TSTP Solution File: SET859-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET859-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 20 05:08:25 EDT 2022
% Result : Unsatisfiable 0.46s 0.62s
% Output : Proof 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 22
% Syntax : Number of formulae : 39 ( 13 unt; 7 typ; 0 def)
% Number of atoms : 143 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 193 ( 91 ~; 85 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 3 >; 4 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 114 ( 103 !; 0 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Zorn_Osucc_type,type,
c_Zorn_Osucc: ( $i * $i * $i ) > $i ).
tff(v_n_type,type,
v_n: $i ).
tff(v_S_type,type,
v_S: $i ).
tff(v_m_type,type,
v_m: $i ).
tff(1,plain,
^ [V_x: $i,V_S: $i,T_a: $i] :
refl(
( c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a)))
<=> c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V_x: $i,V_S: $i,T_a: $i] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a)))
<=> ! [V_x: $i,V_S: $i,T_a: $i] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_x: $i,V_S: $i,T_a: $i] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a)))
<=> ! [V_x: $i,V_S: $i,T_a: $i] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [V_x: $i,V_S: $i,T_a: $i] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
tff(5,plain,
! [V_x: $i,V_S: $i,T_a: $i] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_x: $i,V_S: $i,T_a: $i] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_x: $i,V_S: $i,T_a: $i] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_x: $i,V_S: $i,T_a: $i] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a)))
| c_lessequals(v_n,c_Zorn_Osucc(v_S,v_n,t_a),tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
c_lessequals(v_n,c_Zorn_Osucc(v_S,v_n,t_a),tc_set(tc_set(t_a))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
<=> ~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(12,plain,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
<=> c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(15,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
^ [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
refl(
( ( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
<=> ( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
^ [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
trans(
monotonicity(
rewrite(
( ( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) )),
( ( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_lessequals(V_A,V_C,tc_set(T_a)) )
<=> ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a))
| c_lessequals(V_A,V_C,tc_set(T_a)) ) )),
rewrite(
( ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a))
| c_lessequals(V_A,V_C,tc_set(T_a)) )
<=> ( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) )),
( ( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_lessequals(V_A,V_C,tc_set(T_a)) )
<=> ( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_lessequals(V_A,V_C,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,axiom,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_lessequals(V_A,V_C,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__trans_0) ).
tff(22,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_n,c_Zorn_Osucc(v_S,v_n,t_a),tc_set(tc_set(t_a))) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_n,c_Zorn_Osucc(v_S,v_n,t_a),tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ( c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_n,c_Zorn_Osucc(v_S,v_n,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a))) )
<=> ( c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_n,c_Zorn_Osucc(v_S,v_n,t_a),tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_n,c_Zorn_Osucc(v_S,v_n,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a))) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_n,c_Zorn_Osucc(v_S,v_n,t_a),tc_set(tc_set(t_a))) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_n,c_Zorn_Osucc(v_S,v_n,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a))) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_n,c_Zorn_Osucc(v_S,v_n,t_a),tc_set(tc_set(t_a))) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_n,c_Zorn_Osucc(v_S,v_n,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_n,c_Zorn_Osucc(v_S,v_n,t_a),tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
$false,
inference(unit_resolution,[status(thm)],[31,25,15,12,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET859-1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 08:20:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.46/0.62 % SZS status Unsatisfiable
% 0.46/0.62 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------