TSTP Solution File: LAT275-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT275-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 : Sat Sep 17 18:32:36 EDT 2022
% Result : Unsatisfiable 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 21
% Syntax : Number of formulae : 32 ( 8 unt; 10 typ; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 67 ( 31 ~; 27 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 5 >; 8 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 17 ( 15 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Tarski_Opotype_Opset_type,type,
c_Tarski_Opotype_Opset: ( $i * $i * $i ) > $i ).
tff(tc_Product__Type_Ounit_type,type,
tc_Product__Type_Ounit: $i ).
tff(v_cl_type,type,
v_cl: $i ).
tff(c_Tarski_Olub_type,type,
c_Tarski_Olub: ( $i * $i * $i ) > $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(v_A_type,type,
v_A: $i ).
tff(v_S_type,type,
v_S: $i ).
tff(1,plain,
^ [V_S: $i] :
refl(
( ( ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Tarski_Olub(V_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) )
<=> ( ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Tarski_Olub(V_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V_S: $i] :
( ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Tarski_Olub(V_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) )
<=> ! [V_S: $i] :
( ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Tarski_Olub(V_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [V_S: $i] :
rewrite(
( ( ~ c_lessequals(V_S,v_A,tc_set(t_a))
| c_in(c_Tarski_Olub(V_S,v_cl,t_a),v_A,t_a) )
<=> ( ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Tarski_Olub(V_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [V_S: $i] :
( ~ c_lessequals(V_S,v_A,tc_set(t_a))
| c_in(c_Tarski_Olub(V_S,v_cl,t_a),v_A,t_a) )
<=> ! [V_S: $i] :
( ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Tarski_Olub(V_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [V_S: $i] :
( ~ c_lessequals(V_S,v_A,tc_set(t_a))
| c_in(c_Tarski_Olub(V_S,v_cl,t_a),v_A,t_a) )
<=> ! [V_S: $i] :
( ~ c_lessequals(V_S,v_A,tc_set(t_a))
| c_in(c_Tarski_Olub(V_S,v_cl,t_a),v_A,t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
! [V_S: $i] :
( ~ c_lessequals(V_S,v_A,tc_set(t_a))
| c_in(c_Tarski_Olub(V_S,v_cl,t_a),v_A,t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OS_A_60_61_AA_A_61_61_62_Alub_AS_Acl_A_58_AA_0) ).
tff(7,plain,
! [V_S: $i] :
( ~ c_lessequals(V_S,v_A,tc_set(t_a))
| c_in(c_Tarski_Olub(V_S,v_cl,t_a),v_A,t_a) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [V_S: $i] :
( ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Tarski_Olub(V_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
! [V_S: $i] :
( ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Tarski_Olub(V_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_S: $i] :
( ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Tarski_Olub(V_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ c_in(c_Tarski_Olub(v_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a)
<=> ~ c_in(c_Tarski_Olub(v_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
~ c_in(c_Tarski_Olub(v_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(13,plain,
~ c_in(c_Tarski_Olub(v_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( c_lessequals(v_S,v_A,tc_set(t_a))
<=> c_lessequals(v_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( c_lessequals(v_S,v_A,tc_set(t_a))
<=> c_lessequals(v_S,v_A,tc_set(t_a)) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
c_lessequals(v_S,v_A,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(17,plain,
c_lessequals(v_S,v_A,tc_set(t_a)),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
c_lessequals(v_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)),
inference(modus_ponens,[status(thm)],[17,14]) ).
tff(19,plain,
( ( ~ ! [V_S: $i] :
( ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Tarski_Olub(V_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) )
| ~ c_lessequals(v_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Tarski_Olub(v_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) )
<=> ( ~ ! [V_S: $i] :
( ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Tarski_Olub(V_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) )
| ~ c_lessequals(v_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Tarski_Olub(v_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( ~ ! [V_S: $i] :
( ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Tarski_Olub(V_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) )
| ~ c_lessequals(v_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Tarski_Olub(v_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
( ~ ! [V_S: $i] :
( ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Tarski_Olub(V_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) )
| ~ c_lessequals(v_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Tarski_Olub(v_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
$false,
inference(unit_resolution,[status(thm)],[21,18,13,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT275-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n010.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 : Thu Sep 1 12:50:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.18/0.37 % SZS status Unsatisfiable
% 0.18/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------