TSTP Solution File: GRP679-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP679-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 22:29:25 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 27
% Syntax : Number of formulae : 67 ( 45 unt; 5 typ; 0 def)
% Number of atoms : 87 ( 82 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 33 ( 12 ~; 8 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 4 ( 4 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 : 77 ( 70 !; 0 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(op_c_type,type,
op_c: $i ).
tff(a_type,type,
a: $i ).
tff(ld_type,type,
ld: ( $i * $i ) > $i ).
tff(unit_type,type,
unit: $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(
( ( ld(A,mult(A,B)) = B )
<=> ( ld(A,mult(A,B)) = B ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
<=> ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
<=> ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
tff(5,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(op_c,mult(op_c,mult(a,mult(op_c,op_c)))) = mult(a,mult(op_c,op_c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
ld(op_c,mult(op_c,mult(a,mult(op_c,op_c)))) = mult(a,mult(op_c,op_c)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,axiom,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c08) ).
tff(14,plain,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,mult(mult(op_c,op_c),a)) = mult(mult(mult(op_c,op_c),a),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
mult(op_c,mult(mult(op_c,op_c),a)) = mult(mult(mult(op_c,op_c),a),op_c),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
mult(mult(mult(op_c,op_c),a),op_c) = mult(op_c,mult(mult(op_c,op_c),a)),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [A: $i] :
refl(
( ( mult(unit,A) = A )
<=> ( mult(unit,A) = A ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
! [A: $i] : ( mult(unit,A) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
tff(24,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,op_c) = op_c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
mult(unit,op_c) = op_c,
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
mult(op_c,mult(unit,op_c)) = mult(op_c,op_c),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
mult(mult(op_c,mult(unit,op_c)),a) = mult(mult(op_c,op_c),a),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
<=> ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
tff(35,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(op_c,mult(unit,mult(op_c,a))) = mult(mult(op_c,mult(unit,op_c)),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
mult(op_c,mult(unit,mult(op_c,a))) = mult(mult(op_c,mult(unit,op_c)),a),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(op_c,a)) = mult(op_c,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
mult(unit,mult(op_c,a)) = mult(op_c,a),
inference(unit_resolution,[status(thm)],[40,26]) ).
tff(42,plain,
mult(op_c,a) = mult(unit,mult(op_c,a)),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,a) = mult(a,op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
mult(op_c,a) = mult(a,op_c),
inference(unit_resolution,[status(thm)],[43,16]) ).
tff(45,plain,
mult(a,op_c) = mult(op_c,a),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
mult(a,op_c) = mult(unit,mult(op_c,a)),
inference(transitivity,[status(thm)],[45,42]) ).
tff(47,plain,
mult(op_c,mult(a,op_c)) = mult(op_c,mult(unit,mult(op_c,a))),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
mult(op_c,mult(a,op_c)) = mult(mult(op_c,op_c),a),
inference(transitivity,[status(thm)],[47,39,30]) ).
tff(49,plain,
mult(mult(op_c,mult(a,op_c)),op_c) = mult(mult(mult(op_c,op_c),a),op_c),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(op_c,mult(a,mult(op_c,op_c))) = mult(mult(op_c,mult(a,op_c)),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
mult(op_c,mult(a,mult(op_c,op_c))) = mult(mult(op_c,mult(a,op_c)),op_c),
inference(unit_resolution,[status(thm)],[50,37]) ).
tff(52,plain,
mult(op_c,mult(a,mult(op_c,op_c))) = mult(op_c,mult(mult(op_c,op_c),a)),
inference(transitivity,[status(thm)],[51,49,19]) ).
tff(53,plain,
ld(op_c,mult(op_c,mult(a,mult(op_c,op_c)))) = ld(op_c,mult(op_c,mult(mult(op_c,op_c),a))),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
ld(op_c,mult(op_c,mult(mult(op_c,op_c),a))) = ld(op_c,mult(op_c,mult(a,mult(op_c,op_c)))),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(op_c,mult(op_c,mult(mult(op_c,op_c),a))) = mult(mult(op_c,op_c),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
ld(op_c,mult(op_c,mult(mult(op_c,op_c),a))) = mult(mult(op_c,op_c),a),
inference(unit_resolution,[status(thm)],[55,7]) ).
tff(57,plain,
mult(mult(op_c,op_c),a) = ld(op_c,mult(op_c,mult(mult(op_c,op_c),a))),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
mult(mult(op_c,op_c),a) = mult(a,mult(op_c,op_c)),
inference(transitivity,[status(thm)],[57,54,9]) ).
tff(59,plain,
( ( mult(mult(op_c,op_c),a) != mult(a,mult(op_c,op_c)) )
<=> ( mult(mult(op_c,op_c),a) != mult(a,mult(op_c,op_c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,axiom,
mult(mult(op_c,op_c),a) != mult(a,mult(op_c,op_c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(61,plain,
mult(mult(op_c,op_c),a) != mult(a,mult(op_c,op_c)),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
$false,
inference(unit_resolution,[status(thm)],[61,58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP679-1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n004.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 19:56:49 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.
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------