TSTP Solution File: COM010-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COM010-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 : Tue Sep 6 18:05:46 EDT 2022
% Result : Unsatisfiable 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 23
% Syntax : Number of formulae : 43 ( 25 unt; 10 typ; 0 def)
% Number of atoms : 43 ( 41 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 6 ~; 2 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 15 ( 7 >; 8 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 22 ( 20 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
tff(v_G_type,type,
v_G: $i ).
tff(v_F_type,type,
v_F: $i ).
tff(c_UNITY_Omk__program_type,type,
c_UNITY_Omk__program: ( $i * $i ) > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Pair_type,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(tc_prod_type,type,
tc_prod: ( $i * $i ) > $i ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(c_UNITY_OAllowedActs_type,type,
c_UNITY_OAllowedActs: ( $i * $i ) > $i ).
tff(c_UNITY_OActs_type,type,
c_UNITY_OActs: ( $i * $i ) > $i ).
tff(c_UNITY_OInit_type,type,
c_UNITY_OInit: ( $i * $i ) > $i ).
tff(1,plain,
^ [T_a: $i,V_y: $i] :
refl(
( ( c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(V_y,T_a),c_Pair(c_UNITY_OActs(V_y,T_a),c_UNITY_OAllowedActs(V_y,T_a),tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a)))),tc_set(T_a),tc_prod(tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a))))),T_a) = V_y )
<=> ( c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(V_y,T_a),c_Pair(c_UNITY_OActs(V_y,T_a),c_UNITY_OAllowedActs(V_y,T_a),tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a)))),tc_set(T_a),tc_prod(tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a))))),T_a) = V_y ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [T_a: $i,V_y: $i] : ( c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(V_y,T_a),c_Pair(c_UNITY_OActs(V_y,T_a),c_UNITY_OAllowedActs(V_y,T_a),tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a)))),tc_set(T_a),tc_prod(tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a))))),T_a) = V_y )
<=> ! [T_a: $i,V_y: $i] : ( c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(V_y,T_a),c_Pair(c_UNITY_OActs(V_y,T_a),c_UNITY_OAllowedActs(V_y,T_a),tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a)))),tc_set(T_a),tc_prod(tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a))))),T_a) = V_y ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T_a: $i,V_y: $i] : ( c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(V_y,T_a),c_Pair(c_UNITY_OActs(V_y,T_a),c_UNITY_OAllowedActs(V_y,T_a),tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a)))),tc_set(T_a),tc_prod(tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a))))),T_a) = V_y )
<=> ! [T_a: $i,V_y: $i] : ( c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(V_y,T_a),c_Pair(c_UNITY_OActs(V_y,T_a),c_UNITY_OAllowedActs(V_y,T_a),tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a)))),tc_set(T_a),tc_prod(tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a))))),T_a) = V_y ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [T_a: $i,V_y: $i] : ( c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(V_y,T_a),c_Pair(c_UNITY_OActs(V_y,T_a),c_UNITY_OAllowedActs(V_y,T_a),tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a)))),tc_set(T_a),tc_prod(tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a))))),T_a) = V_y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNITY_Osurjective__mk__program_0) ).
tff(5,plain,
! [T_a: $i,V_y: $i] : ( c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(V_y,T_a),c_Pair(c_UNITY_OActs(V_y,T_a),c_UNITY_OAllowedActs(V_y,T_a),tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a)))),tc_set(T_a),tc_prod(tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a))))),T_a) = V_y ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T_a: $i,V_y: $i] : ( c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(V_y,T_a),c_Pair(c_UNITY_OActs(V_y,T_a),c_UNITY_OAllowedActs(V_y,T_a),tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a)))),tc_set(T_a),tc_prod(tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a))))),T_a) = V_y ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T_a: $i,V_y: $i] : ( c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(V_y,T_a),c_Pair(c_UNITY_OActs(V_y,T_a),c_UNITY_OAllowedActs(V_y,T_a),tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a)))),tc_set(T_a),tc_prod(tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a))))),T_a) = V_y ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(V_y,T_a),c_Pair(c_UNITY_OActs(V_y,T_a),c_UNITY_OAllowedActs(V_y,T_a),tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a)))),tc_set(T_a),tc_prod(tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a))))),T_a) = V_y )
| ( c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(v_G,t_a),c_Pair(c_UNITY_OActs(v_G,t_a),c_UNITY_OAllowedActs(v_G,t_a),tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a)))),tc_set(t_a),tc_prod(tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a))))),t_a) = v_G ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(v_G,t_a),c_Pair(c_UNITY_OActs(v_G,t_a),c_UNITY_OAllowedActs(v_G,t_a),tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a)))),tc_set(t_a),tc_prod(tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a))))),t_a) = v_G,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( c_UNITY_OAllowedActs(v_F,t_a) = c_UNITY_OAllowedActs(v_G,t_a) )
<=> ( c_UNITY_OAllowedActs(v_F,t_a) = c_UNITY_OAllowedActs(v_G,t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
c_UNITY_OAllowedActs(v_F,t_a) = c_UNITY_OAllowedActs(v_G,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(12,plain,
c_UNITY_OAllowedActs(v_F,t_a) = c_UNITY_OAllowedActs(v_G,t_a),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
c_UNITY_OAllowedActs(v_G,t_a) = c_UNITY_OAllowedActs(v_F,t_a),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
( ( c_UNITY_OActs(v_F,t_a) = c_UNITY_OActs(v_G,t_a) )
<=> ( c_UNITY_OActs(v_F,t_a) = c_UNITY_OActs(v_G,t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
c_UNITY_OActs(v_F,t_a) = c_UNITY_OActs(v_G,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(16,plain,
c_UNITY_OActs(v_F,t_a) = c_UNITY_OActs(v_G,t_a),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_UNITY_OActs(v_G,t_a) = c_UNITY_OActs(v_F,t_a),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
c_Pair(c_UNITY_OActs(v_G,t_a),c_UNITY_OAllowedActs(v_G,t_a),tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a)))) = c_Pair(c_UNITY_OActs(v_F,t_a),c_UNITY_OAllowedActs(v_F,t_a),tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a)))),
inference(monotonicity,[status(thm)],[17,13]) ).
tff(19,plain,
( ( c_UNITY_OInit(v_F,t_a) = c_UNITY_OInit(v_G,t_a) )
<=> ( c_UNITY_OInit(v_F,t_a) = c_UNITY_OInit(v_G,t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
c_UNITY_OInit(v_F,t_a) = c_UNITY_OInit(v_G,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(21,plain,
c_UNITY_OInit(v_F,t_a) = c_UNITY_OInit(v_G,t_a),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
c_UNITY_OInit(v_G,t_a) = c_UNITY_OInit(v_F,t_a),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
c_Pair(c_UNITY_OInit(v_G,t_a),c_Pair(c_UNITY_OActs(v_G,t_a),c_UNITY_OAllowedActs(v_G,t_a),tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a)))),tc_set(t_a),tc_prod(tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a))))) = c_Pair(c_UNITY_OInit(v_F,t_a),c_Pair(c_UNITY_OActs(v_F,t_a),c_UNITY_OAllowedActs(v_F,t_a),tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a)))),tc_set(t_a),tc_prod(tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a))))),
inference(monotonicity,[status(thm)],[22,18]) ).
tff(24,plain,
c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(v_G,t_a),c_Pair(c_UNITY_OActs(v_G,t_a),c_UNITY_OAllowedActs(v_G,t_a),tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a)))),tc_set(t_a),tc_prod(tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a))))),t_a) = c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(v_F,t_a),c_Pair(c_UNITY_OActs(v_F,t_a),c_UNITY_OAllowedActs(v_F,t_a),tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a)))),tc_set(t_a),tc_prod(tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a))))),t_a),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(v_F,t_a),c_Pair(c_UNITY_OActs(v_F,t_a),c_UNITY_OAllowedActs(v_F,t_a),tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a)))),tc_set(t_a),tc_prod(tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a))))),t_a) = c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(v_G,t_a),c_Pair(c_UNITY_OActs(v_G,t_a),c_UNITY_OAllowedActs(v_G,t_a),tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a)))),tc_set(t_a),tc_prod(tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a))))),t_a),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(V_y,T_a),c_Pair(c_UNITY_OActs(V_y,T_a),c_UNITY_OAllowedActs(V_y,T_a),tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a)))),tc_set(T_a),tc_prod(tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a))))),T_a) = V_y )
| ( c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(v_F,t_a),c_Pair(c_UNITY_OActs(v_F,t_a),c_UNITY_OAllowedActs(v_F,t_a),tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a)))),tc_set(t_a),tc_prod(tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a))))),t_a) = v_F ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(v_F,t_a),c_Pair(c_UNITY_OActs(v_F,t_a),c_UNITY_OAllowedActs(v_F,t_a),tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a)))),tc_set(t_a),tc_prod(tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a))))),t_a) = v_F,
inference(unit_resolution,[status(thm)],[26,7]) ).
tff(28,plain,
v_F = c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(v_F,t_a),c_Pair(c_UNITY_OActs(v_F,t_a),c_UNITY_OAllowedActs(v_F,t_a),tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a)))),tc_set(t_a),tc_prod(tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a))))),t_a),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
v_F = v_G,
inference(transitivity,[status(thm)],[28,25,9]) ).
tff(30,plain,
( ( v_F != v_G )
<=> ( v_F != v_G ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
v_F != v_G,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(32,plain,
v_F != v_G,
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
$false,
inference(unit_resolution,[status(thm)],[32,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : COM010-2 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 30 13:44:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.38 % SZS status Unsatisfiable
% 0.13/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------