%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO373^5 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 11:08:09 AM UTC 2026
% Result : Theorem 0.07s 0.22s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 36 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 179 ( 43 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 156 ( 37 ~; 26 |; 4 &; 77 @)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 0 ^; 29 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_b,type,
b: $tType ).
thf(tp_f,type,
f: b > $o ).
thf(tp_g,type,
g: b > $o ).
thf(tp_sK1_Xq,type,
sK1_Xq: ( b > $o ) > $o ).
thf(tp_sK2_E,type,
sK2_E: b ).
thf(1,conjecture,
( ! [Xx: b] :
( ( f @ Xx )
<=> ( g @ Xx ) )
=> ! [Xq: ( b > $o ) > $o] :
( ( Xq @ f )
=> ( Xq @ g ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEXT_SET) ).
thf(2,negated_conjecture,
( ( ! [Xx: b] :
( ( f @ Xx )
<=> ( g @ Xx ) )
=> ! [Xq: ( b > $o ) > $o] :
( ( Xq @ f )
=> ( Xq @ g ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: b] :
( ( f @ Xx )
<=> ( g @ Xx ) )
=> ! [Xq: ( b > $o ) > $o] :
( ( Xq @ f )
=> ( Xq @ g ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx: b] :
( ( f @ Xx )
<=> ( g @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xq: ( b > $o ) > $o] :
( ( Xq @ f )
=> ( Xq @ g ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [Xq: ( b > $o ) > $o] :
( ( Xq @ f )
=> ( Xq @ g ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ( sK1_Xq @ f )
& ~ ( sK1_Xq @ g ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [Xx: b] :
( ~ ( f @ Xx )
| ( g @ Xx ) )
& ! [Xx: b] :
( ~ ( g @ Xx )
| ( f @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [Xx: b] :
( ~ ( f @ Xx )
| ( g @ Xx ) )
& ! [Xx: b] :
( ~ ( g @ Xx )
| ( f @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ( sK1_Xq @ f )
& ~ ( sK1_Xq @ g ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ( ~ ! [SX0: b] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ~ ! [SX0: b] :
( ~ ( g @ SX0 )
| ( f @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( ~ ( sK1_Xq @ f )
| ~ ~ ( sK1_Xq @ g ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ! [SX0: b] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ~ ! [SX0: b] :
( ~ ( g @ SX0 )
| ( f @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ( sK1_Xq @ f )
| ~ ~ ( sK1_Xq @ g ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ! [SX0: b] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ! [SX0: b] :
( ~ ( g @ SX0 )
| ( f @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
( ( ~ ( sK1_Xq @ f ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ~ ( sK1_Xq @ g ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(19,plain,
( ( ! [SX0: b] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(20,plain,
( ( ! [SX0: b] :
( ~ ( g @ SX0 )
| ( f @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(21,plain,
( ( sK1_Xq @ f )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(22,plain,
( ( ~ ( sK1_Xq @ g ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(23,plain,
! [SV1: b] :
( ( ~ ( f @ SV1 )
| ( g @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV2: b] :
( ( ~ ( g @ SV2 )
| ( f @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
( ( sK1_Xq @ g )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV1: b] :
( ( ( ~ ( f @ SV1 ) )
= $true )
| ( ( g @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV2: b] :
( ( ( ~ ( g @ SV2 ) )
= $true )
| ( ( f @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV1: b] :
( ( ( f @ SV1 )
= $false )
| ( ( g @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV2: b] :
( ( ( g @ SV2 )
= $false )
| ( ( f @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(30,plain,
( ( ( sK1_Xq @ g )
= ( sK1_Xq @ f ) )
= $false ),
inference(res,[status(thm)],[25,21]) ).
thf(31,plain,
( ( ( g @ sK2_E )
= $true )
| ( ( f @ sK2_E )
= $true ) ),
inference(extuni,[status(esa)],[30]) ).
thf(32,plain,
( ( ( g @ sK2_E )
= $false )
| ( ( f @ sK2_E )
= $false ) ),
inference(extuni,[status(esa)],[30]) ).
thf(33,plain,
! [SV3: b] :
( ( ( f @ SV3 )
= $false )
| ( ( g @ SV3 )
= $true ) ),
inference(rename,[status(thm)],[28]) ).
thf(38,plain,
! [SV4: b] :
( ( ( g @ SV4 )
= $false )
| ( ( f @ SV4 )
= $true ) ),
inference(rename,[status(thm)],[29]) ).
thf(47,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,38,33,32,31,25]) ).
thf(48,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO373^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.17 % Computer : n015.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 17:42:39 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.22
% 0.07/0.22 No.of.Axioms: 0
% 0.07/0.22
% 0.07/0.22 Length.of.Defs: 0
% 0.07/0.22
% 0.07/0.22 Contains.Choice.Funs: false
% 0.07/0.22 .
% 0.07/0.22
% 0.07/0.22 ********************************
% 0.07/0.22 * All subproblems solved! *
% 0.07/0.22 ********************************
% 0.07/0.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:47,loop_count:5,foatp_calls:2,translation:fof_full)
% 0.07/0.22
% 0.07/0.22 %**** Beginning of derivation protocol ****
% 0.07/0.22 % SZS output start CNFRefutation
% See solution above
% 0.07/0.22
% 0.07/0.22 %**** End of derivation protocol ****
% 0.07/0.22 %**** no. of clauses in derivation: 36 ****
% 0.07/0.22 %**** clause counter: 47 ****
% 0.07/0.22
% 0.07/0.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:47,loop_count:5,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------