%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG199+1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 : Sat Jun 21 04:58:39 AM UTC 2025
% Result : Theorem 0.18s 0.46s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 31 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 267 ( 266 equ)
% Maximal formula atoms : 42 ( 8 avg)
% Number of connectives : 416 ( 180 ~; 144 |; 80 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(e6_type,type,
e6: $i ).
tff(op_type,type,
op: ( $i * $i ) > $i ).
tff(e5_type,type,
e5: $i ).
tff(e4_type,type,
e4: $i ).
tff(e3_type,type,
e3: $i ).
tff(e2_type,type,
e2: $i ).
tff(e1_type,type,
e1: $i ).
tff(e0_type,type,
e0: $i ).
tff(1,plain,
( ( op(e6,e6) != e6 )
<=> ( op(e6,e6) != e6 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ~ ~ ( ( op(e0,e0) != e0 )
& ( op(e1,e1) != e1 )
& ( op(e2,e2) != e2 )
& ( op(e3,e3) != e3 )
& ( op(e4,e4) != e4 )
& ( op(e5,e5) != e5 )
& ( op(e6,e6) != e6 )
& ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
& ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ) )
<=> ( ( op(e0,e0) != e0 )
& ( op(e1,e1) != e1 )
& ( op(e2,e2) != e2 )
& ( op(e3,e3) != e3 )
& ( op(e4,e4) != e4 )
& ( op(e5,e5) != e5 )
& ( op(e6,e6) != e6 )
& ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
& ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,plain,
( ~ ( ( op(e0,e0) != e0 )
& ( op(e1,e1) != e1 )
& ( op(e2,e2) != e2 )
& ( op(e3,e3) != e3 )
& ( op(e4,e4) != e4 )
& ( op(e5,e5) != e5 )
& ( op(e6,e6) != e6 )
& ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
& ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ) )
<=> ~ ( ( op(e0,e0) != e0 )
& ( op(e1,e1) != e1 )
& ( op(e2,e2) != e2 )
& ( op(e3,e3) != e3 )
& ( op(e4,e4) != e4 )
& ( op(e5,e5) != e5 )
& ( op(e6,e6) != e6 )
& ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
& ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
( ~ ~ ( ( op(e0,e0) != e0 )
& ( op(e1,e1) != e1 )
& ( op(e2,e2) != e2 )
& ( op(e3,e3) != e3 )
& ( op(e4,e4) != e4 )
& ( op(e5,e5) != e5 )
& ( op(e6,e6) != e6 )
& ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
& ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ) )
<=> ~ ~ ( ( op(e0,e0) != e0 )
& ( op(e1,e1) != e1 )
& ( op(e2,e2) != e2 )
& ( op(e3,e3) != e3 )
& ( op(e4,e4) != e4 )
& ( op(e5,e5) != e5 )
& ( op(e6,e6) != e6 )
& ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
& ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ) ) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
( ~ ~ ( ( op(e0,e0) != e0 )
& ( op(e1,e1) != e1 )
& ( op(e2,e2) != e2 )
& ( op(e3,e3) != e3 )
& ( op(e4,e4) != e4 )
& ( op(e5,e5) != e5 )
& ( op(e6,e6) != e6 )
& ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
& ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ) )
<=> ( ( op(e0,e0) != e0 )
& ( op(e1,e1) != e1 )
& ( op(e2,e2) != e2 )
& ( op(e3,e3) != e3 )
& ( op(e4,e4) != e4 )
& ( op(e5,e5) != e5 )
& ( op(e6,e6) != e6 )
& ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
& ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,axiom,
~ ~ ( ( op(e0,e0) != e0 )
& ( op(e1,e1) != e1 )
& ( op(e2,e2) != e2 )
& ( op(e3,e3) != e3 )
& ( op(e4,e4) != e4 )
& ( op(e5,e5) != e5 )
& ( op(e6,e6) != e6 )
& ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
& ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(7,plain,
( ( op(e0,e0) != e0 )
& ( op(e1,e1) != e1 )
& ( op(e2,e2) != e2 )
& ( op(e3,e3) != e3 )
& ( op(e4,e4) != e4 )
& ( op(e5,e5) != e5 )
& ( op(e6,e6) != e6 )
& ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
& ( ( op(e0,e0) != e0 )
| ( op(e1,e1) != e1 )
| ( op(e2,e2) != e2 )
| ( op(e3,e3) != e3 )
| ( op(e4,e4) != e4 )
| ( op(e5,e5) != e5 )
| ( op(e6,e6) != e6 ) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
op(e6,e6) != e6,
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
op(e6,e6) != e6,
inference(modus_ponens,[status(thm)],[8,1]) ).
tff(10,plain,
( ( op(e5,e5) != e5 )
<=> ( op(e5,e5) != e5 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
op(e5,e5) != e5,
inference(and_elim,[status(thm)],[7]) ).
tff(12,plain,
op(e5,e5) != e5,
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( ( op(e4,e4) != e4 )
<=> ( op(e4,e4) != e4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,plain,
op(e4,e4) != e4,
inference(and_elim,[status(thm)],[7]) ).
tff(15,plain,
op(e4,e4) != e4,
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( ( op(e3,e3) != e3 )
<=> ( op(e3,e3) != e3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
op(e3,e3) != e3,
inference(and_elim,[status(thm)],[7]) ).
tff(18,plain,
op(e3,e3) != e3,
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( ( op(e2,e2) != e2 )
<=> ( op(e2,e2) != e2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
op(e2,e2) != e2,
inference(and_elim,[status(thm)],[7]) ).
tff(21,plain,
op(e2,e2) != e2,
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( ( op(e1,e1) != e1 )
<=> ( op(e1,e1) != e1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
op(e1,e1) != e1,
inference(and_elim,[status(thm)],[7]) ).
tff(24,plain,
op(e1,e1) != e1,
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
( ( op(e0,e0) != e0 )
<=> ( op(e0,e0) != e0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
op(e0,e0) != e0,
inference(and_elim,[status(thm)],[7]) ).
tff(27,plain,
op(e0,e0) != e0,
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) )
<=> ( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) ),
inference(and_elim,[status(thm)],[7]) ).
tff(30,plain,
( ( op(e0,e0) = e0 )
| ( op(e1,e1) = e1 )
| ( op(e2,e2) = e2 )
| ( op(e3,e3) = e3 )
| ( op(e4,e4) = e4 )
| ( op(e5,e5) = e5 )
| ( op(e6,e6) = e6 ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
$false,
inference(unit_resolution,[status(thm)],[30,27,24,21,18,15,12,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG199+1 : TPTP v9.0.0. Released v2.7.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 10:48:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.46 % SZS status Theorem
% 0.18/0.46 % SZS output start Proof
% See solution above
% 0.18/0.49 % E exiting
%------------------------------------------------------------------------------