TSTP Solution File: CSR031+4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CSR031+4 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 14:27:12 EDT 2022
% Result : Theorem 16.60s 11.77s
% Output : Proof 17.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 22
% Syntax : Number of formulae : 41 ( 11 unt; 5 typ; 0 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 164 ( 86 ~; 48 |; 9 &)
% ( 18 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 3 >; 1 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 51 ( 45 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
tff(collection_type,type,
collection: $i > $o ).
tff(c_tptptptpcol_16_8398_type,type,
c_tptptptpcol_16_8398: $i ).
tff(individual_type,type,
individual: $i > $o ).
tff(disjointwith_type,type,
disjointwith: ( $i * $i ) > $o ).
tff(c_tptpcol_16_18488_type,type,
c_tptpcol_16_18488: $i ).
tff(1,plain,
( individual(c_tptptptpcol_16_8398)
<=> individual(c_tptptptpcol_16_8398) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
individual(c_tptptptpcol_16_8398),
file('/export/starexec/sandbox/benchmark/Axioms/CSR002+3.ax',ax3_20191) ).
tff(3,plain,
individual(c_tptptptpcol_16_8398),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [OBJ: $i] :
refl(
( ( ~ collection(OBJ)
| ~ individual(OBJ) )
<=> ( ~ collection(OBJ)
| ~ individual(OBJ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [OBJ: $i] :
( ~ collection(OBJ)
| ~ individual(OBJ) )
<=> ! [OBJ: $i] :
( ~ collection(OBJ)
| ~ individual(OBJ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
^ [OBJ: $i] :
trans(
monotonicity(
rewrite(
( ( collection(OBJ)
& individual(OBJ) )
<=> ~ ( ~ collection(OBJ)
| ~ individual(OBJ) ) )),
( ~ ( collection(OBJ)
& individual(OBJ) )
<=> ~ ~ ( ~ collection(OBJ)
| ~ individual(OBJ) ) )),
rewrite(
( ~ ~ ( ~ collection(OBJ)
| ~ individual(OBJ) )
<=> ( ~ collection(OBJ)
| ~ individual(OBJ) ) )),
( ~ ( collection(OBJ)
& individual(OBJ) )
<=> ( ~ collection(OBJ)
| ~ individual(OBJ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [OBJ: $i] :
~ ( collection(OBJ)
& individual(OBJ) )
<=> ! [OBJ: $i] :
( ~ collection(OBJ)
| ~ individual(OBJ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [OBJ: $i] :
~ ( collection(OBJ)
& individual(OBJ) )
<=> ! [OBJ: $i] :
~ ( collection(OBJ)
& individual(OBJ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
! [OBJ: $i] :
~ ( collection(OBJ)
& individual(OBJ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR002+3.ax',ax3_4028) ).
tff(10,plain,
! [OBJ: $i] :
~ ( collection(OBJ)
& individual(OBJ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [OBJ: $i] :
~ ( collection(OBJ)
& individual(OBJ) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [OBJ: $i] :
( ~ collection(OBJ)
| ~ individual(OBJ) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
! [OBJ: $i] :
( ~ collection(OBJ)
| ~ individual(OBJ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [OBJ: $i] :
( ~ collection(OBJ)
| ~ individual(OBJ) )
| ~ collection(c_tptptptpcol_16_8398)
| ~ individual(c_tptptptpcol_16_8398) )
<=> ( ~ ! [OBJ: $i] :
( ~ collection(OBJ)
| ~ individual(OBJ) )
| ~ collection(c_tptptptpcol_16_8398)
| ~ individual(c_tptptptpcol_16_8398) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [OBJ: $i] :
( ~ collection(OBJ)
| ~ individual(OBJ) )
| ~ collection(c_tptptptpcol_16_8398)
| ~ individual(c_tptptptpcol_16_8398) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [OBJ: $i] :
( ~ collection(OBJ)
| ~ individual(OBJ) )
| ~ collection(c_tptptptpcol_16_8398)
| ~ individual(c_tptptptpcol_16_8398) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ collection(c_tptptptpcol_16_8398),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488)
<=> disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ~ ~ disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488)
<=> disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
~ ~ disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',query181) ).
tff(21,plain,
disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,plain,
^ [INS: $i,ARG2: $i] :
refl(
( ( collection(INS)
| ~ disjointwith(INS,ARG2) )
<=> ( collection(INS)
| ~ disjointwith(INS,ARG2) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) )
<=> ! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) )
<=> ! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
^ [INS: $i,ARG2: $i] :
rewrite(
( ( disjointwith(INS,ARG2)
=> collection(INS) )
<=> ( collection(INS)
| ~ disjointwith(INS,ARG2) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [INS: $i,ARG2: $i] :
( disjointwith(INS,ARG2)
=> collection(INS) )
<=> ! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,axiom,
! [INS: $i,ARG2: $i] :
( disjointwith(INS,ARG2)
=> collection(INS) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR002+3.ax',ax3_41385) ).
tff(29,plain,
! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) ),
inference(modus_ponens,[status(thm)],[31,24]) ).
tff(33,plain,
( ( ~ ! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) )
| collection(c_tptptptpcol_16_8398)
| ~ disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488) )
<=> ( ~ ! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) )
| collection(c_tptptptpcol_16_8398)
| ~ disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ~ ! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) )
| collection(c_tptptptpcol_16_8398)
| ~ disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
( ~ ! [INS: $i,ARG2: $i] :
( collection(INS)
| ~ disjointwith(INS,ARG2) )
| collection(c_tptptptpcol_16_8398)
| ~ disjointwith(c_tptptptpcol_16_8398,c_tptpcol_16_18488) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
$false,
inference(unit_resolution,[status(thm)],[35,32,22,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CSR031+4 : TPTP v8.1.0. Released v3.4.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n017.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 : Tue Aug 30 16:12:50 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.21/0.35 Usage: tptp [options] [-file:]file
% 0.21/0.35 -h, -? prints this message.
% 0.21/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.21/0.35 -m, -model generate model.
% 0.21/0.35 -p, -proof generate proof.
% 0.21/0.35 -c, -core generate unsat core of named formulas.
% 0.21/0.35 -st, -statistics display statistics.
% 0.21/0.35 -t:timeout set timeout (in second).
% 0.21/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.21/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.21/0.35 -<param>:<value> configuration parameter and value.
% 0.21/0.35 -o:<output-file> file to place output in.
% 16.60/11.77 % SZS status Theorem
% 16.60/11.77 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------