TSTP Solution File: ALG350-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG350-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 16:09:53 EDT 2022
% Result : Unsatisfiable 0.22s 0.52s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 24
% Syntax : Number of formulae : 42 ( 10 unt; 8 typ; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 127 ( 59 ~; 54 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 4 >; 5 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 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_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(v_Y_____type,type,
v_Y____: $i ).
tff(v_xa_type,type,
v_xa: $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_P_type,type,
v_P: $i ).
tff(1,plain,
( ~ c_lessequals(v_xa,v_Y____,tc_RealDef_Oreal)
<=> ~ c_lessequals(v_xa,v_Y____,tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ c_lessequals(v_xa,v_Y____,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(3,plain,
~ c_lessequals(v_xa,v_Y____,tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_x: $i,V_y: $i] :
refl(
( ( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(V_x,V_y,tc_RealDef_Oreal) )
<=> ( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_x: $i,V_y: $i] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(V_x,V_y,tc_RealDef_Oreal) )
<=> ! [V_x: $i,V_y: $i] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_x: $i,V_y: $i] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(V_x,V_y,tc_RealDef_Oreal) )
<=> ! [V_x: $i,V_y: $i] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [V_x: $i,V_y: $i] :
rewrite(
( ( c_lessequals(V_x,V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) )
<=> ( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [V_x: $i,V_y: $i] :
( c_lessequals(V_x,V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) )
<=> ! [V_x: $i,V_y: $i] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_x: $i,V_y: $i] :
( c_lessequals(V_x,V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_0) ).
tff(10,plain,
! [V_x: $i,V_y: $i] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(V_x,V_y,tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_x: $i,V_y: $i] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(V_x,V_y,tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_x: $i,V_y: $i] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(V_x,V_y,tc_RealDef_Oreal) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_x: $i,V_y: $i] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(V_x,V_y,tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_x: $i,V_y: $i] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(V_x,V_y,tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_xa,v_Y____,tc_RealDef_Oreal)
| c_lessequals(v_xa,v_Y____,tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,V_y: $i] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(V_x,V_y,tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_xa,v_Y____,tc_RealDef_Oreal)
| c_lessequals(v_xa,v_Y____,tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [V_x: $i,V_y: $i] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(V_x,V_y,tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_xa,v_Y____,tc_RealDef_Oreal)
| c_lessequals(v_xa,v_Y____,tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [V_x: $i,V_y: $i] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(V_x,V_y,tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_xa,v_Y____,tc_RealDef_Oreal)
| c_lessequals(v_xa,v_Y____,tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ c_HOL_Oord__class_Oless(v_xa,v_Y____,tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( hBOOL(hAPP(v_P,v_xa))
<=> hBOOL(hAPP(v_P,v_xa)) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
hBOOL(hAPP(v_P,v_xa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(20,plain,
hBOOL(hAPP(v_P,v_xa)),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
^ [V_x: $i] :
refl(
( ( ~ hBOOL(hAPP(v_P,V_x))
| c_HOL_Oord__class_Oless(V_x,v_Y____,tc_RealDef_Oreal) )
<=> ( ~ hBOOL(hAPP(v_P,V_x))
| c_HOL_Oord__class_Oless(V_x,v_Y____,tc_RealDef_Oreal) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [V_x: $i] :
( ~ hBOOL(hAPP(v_P,V_x))
| c_HOL_Oord__class_Oless(V_x,v_Y____,tc_RealDef_Oreal) )
<=> ! [V_x: $i] :
( ~ hBOOL(hAPP(v_P,V_x))
| c_HOL_Oord__class_Oless(V_x,v_Y____,tc_RealDef_Oreal) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [V_x: $i] :
( ~ hBOOL(hAPP(v_P,V_x))
| c_HOL_Oord__class_Oless(V_x,v_Y____,tc_RealDef_Oreal) )
<=> ! [V_x: $i] :
( ~ hBOOL(hAPP(v_P,V_x))
| c_HOL_Oord__class_Oless(V_x,v_Y____,tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
^ [V_x: $i] :
rewrite(
( ( c_HOL_Oord__class_Oless(V_x,v_Y____,tc_RealDef_Oreal)
| ~ hBOOL(hAPP(v_P,V_x)) )
<=> ( ~ hBOOL(hAPP(v_P,V_x))
| c_HOL_Oord__class_Oless(V_x,v_Y____,tc_RealDef_Oreal) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [V_x: $i] :
( c_HOL_Oord__class_Oless(V_x,v_Y____,tc_RealDef_Oreal)
| ~ hBOOL(hAPP(v_P,V_x)) )
<=> ! [V_x: $i] :
( ~ hBOOL(hAPP(v_P,V_x))
| c_HOL_Oord__class_Oless(V_x,v_Y____,tc_RealDef_Oreal) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [V_x: $i] :
( c_HOL_Oord__class_Oless(V_x,v_Y____,tc_RealDef_Oreal)
| ~ hBOOL(hAPP(v_P,V_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Y_0) ).
tff(27,plain,
! [V_x: $i] :
( ~ hBOOL(hAPP(v_P,V_x))
| c_HOL_Oord__class_Oless(V_x,v_Y____,tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [V_x: $i] :
( ~ hBOOL(hAPP(v_P,V_x))
| c_HOL_Oord__class_Oless(V_x,v_Y____,tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [V_x: $i] :
( ~ hBOOL(hAPP(v_P,V_x))
| c_HOL_Oord__class_Oless(V_x,v_Y____,tc_RealDef_Oreal) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [V_x: $i] :
( ~ hBOOL(hAPP(v_P,V_x))
| c_HOL_Oord__class_Oless(V_x,v_Y____,tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [V_x: $i] :
( ~ hBOOL(hAPP(v_P,V_x))
| c_HOL_Oord__class_Oless(V_x,v_Y____,tc_RealDef_Oreal) )
| ~ hBOOL(hAPP(v_P,v_xa))
| c_HOL_Oord__class_Oless(v_xa,v_Y____,tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i] :
( ~ hBOOL(hAPP(v_P,V_x))
| c_HOL_Oord__class_Oless(V_x,v_Y____,tc_RealDef_Oreal) )
| ~ hBOOL(hAPP(v_P,v_xa))
| c_HOL_Oord__class_Oless(v_xa,v_Y____,tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ~ ! [V_x: $i] :
( ~ hBOOL(hAPP(v_P,V_x))
| c_HOL_Oord__class_Oless(V_x,v_Y____,tc_RealDef_Oreal) )
| ~ hBOOL(hAPP(v_P,v_xa))
| c_HOL_Oord__class_Oless(v_xa,v_Y____,tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [V_x: $i] :
( ~ hBOOL(hAPP(v_P,V_x))
| c_HOL_Oord__class_Oless(V_x,v_Y____,tc_RealDef_Oreal) )
| ~ hBOOL(hAPP(v_P,v_xa))
| c_HOL_Oord__class_Oless(v_xa,v_Y____,tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
$false,
inference(unit_resolution,[status(thm)],[33,30,20,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ALG350-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 29 15:55:22 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.22/0.52 % SZS status Unsatisfiable
% 0.22/0.52 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------