TSTP Solution File: SWW218+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW218+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 20:57:56 EDT 2022
% Result : Theorem 0.40s 0.61s
% Output : Proof 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 31 ( 3 unt; 11 typ; 0 def)
% Number of atoms : 89 ( 15 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 86 ( 17 ~; 9 |; 30 &)
% ( 28 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 6 >; 8 *; 0 +; 0 <<)
% Number of predicates : 6 ( 3 usr; 3 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 15 !; 45 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
tff(v_thesis_____type,type,
v_thesis____: $o ).
tff(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(c_Groups_Ouminus__class_Ouminus_type,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(v_p_type,type,
v_p: $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(v_r_type,type,
v_r: $i ).
tff(1,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( v_thesis____
| $false )
<=> v_thesis____ ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
? [B_s: $i] :
! [B_y: $i] :
( ? [B_x: $i] :
( ? [B_z: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
& ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) ) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_As_O_AALL_Ay_O_A_IEX_Ax_O_A_IEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_G_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_096) ).
tff(4,plain,
( ? [B_s: $i] :
! [B_y: $i] :
( ? [B_x: $i] :
( ? [B_z: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
& ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) ) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) )
<=> $true ),
inference(iff_true,[status(thm)],[3]) ).
tff(5,plain,
( ~ ? [B_s: $i] :
! [B_y: $i] :
( ? [B_x: $i] :
( ? [B_z: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
& ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) ) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( ~ ? [B_s: $i] :
! [B_y: $i] :
( ? [B_x: $i] :
( ? [B_z: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
& ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) ) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) )
<=> $false ),
inference(transitivity,[status(thm)],[5,1]) ).
tff(7,plain,
( ( v_thesis____
| ~ ? [B_s: $i] :
! [B_y: $i] :
( ? [B_x: $i] :
( ? [B_z: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
& ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) ) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) ) )
<=> ( v_thesis____
| $false ) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( ( v_thesis____
| ~ ? [B_s: $i] :
! [B_y: $i] :
( ? [B_x: $i] :
( ? [B_z: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
& ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) ) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) ) )
<=> v_thesis____ ),
inference(transitivity,[status(thm)],[7,2]) ).
tff(9,plain,
( ~ ? [B_s: $i] :
! [B_y: $i] :
( ? [B_x: $i] :
( ? [B_z: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
& ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) ) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) )
<=> ~ ? [B_s: $i] :
! [B_y: $i] :
( ? [B_x: $i] :
( ? [B_z: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
& ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) ) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
( ( v_thesis____
| ~ ? [B_s: $i] :
! [B_y: $i] :
( ? [B_x: $i] :
( ? [B_z: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
& ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) ) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) ) )
<=> ( v_thesis____
| ~ ? [B_s: $i] :
! [B_y: $i] :
( ? [B_x: $i] :
( ? [B_z: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
& ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) ) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) ) ) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( ( ? [B_s: $i] :
! [B_y: $i] :
( ? [B_x: $i] :
( ? [B_z: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
& ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) ) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) )
=> v_thesis____ )
<=> ( v_thesis____
| ~ ? [B_s: $i] :
! [B_y: $i] :
( ? [B_x: $i] :
( ? [B_z: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
& ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) ) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
( ? [B_s: $i] :
! [B_y: $i] :
( ? [B_x: $i] :
( ? [B_z: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
& ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) ) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) )
=> v_thesis____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(13,plain,
( v_thesis____
| ~ ? [B_s: $i] :
! [B_y: $i] :
( ? [B_x: $i] :
( ? [B_z: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
& ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) ) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( v_thesis____
| ~ ? [B_s: $i] :
! [B_y: $i] :
( ? [B_x: $i] :
( ? [B_z: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
& ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) ) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) ) ),
inference(modus_ponens,[status(thm)],[13,10]) ).
tff(15,plain,
v_thesis____,
inference(modus_ponens,[status(thm)],[14,8]) ).
tff(16,plain,
( v_thesis____
<=> $true ),
inference(iff_true,[status(thm)],[15]) ).
tff(17,plain,
( ~ v_thesis____
<=> ~ $true ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( ~ v_thesis____
<=> $false ),
inference(transitivity,[status(thm)],[17,1]) ).
tff(19,axiom,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(20,plain,
$false,
inference(modus_ponens,[status(thm)],[19,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWW218+1 : TPTP v8.1.0. Released v5.2.0.
% 0.04/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n005.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Sep 4 12:54:33 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.36 Usage: tptp [options] [-file:]file
% 0.15/0.36 -h, -? prints this message.
% 0.15/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.36 -m, -model generate model.
% 0.15/0.36 -p, -proof generate proof.
% 0.15/0.36 -c, -core generate unsat core of named formulas.
% 0.15/0.36 -st, -statistics display statistics.
% 0.15/0.36 -t:timeout set timeout (in second).
% 0.15/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.36 -<param>:<value> configuration parameter and value.
% 0.15/0.36 -o:<output-file> file to place output in.
% 0.40/0.61 % SZS status Theorem
% 0.40/0.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------