%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO040^2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 11:07:26 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 36 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 458 ( 106 equ; 0 cnn)
% Maximal formula atoms : 4 ( 12 avg)
% Number of connectives : 224 ( 2 ~; 58 |; 0 &; 164 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_f,type,
f: $o > $o ).
thf(tp_h,type,
h: $o > $i ).
thf(tp_x,type,
x: $o ).
thf(1,conjecture,
( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
= ( h @ ( f @ x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',2) ).
thf(2,negated_conjecture,
( ( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
= ( h @ ( f @ x ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
= ( h @ ( f @ x ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
!= ( h @ ( f @ x ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
!= ( h @ ( f @ x ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
= ( h @ ( f @ x ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5]) ).
thf(7,plain,
( ( ( f @ ( f @ x ) )
= $true )
| ( x = $true ) ),
inference(extuni,[status(esa)],[6]) ).
thf(8,plain,
( ( ( f @ ( f @ x ) )
= $false )
| ( x = $false ) ),
inference(extuni,[status(esa)],[6]) ).
thf(9,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( ( f @ x )
= $true ) ),
inference(extuni,[status(esa)],[6]) ).
thf(10,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $false ) ),
inference(extuni,[status(esa)],[6]) ).
thf(27,plain,
( ( ( ( f @ x )
= ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( x = $false ) ),
inference(res,[status(thm)],[9,8]) ).
thf(28,plain,
( ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $true )
| ( x = $false ) ),
inference(res,[status(thm)],[9,8]) ).
thf(31,plain,
( ( ( f @ x )
= $true )
| ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false ) ),
inference(fac_restr,[status(thm)],[9]) ).
thf(34,plain,
( ( x = $false )
| ( ( f @ x )
= $true )
| ( ( f @ ( f @ x ) )
= $true )
| ( ( f @ x )
= $true ) ),
inference(extuni,[status(esa)],[28]) ).
thf(37,plain,
( ( x = $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( x = $false )
| ( ( f @ x )
= $false ) ),
inference(extuni,[status(esa)],[27]) ).
thf(38,plain,
( ( ( f @ ( f @ x ) )
= $true )
| ( x = $true )
| ( ( f @ x )
= $true ) ),
inference(extuni,[status(esa)],[31]) ).
thf(39,plain,
( ( ( f @ ( f @ x ) )
= $false )
| ( x = $false )
| ( ( f @ x )
= $true ) ),
inference(extuni,[status(esa)],[31]) ).
thf(40,plain,
( ( x = $false )
| ( ( f @ x )
= $true )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(sim,[status(thm)],[34]) ).
thf(41,plain,
( ( x = $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( ( f @ x )
= $false ) ),
inference(sim,[status(thm)],[37]) ).
thf(43,plain,
( ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false )
| ( ( f @ x )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $true ) ),
inference(res,[status(thm)],[10,9]) ).
thf(44,plain,
( ( ( ( f @ x )
= ( f @ ( f @ ( f @ x ) ) ) )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $true ) ),
inference(res,[status(thm)],[10,9]) ).
thf(48,plain,
( ( ( ( f @ x )
= ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true ) ),
inference(res,[status(thm)],[10,7]) ).
thf(49,plain,
( ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $false )
| ( x = $true ) ),
inference(res,[status(thm)],[10,7]) ).
thf(50,plain,
( ( ( f @ x )
= $false )
| ( ( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) )
= $false ) ),
inference(fac_restr,[status(thm)],[10]) ).
thf(54,plain,
( ( x = $true )
| ( ( f @ x )
= $false )
| ( ( f @ ( f @ x ) )
= $false )
| ( ( f @ x )
= $false ) ),
inference(extuni,[status(esa)],[49]) ).
thf(55,plain,
( ( x = $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( ( f @ x )
= $true ) ),
inference(extuni,[status(esa)],[48]) ).
thf(58,plain,
( ( ( f @ x )
= $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $true )
| ( ( f @ ( f @ x ) )
= $true ) ),
inference(extuni,[status(esa)],[44]) ).
thf(59,plain,
( ( ( f @ x )
= $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( x = $false )
| ( ( f @ ( f @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[44]) ).
thf(60,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( ( f @ x )
= $false )
| ( ( f @ ( f @ x ) )
= $true )
| ( x = $true ) ),
inference(extuni,[status(esa)],[43]) ).
thf(61,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( ( f @ x )
= $false )
| ( ( f @ ( f @ x ) )
= $false )
| ( x = $false ) ),
inference(extuni,[status(esa)],[43]) ).
thf(63,plain,
( ( ( f @ ( f @ x ) )
= $true )
| ( x = $true )
| ( ( f @ x )
= $false ) ),
inference(extuni,[status(esa)],[50]) ).
thf(64,plain,
( ( ( f @ ( f @ x ) )
= $false )
| ( x = $false )
| ( ( f @ x )
= $false ) ),
inference(extuni,[status(esa)],[50]) ).
thf(65,plain,
( ( x = $true )
| ( ( f @ x )
= $false )
| ( ( f @ ( f @ x ) )
= $false ) ),
inference(sim,[status(thm)],[54]) ).
thf(66,plain,
( ( x = $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ( ( f @ x )
= $true ) ),
inference(sim,[status(thm)],[55]) ).
thf(67,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[6,66,65,64,63,61,60,59,58,41,40,39,38,10,9,8,7]) ).
thf(68,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO040^2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n020.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Oct 6 17:31:51 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.23
% 0.08/0.23 No.of.Axioms: 0
% 0.08/0.23
% 0.08/0.23 Length.of.Defs: 0
% 0.08/0.23
% 0.08/0.23 Contains.Choice.Funs: false
% 0.08/0.23 .
% 0.08/0.23
% 0.08/0.23 ********************************
% 0.08/0.23 * All subproblems solved! *
% 0.08/0.23 ********************************
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox/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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:67,loop_count:10,foatp_calls:4,translation:fof_full)
% 0.08/0.23
% 0.08/0.23 %**** Beginning of derivation protocol ****
% 0.08/0.23 % SZS output start CNFRefutation
% See solution above
% 0.08/0.23
% 0.08/0.23 %**** End of derivation protocol ****
% 0.08/0.23 %**** no. of clauses in derivation: 36 ****
% 0.08/0.23 %**** clause counter: 67 ****
% 0.08/0.23
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox/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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:67,loop_count:10,foatp_calls:4,translation:fof_full)
%------------------------------------------------------------------------------