TSTP Solution File: ALG044+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG044+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 16:07:29 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 34 ( 11 unt; 5 typ; 0 def)
% Number of atoms : 71 ( 64 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 74 ( 32 ~; 0 |; 29 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 3 ( 0 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(op_type,type,
op: ( $i * $i ) > $i ).
tff(e1_type,type,
e1: $i ).
tff(e3_type,type,
e3: $i ).
tff(e0_type,type,
e0: $i ).
tff(e2_type,type,
e2: $i ).
tff(1,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( op(e1,e1) = op(e1,e1) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( op(op(e1,e1),op(e1,e1)) = op(e1,op(e1,op(e1,e1))) )
<=> ( op(e1,e1) = op(e1,op(e1,op(e1,e1))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ( op(e3,e3) = op(e1,op(e1,e3)) )
<=> ( op(op(e1,e1),op(e1,e1)) = op(e1,op(e1,op(e1,e1))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ( op(e3,e3) = e0 )
<=> ( op(e3,e3) = op(e1,op(e1,e3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
( ( op(e3,e3) = e0 )
<=> ( op(e3,e3) = e0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
( ( op(e0,e0) = e0 )
& ( op(e0,e1) = e1 )
& ( op(e0,e2) = e2 )
& ( op(e0,e3) = e3 )
& ( op(e1,e0) = e1 )
& ( op(e1,e1) = e3 )
& ( op(e1,e2) = e0 )
& ( op(e1,e3) = e2 )
& ( op(e2,e0) = e2 )
& ( op(e2,e1) = e0 )
& ( op(e2,e2) = e3 )
& ( op(e2,e3) = e1 )
& ( op(e3,e0) = e3 )
& ( op(e3,e1) = e2 )
& ( op(e3,e2) = e1 )
& ( op(e3,e3) = e0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
tff(8,plain,
op(e3,e3) = e0,
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
op(e3,e3) = e0,
inference(modus_ponens,[status(thm)],[8,6]) ).
tff(10,plain,
op(e3,e3) = op(e1,op(e1,e3)),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
op(op(e1,e1),op(e1,e1)) = op(e1,op(e1,op(e1,e1))),
inference(modus_ponens,[status(thm)],[10,4]) ).
tff(12,plain,
op(e1,e1) = op(e1,op(e1,op(e1,e1))),
inference(modus_ponens,[status(thm)],[11,3]) ).
tff(13,plain,
op(e1,op(e1,op(e1,e1))) = op(e1,e1),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
( ( op(e1,op(e1,op(e1,e1))) = op(e1,e1) )
<=> ( op(e1,e1) = op(e1,e1) ) ),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
( ( op(e1,op(e1,op(e1,e1))) = op(e1,e1) )
<=> $true ),
inference(transitivity,[status(thm)],[14,2]) ).
tff(16,plain,
( ( op(e1,op(e1,op(e1,e1))) != op(e1,e1) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ( op(e1,op(e1,op(e1,e1))) != op(e1,e1) )
<=> $false ),
inference(transitivity,[status(thm)],[16,1]) ).
tff(18,plain,
( ( op(e1,op(e1,e3)) != e3 )
<=> ( op(e1,op(e1,op(e1,e1))) != op(e1,e1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ( e0 != e3 )
<=> ( op(e1,op(e1,e3)) != e3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( ( e0 != e3 )
<=> ( e0 != e3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
( ( e0 != e1 )
& ( e0 != e2 )
& ( e0 != e3 )
& ( e1 != e2 )
& ( e1 != e3 )
& ( e2 != e3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
tff(22,plain,
( ( e0 != e1 )
& ( e0 != e2 )
& ( e0 != e3 )
& ( e1 != e2 )
& ( e1 != e3 ) ),
inference(and_elim,[status(thm)],[21]) ).
tff(23,plain,
( ( e0 != e1 )
& ( e0 != e2 )
& ( e0 != e3 )
& ( e1 != e2 ) ),
inference(and_elim,[status(thm)],[22]) ).
tff(24,plain,
( ( e0 != e1 )
& ( e0 != e2 )
& ( e0 != e3 ) ),
inference(and_elim,[status(thm)],[23]) ).
tff(25,plain,
e0 != e3,
inference(and_elim,[status(thm)],[24]) ).
tff(26,plain,
e0 != e3,
inference(modus_ponens,[status(thm)],[25,20]) ).
tff(27,plain,
op(e1,op(e1,e3)) != e3,
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
op(e1,op(e1,op(e1,e1))) != op(e1,e1),
inference(modus_ponens,[status(thm)],[27,18]) ).
tff(29,plain,
$false,
inference(modus_ponens,[status(thm)],[28,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG044+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 29 13:15:45 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------