TSTP Solution File: SYO041^2 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO041^2 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 May 21 08:59:04 EDT 2024
% Result : Theorem 5.33s 2.60s
% Output : Refutation 5.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 5
% Syntax : Number of formulae : 63 ( 16 unt; 4 typ; 0 def)
% Number of atoms : 404 ( 63 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 288 ( 69 ~; 52 |; 12 &; 155 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 ^ 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(f_type,type,
f: $o > $o ).
thf(g_type,type,
g: $o > $o ).
thf(x_type,type,
x: $o ).
thf(y_type,type,
y: $o ).
thf(1,conjecture,
~ ( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',3) ).
thf(2,negated_conjecture,
~ ~ ( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ) ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(6,plain,
( ( g @ y )
= x ),
inference(cnf,[status(esa)],[4]) ).
thf(10,plain,
( ( g @ y )
= x ),
inference(lifteq,[status(thm)],[6]) ).
thf(7,plain,
( ( g @ x )
= y ),
inference(cnf,[status(esa)],[4]) ).
thf(11,plain,
( ( g @ x )
= y ),
inference(lifteq,[status(thm)],[7]) ).
thf(5,plain,
( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(9,plain,
( ( g @ ( f @ x ) )
= ( f @ ( f @ ( f @ x ) ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(28,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= y )
| ( ( g @ ( f @ x ) )
!= ( g @ x ) ) ),
inference(paramod_ordered,[status(thm)],[11,9]) ).
thf(29,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= y )
| ( ( f @ x )
!= x ) ),
inference(simp,[status(thm)],[28]) ).
thf(25,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= x )
| ( ( g @ ( f @ x ) )
!= ( g @ y ) ) ),
inference(paramod_ordered,[status(thm)],[9,10]) ).
thf(31,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= x )
| ( ( f @ x )
!= y ) ),
inference(simp,[status(thm)],[25]) ).
thf(117,plain,
( ( ( f @ x )
!= y )
| ( y = x )
| ( ( f @ x )
!= x )
| ( ( f @ ( f @ ( f @ x ) ) )
!= ( f @ ( f @ ( f @ x ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,29]) ).
thf(118,plain,
( ( ( f @ x )
!= y )
| ( y = x )
| ( ( f @ x )
!= x ) ),
inference(pattern_uni,[status(thm)],[117:[]]) ).
thf(8,plain,
x != y,
inference(cnf,[status(esa)],[4]) ).
thf(12,plain,
y != x,
inference(lifteq,[status(thm)],[8]) ).
thf(187,plain,
( ( ( f @ x )
!= y )
| ( ( f @ x )
!= x ) ),
inference(simplifyReflect,[status(thm)],[118,12]) ).
thf(192,plain,
( ( ( f @ x )
!= x )
| ( ( f @ ( f @ ( f @ x ) ) )
!= ( f @ x ) ) ),
inference(paramod_ordered,[status(thm)],[29,187]) ).
thf(196,plain,
( ( ( f @ x )
!= x )
| ( ( f @ ( f @ x ) )
!= x ) ),
inference(simp,[status(thm)],[192]) ).
thf(212,plain,
( ( ( f @ x )
!= x )
| ( ( f @ ( f @ x ) )
!= ( f @ x ) )
| ( x != x ) ),
inference(eqfactor_ordered,[status(thm)],[196]) ).
thf(216,plain,
( ( ( f @ x )
!= x )
| ( ( f @ x )
!= x ) ),
inference(simp,[status(thm)],[212]) ).
thf(222,plain,
( ( f @ x )
!= x ),
inference(simp,[status(thm)],[216]) ).
thf(227,plain,
( ( f @ x )
| x ),
inference(bool_ext,[status(thm)],[222]) ).
thf(14,plain,
( y
| x ),
inference(bool_ext,[status(thm)],[12]) ).
thf(34,plain,
( x
| ( ( g @ $true )
= x )
| ( y != y ) ),
inference(paramod_ordered,[status(thm)],[14,10]) ).
thf(35,plain,
( x
| ( ( g @ $true )
= x ) ),
inference(pattern_uni,[status(thm)],[34:[]]) ).
thf(43,plain,
( x
| ~ ( g @ $true )
| x ),
inference(bool_ext,[status(thm)],[35]) ).
thf(55,plain,
( x
| ~ ( g @ $true ) ),
inference(simp,[status(thm)],[43]) ).
thf(57,plain,
( x
| ~ ( f @ ( f @ ( f @ x ) ) )
| ( ( g @ ( f @ x ) )
!= ( g @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[9,55]) ).
thf(61,plain,
( x
| ~ ( f @ ( f @ ( f @ x ) ) )
| ~ ( f @ x ) ),
inference(simp,[status(thm)],[57]) ).
thf(65,plain,
( x
| ~ ( f @ x )
| ( ( f @ ( f @ ( f @ x ) ) )
!= ( f @ x ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[61]) ).
thf(67,plain,
( x
| ~ ( f @ x )
| ( ( f @ ( f @ x ) )
!= x ) ),
inference(simp,[status(thm)],[65]) ).
thf(69,plain,
( x
| ~ ( f @ x )
| ( f @ ( f @ x ) )
| x ),
inference(bool_ext,[status(thm)],[67]) ).
thf(70,plain,
( x
| ~ ( f @ x )
| ( f @ ( f @ x ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(72,plain,
( x
| ~ ( f @ x )
| ~ ( f @ $true )
| ( ( f @ ( f @ x ) )
!= ( f @ ( f @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[70,61]) ).
thf(73,plain,
( x
| ~ ( f @ x )
| ~ ( f @ $true ) ),
inference(pattern_uni,[status(thm)],[72:[]]) ).
thf(92,plain,
( x
| ~ ( f @ x )
| ( ( f @ ( f @ x ) )
!= ( f @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[70,73]) ).
thf(95,plain,
( x
| ~ ( f @ x )
| ~ ( f @ x ) ),
inference(simp,[status(thm)],[92]) ).
thf(98,plain,
( x
| ~ ( f @ x ) ),
inference(simp,[status(thm)],[95]) ).
thf(237,plain,
( x
| ( ( f @ x )
!= ( f @ x ) ) ),
inference(paramod_ordered,[status(thm)],[227,98]) ).
thf(238,plain,
x,
inference(pattern_uni,[status(thm)],[237:[]]) ).
thf(257,plain,
g @ y,
inference(rewrite,[status(thm)],[10,238]) ).
thf(13,plain,
( ~ y
| ~ x ),
inference(bool_ext,[status(thm)],[12]) ).
thf(259,plain,
( ~ y
| ~ $true ),
inference(rewrite,[status(thm)],[13,238]) ).
thf(260,plain,
~ y,
inference(simp,[status(thm)],[259]) ).
thf(269,plain,
g @ $false,
inference(rewrite,[status(thm)],[257,260]) ).
thf(258,plain,
( ( g @ ( f @ $true ) )
= ( f @ ( f @ ( f @ $true ) ) ) ),
inference(rewrite,[status(thm)],[9,238]) ).
thf(226,plain,
( ~ ( f @ x )
| ~ x ),
inference(bool_ext,[status(thm)],[222]) ).
thf(262,plain,
( ~ ( f @ $true )
| ~ $true ),
inference(rewrite,[status(thm)],[226,238]) ).
thf(263,plain,
~ ( f @ $true ),
inference(simp,[status(thm)],[262]) ).
thf(282,plain,
( ( g @ $false )
= ( f @ ( f @ $false ) ) ),
inference(rewrite,[status(thm)],[258,263]) ).
thf(283,plain,
f @ ( f @ $false ),
inference(rewrite,[status(thm)],[269,282]) ).
thf(289,plain,
( ( f @ ( f @ $false ) )
!= ( f @ $true ) ),
inference(paramod_ordered,[status(thm)],[283,263]) ).
thf(293,plain,
~ ( f @ $false ),
inference(simp,[status(thm)],[289]) ).
thf(298,plain,
f @ $false,
inference(rewrite,[status(thm)],[283,293]) ).
thf(301,plain,
$false,
inference(rewrite,[status(thm)],[298,293]) ).
thf(302,plain,
$false,
inference(simp,[status(thm)],[301]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SYO041^2 : TPTP v8.2.0. Released v4.1.0.
% 0.02/0.12 % Command : run_Leo-III %s %d
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon May 20 09:45:09 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.91/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/1.08 % [INFO] Parsing done (157ms).
% 1.29/1.09 % [INFO] Running in sequential loop mode.
% 1.66/1.44 % [INFO] nitpick registered as external prover.
% 1.66/1.44 % [INFO] Scanning for conjecture ...
% 1.91/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.97/1.55 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.97/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 1.97/1.56 % [INFO] Type checking passed.
% 1.97/1.56 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 5.33/2.60 % [INFO] Killing All external provers ...
% 5.33/2.60 % Time passed: 2134ms (effective reasoning time: 1504ms)
% 5.33/2.60 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 5.33/2.60 % Axioms used in derivation (0):
% 5.33/2.60 % No. of inferences in proof: 59
% 5.33/2.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2134 ms resp. 1504 ms w/o parsing
% 5.33/2.65 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.33/2.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------