%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO500^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 11:08:36 AM UTC 2026
% Result : Theorem 0.10s 0.28s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 52 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 643 ( 140 equ; 0 cnn)
% Maximal formula atoms : 4 ( 12 avg)
% Number of connectives : 326 ( 15 ~; 78 |; 0 &; 233 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_f,type,
f: $o > $o ).
thf(tp_x,type,
x: $o ).
thf(1,conjecture,
( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
!= ( f @ x ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
!= ( f @ x ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ( ( f @ ( f @ ( f @ x ) ) )
| ( f @ x ) )
| ~ ( ~ ( f @ ( f @ ( f @ x ) ) )
| ~ ( f @ x ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[6]) ).
thf(8,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( ( f @ ( f @ ( f @ x ) ) )
| ( f @ x ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ( ~ ( f @ ( f @ ( f @ x ) ) )
| ~ ( f @ x ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7]) ).
thf(11,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
| ( f @ x ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( f @ ( f @ ( f @ x ) ) )
| ~ ( f @ x ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[10]) ).
thf(13,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( ( f @ x )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ( ~ ( f @ ( f @ ( f @ x ) ) ) )
= $true )
| ( ( ~ ( f @ x ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( ~ ( f @ x ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(16,plain,
( ( ( f @ x )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(17,plain,
( ( ( f @ x )
= $true )
| ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false ) ),
inference(fac_restr,[status(thm)],[13]) ).
thf(18,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( ( f @ x )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[16]) ).
thf(20,plain,
( ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false )
| ( ( f @ x )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[17]) ).
thf(22,plain,
( ( ( ( f @ x )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[18]) ).
thf(40,plain,
( ( ( f @ x )
= $true )
| ( ( f @ ( f @ x ) )
= $false )
| ( x = $false ) ),
inference(extuni,[status(esa)],[20]) ).
thf(41,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(extuni,[status(esa)],[22]) ).
thf(42,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $false )
| ( ( f @ ( f @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[22]) ).
thf(43,plain,
( ( ( f @ ( f @ x ) )
= $true )
| ( x = $true ) ),
inference(extuni,[status(esa)],[8]) ).
thf(44,plain,
( ( ( f @ ( f @ x ) )
= $false )
| ( x = $false ) ),
inference(extuni,[status(esa)],[8]) ).
thf(48,plain,
( ( ( f @ ( f @ x ) )
= $false )
| ( x = $false ) ),
inference(extuni,[status(esa)],[8]) ).
thf(51,plain,
( ( ( f @ x )
= $true )
| ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false ) ),
inference(fac_restr,[status(thm)],[13]) ).
thf(52,plain,
( ( ( f @ ( f @ x ) )
= $true )
| ( x = $true )
| ( ( f @ x )
= $true ) ),
inference(extuni,[status(esa)],[51]) ).
thf(53,plain,
( ( ( f @ ( f @ x ) )
= $false )
| ( x = $false )
| ( ( f @ x )
= $true ) ),
inference(extuni,[status(esa)],[51]) ).
thf(54,plain,
( ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false )
| ( ( f @ x )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $true ) ),
inference(res,[status(thm)],[16,13]) ).
thf(57,plain,
( ( ( ( f @ x )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $true ) ),
inference(res,[status(thm)],[16,13]) ).
thf(58,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( ( f @ x )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[16]) ).
thf(59,plain,
( ( ( f @ x )
= $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(extuni,[status(esa)],[57]) ).
thf(60,plain,
( ( ( f @ x )
= $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $false )
| ( ( f @ ( f @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[57]) ).
thf(63,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( ( f @ x )
= $false )
| ( ( f @ ( f @ x ) )
= $true )
| ( x = $true ) ),
inference(extuni,[status(esa)],[54]) ).
thf(64,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( ( f @ x )
= $false )
| ( ( f @ ( f @ x ) )
= $false )
| ( x = $false ) ),
inference(extuni,[status(esa)],[54]) ).
thf(65,plain,
( ( x = $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(extuni,[status(esa)],[58]) ).
thf(66,plain,
( ( x = $false )
| ( ( f @ ( f @ x ) )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(extuni,[status(esa)],[58]) ).
thf(68,plain,
( ( ( ( f @ ( f @ x ) )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false )
| ( x = $true )
| ( ( f @ x )
= $false ) ),
inference(res,[status(thm)],[43,16]) ).
thf(70,plain,
( ( ( ( f @ ( f @ x ) )
= ( f @ x ) )
= $false )
| ( x = $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(res,[status(thm)],[43,16]) ).
thf(74,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( ( f @ x )
= $true )
| ( x = $true ) ),
inference(extuni,[status(esa)],[70]) ).
thf(79,plain,
( ( ( f @ x )
= $false )
| ( x = $true )
| ( ( f @ x )
= $false )
| ( ( f @ ( f @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[68]) ).
thf(80,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( ( f @ x )
= $true ) ),
inference(sim,[status(thm)],[74]) ).
thf(81,plain,
( ( ( f @ x )
= $false )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $false ) ),
inference(sim,[status(thm)],[79]) ).
thf(87,plain,
( ( ( ( f @ ( f @ x ) )
= ( f @ x ) )
= $false )
| ( x = $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $true ) ),
inference(res,[status(thm)],[44,13]) ).
thf(89,plain,
( ( ( ( f @ ( f @ x ) )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false )
| ( x = $false )
| ( ( f @ x )
= $true ) ),
inference(res,[status(thm)],[44,13]) ).
thf(93,plain,
( ( ( f @ x )
= $true )
| ( x = $false )
| ( ( f @ x )
= $true )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(extuni,[status(esa)],[89]) ).
thf(96,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( x = $false )
| ( ( f @ x )
= $false )
| ( x = $false ) ),
inference(extuni,[status(esa)],[87]) ).
thf(99,plain,
( ( ( f @ x )
= $true )
| ( x = $false )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(sim,[status(thm)],[93]) ).
thf(100,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( x = $false )
| ( ( f @ x )
= $false ) ),
inference(sim,[status(thm)],[96]) ).
thf(101,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[8,100,99,81,80,66,65,64,63,60,59,53,52,48,44,43,42,41,40,16,13]) ).
thf(102,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO500^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.18 % Computer : n013.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 17:41:06 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.28
% 0.10/0.28 No.of.Axioms: 0
% 0.10/0.28
% 0.10/0.28 Length.of.Defs: 0
% 0.10/0.28
% 0.10/0.28 Contains.Choice.Funs: false
% 0.10/0.28 .
% 0.10/0.28
% 0.10/0.28 ********************************
% 0.10/0.28 * All subproblems solved! *
% 0.10/0.28 ********************************
% 0.10/0.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:101,loop_count:10,foatp_calls:4,translation:fof_full)
% 0.10/0.28
% 0.10/0.28 %**** Beginning of derivation protocol ****
% 0.10/0.28 % SZS output start CNFRefutation
% See solution above
% 0.10/0.28
% 0.10/0.28 %**** End of derivation protocol ****
% 0.10/0.28 %**** no. of clauses in derivation: 52 ****
% 0.10/0.28 %**** clause counter: 101 ****
% 0.10/0.28
% 0.10/0.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:101,loop_count:10,foatp_calls:4,translation:fof_full)
%------------------------------------------------------------------------------