TSTP Solution File: SWV689-1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV689-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 : Thu Sep 29 15:24:05 EDT 2022
% Result : Unsatisfiable 0.50s 0.62s
% Output : Proof 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 16
% Syntax : Number of formulae : 26 ( 7 unt; 6 typ; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 66 ( 31 ~; 27 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 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 : 6 ( 2 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 51 ( 45 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(v_n_type,type,
v_n: $i ).
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(v_k_type,type,
v_k: $i ).
tff(v_i_type,type,
v_i: $i ).
tff(1,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat)
<=> ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(3,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_HOL_Oord__class_Oless(v_i,v_n,tc_nat)
<=> c_HOL_Oord__class_Oless(v_i,v_n,tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_assms_0) ).
tff(6,plain,
c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V_n: $i,V_j: $i,V_k: $i] :
refl(
( ( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) )
<=> ( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) )
<=> ! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) )
<=> ! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
^ [V_n: $i,V_j: $i,V_k: $i] :
rewrite(
( ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) )
<=> ( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [V_n: $i,V_j: $i,V_k: $i] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) )
<=> ! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [V_n: $i,V_j: $i,V_k: $i] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
tff(13,plain,
! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) )
| ~ c_HOL_Oord__class_Oless(v_i,v_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat) )
<=> ( ~ ! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) )
| ~ c_HOL_Oord__class_Oless(v_i,v_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) )
| ~ c_HOL_Oord__class_Oless(v_i,v_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) )
| ~ c_HOL_Oord__class_Oless(v_i,v_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
$false,
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV689-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n022.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 : Sun Sep 4 07:04:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.35 Usage: tptp [options] [-file:]file
% 0.20/0.35 -h, -? prints this message.
% 0.20/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.35 -m, -model generate model.
% 0.20/0.35 -p, -proof generate proof.
% 0.20/0.35 -c, -core generate unsat core of named formulas.
% 0.20/0.35 -st, -statistics display statistics.
% 0.20/0.35 -t:timeout set timeout (in second).
% 0.20/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.35 -<param>:<value> configuration parameter and value.
% 0.20/0.35 -o:<output-file> file to place output in.
% 0.50/0.62 % SZS status Unsatisfiable
% 0.50/0.62 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------