%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU908^5 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 10:49:13 AM UTC 2026
% Result : Theorem 0.07s 0.20s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 28 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 84 ( 34 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 200 ( 23 ~; 24 |; 0 &; 123 @)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 0 ^; 51 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_f,type,
f: a > a ).
thf(tp_sK1_Xx,type,
sK1_Xx: a ).
thf(tp_sK2_SX0,type,
sK2_SX0: a > $o ).
thf(tp_sK3_SY9,type,
sK3_SY9: ( a > $o ) > a ).
thf(1,conjecture,
! [Xx: a] :
( ! [Xp: a > $o] :
( ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xp @ ( f @ Xx0 ) ) )
=> ( Xp @ Xx ) )
=> ! [Xp: a > $o] :
( ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xp @ ( f @ Xx0 ) ) )
=> ( Xp @ ( f @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM527_pme) ).
thf(2,negated_conjecture,
( ( ! [Xx: a] :
( ! [Xp: a > $o] :
( ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xp @ ( f @ Xx0 ) ) )
=> ( Xp @ Xx ) )
=> ! [Xp: a > $o] :
( ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xp @ ( f @ Xx0 ) ) )
=> ( Xp @ ( f @ Xx ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: a] :
( ! [Xp: a > $o] :
( ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xp @ ( f @ Xx0 ) ) )
=> ( Xp @ Xx ) )
=> ! [Xp: a > $o] :
( ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ( Xp @ ( f @ Xx0 ) ) )
=> ( Xp @ ( f @ Xx ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY5: a > $o] :
( ! [Xx0: a] :
( ( SY5 @ Xx0 )
=> ( SY5 @ ( f @ Xx0 ) ) )
=> ( SY5 @ sK1_Xx ) )
=> ! [SY7: a > $o] :
( ! [Xx0: a] :
( ( SY7 @ Xx0 )
=> ( SY7 @ ( f @ Xx0 ) ) )
=> ( SY7 @ ( f @ sK1_Xx ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY5: a > $o] :
( ! [Xx0: a] :
( ( SY5 @ Xx0 )
=> ( SY5 @ ( f @ Xx0 ) ) )
=> ( SY5 @ sK1_Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [SY7: a > $o] :
( ! [Xx0: a] :
( ( SY7 @ Xx0 )
=> ( SY7 @ ( f @ Xx0 ) ) )
=> ( SY7 @ ( f @ sK1_Xx ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ! [SY7: a > $o] :
( ! [Xx0: a] :
( ( SY7 @ Xx0 )
=> ( SY7 @ ( f @ Xx0 ) ) )
=> ( SY7 @ ( f @ sK1_Xx ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY5: a > $o] :
( ! [Xx0: a] :
( ( SY5 @ Xx0 )
=> ( SY5 @ ( f @ Xx0 ) ) )
=> ( SY5 @ sK1_Xx ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ~ ! [SY7: a > $o] :
( ! [Xx0: a] :
( ( SY7 @ Xx0 )
=> ( SY7 @ ( f @ Xx0 ) ) )
=> ( SY7 @ ( f @ sK1_Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [SX0: a > $o] :
( ~ ! [SX1: a] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( f @ SX1 ) ) )
| ( SX0 @ sK1_Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ! [SX0: a > $o] :
( ~ ! [SX1: a] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( f @ SX1 ) ) )
| ( SX0 @ ( f @ sK1_Xx ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: a > $o] :
( ( ~ ! [SY9: a] :
( ~ ( SV1 @ SY9 )
| ( SV1 @ ( f @ SY9 ) ) )
| ( SV1 @ sK1_Xx ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [SX0: a > $o] :
( ~ ! [SX1: a] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( f @ SX1 ) ) )
| ( SX0 @ ( f @ sK1_Xx ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV1: a > $o] :
( ( ( ~ ! [SY9: a] :
( ~ ( SV1 @ SY9 )
| ( SV1 @ ( f @ SY9 ) ) ) )
= $true )
| ( ( SV1 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ! [SY10: a] :
( ~ ( sK2_SX0 @ SY10 )
| ( sK2_SX0 @ ( f @ SY10 ) ) )
| ( sK2_SX0 @ ( f @ sK1_Xx ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(16,plain,
! [SV1: a > $o] :
( ( ( ! [SY9: a] :
( ~ ( SV1 @ SY9 )
| ( SV1 @ ( f @ SY9 ) ) ) )
= $false )
| ( ( SV1 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ! [SY10: a] :
( ~ ( sK2_SX0 @ SY10 )
| ( sK2_SX0 @ ( f @ SY10 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( sK2_SX0 @ ( f @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(19,plain,
! [SV1: a > $o] :
( ( ( ~ ( SV1 @ ( sK3_SY9 @ SV1 ) )
| ( SV1 @ ( f @ ( sK3_SY9 @ SV1 ) ) ) )
= $false )
| ( ( SV1 @ sK1_Xx )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(20,plain,
( ( ! [SY10: a] :
( ~ ( sK2_SX0 @ SY10 )
| ( sK2_SX0 @ ( f @ SY10 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV1: a > $o] :
( ( ( ~ ( SV1 @ ( sK3_SY9 @ SV1 ) ) )
= $false )
| ( ( SV1 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(22,plain,
! [SV1: a > $o] :
( ( ( SV1 @ ( f @ ( sK3_SY9 @ SV1 ) ) )
= $false )
| ( ( SV1 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(23,plain,
! [SV2: a] :
( ( ~ ( sK2_SX0 @ SV2 )
| ( sK2_SX0 @ ( f @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV1: a > $o] :
( ( ( SV1 @ ( sK3_SY9 @ SV1 ) )
= $true )
| ( ( SV1 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV2: a] :
( ( ( ~ ( sK2_SX0 @ SV2 ) )
= $true )
| ( ( sK2_SX0 @ ( f @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV2: a] :
( ( ( sK2_SX0 @ SV2 )
= $false )
| ( ( sK2_SX0 @ ( f @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(27,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,26,24,22]) ).
thf(28,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU908^5 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.17 % Computer : n004.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 15:37:54 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.20
% 0.07/0.20 No.of.Axioms: 0
% 0.07/0.20
% 0.07/0.20 Length.of.Defs: 0
% 0.07/0.20
% 0.07/0.20 Contains.Choice.Funs: false
% 0.07/0.20
% 0.07/0.20 ********************************
% 0.07/0.20 * All subproblems solved! *
% 0.07/0.20 ********************************
% 0.07/0.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,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:27,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.20
% 0.07/0.20 %**** Beginning of derivation protocol ****
% 0.07/0.20 % SZS output start CNFRefutation
% See solution above
% 0.07/0.20
% 0.07/0.20 %**** End of derivation protocol ****
% 0.07/0.20 %**** no. of clauses in derivation: 28 ****
% 0.07/0.20 %**** clause counter: 27 ****
% 0.07/0.20
% 0.07/0.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,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:27,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------