,mult(B,C)),A),B) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,mult(A,B))) = mult(mult(mult(A,mult(B,C)),A),B) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,mult(A,B))) = mult(mult(mult(A,mult(B,C)),A),B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,mult(A,B))) = mult(mult(mult(A,mult(B,C)),A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c09) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,mult(A,B))) = mult(mult(mult(A,mult(B,C)),A),B) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,mult(A,B))) = mult(mult(mult(A,mult(B,C)),A),B) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,mult(A,B))) = mult(mult(mult(A,mult(B,C)),A),B) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,mult(A,B))) = mult(mult(mult(A,mult(B,C)),A),B) )
| ( mult(mult(unit,a),mult(b,mult(unit,a))) = mult(mult(mult(unit,mult(a,b)),unit),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(20,plain,
mult(mult(unit,a),mult(b,mult(unit,a))) = mult(mult(mult(unit,mult(a,b)),unit),a),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
mult(mult(mult(unit,mult(a,b)),unit),a) = mult(mult(unit,a),mult(b,mult(unit,a))),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
^ [A: $i] :
refl(
( ( mult(A,unit) = A )
<=> ( mult(A,unit) = A ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
! [A: $i] : ( mult(A,unit) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
tff(26,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(mult(unit,mult(a,b)),unit) = mult(unit,mult(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
mult(mult(unit,mult(a,b)),unit) = mult(unit,mult(a,b)),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
mult(unit,mult(a,b)) = mult(mult(unit,mult(a,b)),unit),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(a,b)) = mult(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
mult(unit,mult(a,b)) = mult(a,b),
inference(unit_resolution,[status(thm)],[32,7]) ).
tff(34,plain,
mult(a,b) = mult(unit,mult(a,b)),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
mult(a,b) = mult(mult(unit,mult(a,b)),unit),
inference(transitivity,[status(thm)],[34,31]) ).
tff(36,plain,
mult(mult(a,b),a) = mult(mult(mult(unit,mult(a,b)),unit),a),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
mult(mult(a,b),a) = mult(a,mult(b,a)),
inference(transitivity,[status(thm)],[36,21,11]) ).
tff(38,plain,
( ( mult(mult(a,b),a) != mult(a,mult(b,a)) )
<=> ( mult(mult(a,b),a) != mult(a,mult(b,a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
mult(mult(a,b),a) != mult(a,mult(b,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(40,plain,
mult(mult(a,b),a) != mult(a,mult(b,a)),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
$false,
inference(unit_resolution,[status(thm)],[40,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : GRP671-1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n001.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 20:12:19 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.
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------