%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO359^5 : 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 : n008.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 11:08:07 AM UTC 2026
% Result : Theorem 0.07s 0.23s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 1
% Syntax : Number of formulae : 57 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 494 ( 142 equ; 0 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 450 ( 86 ~; 127 |; 0 &; 211 @)
% ( 10 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 56 ( 0 ^; 56 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_b,type,
b: $tType ).
thf(tp_gtype,type,
gtype: $tType ).
thf(tp_f,type,
f: b > $o ).
thf(tp_g,type,
g: b > $o ).
thf(tp_h,type,
h: ( b > $o ) > gtype ).
thf(tp_sK1_SX0,type,
sK1_SX0: b ).
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 ) ) )
=> ( ! [Xx: b] :
( ( f @ Xx )
<=> ( g @ Xx ) )
=> ( ( h @ f )
= ( h @ g ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEXT1) ).
thf(2,negated_conjecture,
( ( ( ! [Xx: b] :
( ( f @ Xx )
<=> ( g @ Xx ) )
=> ! [Xq: ( b > $o ) > $o] :
( ( Xq @ f )
=> ( Xq @ g ) ) )
=> ( ! [Xx: b] :
( ( f @ Xx )
<=> ( g @ Xx ) )
=> ( ( h @ f )
= ( h @ 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 ) ) )
=> ( ! [Xx: b] :
( ( f @ Xx )
<=> ( g @ Xx ) )
=> ( ( h @ f )
= ( h @ g ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx: b] :
( ( f @ Xx )
<=> ( g @ Xx ) )
=> ! [Xq: ( b > $o ) > $o] :
( ( Xq @ f )
=> ( Xq @ g ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: b] :
( ( f @ Xx )
<=> ( g @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ( h @ f )
= ( h @ g ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ( h @ f )
!= ( h @ g ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [Xx: b] :
( ( f @ Xx )
<=> ( g @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [Xx: b] :
( ( f @ Xx )
<=> ( g @ Xx ) )
=> ! [Xq: ( b > $o ) > $o] :
( ( Xq @ f )
=> ( Xq @ g ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(10,plain,
( ( ( h @ f )
!= ( h @ g ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: b] :
~ ( ~ ( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ~ ( ~ ( g @ SX0 )
| ( f @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(12,plain,
( ( ~ ! [SX0: b] :
~ ( ~ ( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ~ ( ~ ( g @ SX0 )
| ( f @ SX0 ) ) )
| ! [SX0: ( b > $o ) > $o] :
( ~ ( SX0 @ f )
| ( SX0 @ g ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(13,plain,
( ( ( h @ f )
= ( h @ g ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(14,plain,
! [SV1: b] :
( ( ~ ( ~ ( ~ ( f @ SV1 )
| ( g @ SV1 ) )
| ~ ( ~ ( g @ SV1 )
| ( f @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
( ( ( ~ ! [SX0: b] :
~ ( ~ ( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ~ ( ~ ( g @ SX0 )
| ( f @ SX0 ) ) ) )
= $true )
| ( ( ! [SX0: ( b > $o ) > $o] :
( ~ ( SX0 @ f )
| ( SX0 @ g ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(16,plain,
! [SV1: b] :
( ( ~ ( ~ ( f @ SV1 )
| ( g @ SV1 ) )
| ~ ( ~ ( g @ SV1 )
| ( f @ SV1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ( ! [SX0: b] :
~ ( ~ ( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ~ ( ~ ( g @ SX0 )
| ( f @ SX0 ) ) ) )
= $false )
| ( ( ! [SX0: ( b > $o ) > $o] :
( ~ ( SX0 @ f )
| ( SX0 @ g ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
! [SV1: b] :
( ( ~ ( ~ ( f @ SV1 )
| ( g @ SV1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(19,plain,
! [SV1: b] :
( ( ~ ( ~ ( g @ SV1 )
| ( f @ SV1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ( ~ ( ~ ( ~ ( f @ sK1_SX0 )
| ( g @ sK1_SX0 ) )
| ~ ( ~ ( g @ sK1_SX0 )
| ( f @ sK1_SX0 ) ) ) )
= $false )
| ( ( ! [SX0: ( b > $o ) > $o] :
( ~ ( SX0 @ f )
| ( SX0 @ g ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(21,plain,
! [SV1: b] :
( ( ~ ( f @ SV1 )
| ( g @ SV1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV1: b] :
( ( ~ ( g @ SV1 )
| ( f @ SV1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ( ~ ( ~ ( f @ sK1_SX0 )
| ( g @ sK1_SX0 ) )
| ~ ( ~ ( g @ sK1_SX0 )
| ( f @ sK1_SX0 ) ) )
= $true )
| ( ( ! [SX0: ( b > $o ) > $o] :
( ~ ( SX0 @ f )
| ( SX0 @ g ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV1: b] :
( ( ( ~ ( f @ SV1 ) )
= $true )
| ( ( g @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV1: b] :
( ( ( ~ ( g @ SV1 ) )
= $true )
| ( ( f @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( ( ~ ( ~ ( f @ sK1_SX0 )
| ( g @ sK1_SX0 ) ) )
= $true )
| ( ( ~ ( ~ ( g @ sK1_SX0 )
| ( f @ sK1_SX0 ) ) )
= $true )
| ( ( ! [SX0: ( b > $o ) > $o] :
( ~ ( SX0 @ f )
| ( SX0 @ g ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV1: b] :
( ( ( f @ SV1 )
= $false )
| ( ( g @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV1: b] :
( ( ( g @ SV1 )
= $false )
| ( ( f @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
( ( ( ~ ( f @ sK1_SX0 )
| ( g @ sK1_SX0 ) )
= $false )
| ( ( ~ ( ~ ( g @ sK1_SX0 )
| ( f @ sK1_SX0 ) ) )
= $true )
| ( ( ! [SX0: ( b > $o ) > $o] :
( ~ ( SX0 @ f )
| ( SX0 @ g ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( ( ~ ( f @ sK1_SX0 ) )
= $false )
| ( ( ~ ( ~ ( g @ sK1_SX0 )
| ( f @ sK1_SX0 ) ) )
= $true )
| ( ( ! [SX0: ( b > $o ) > $o] :
( ~ ( SX0 @ f )
| ( SX0 @ g ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(31,plain,
( ( ( g @ sK1_SX0 )
= $false )
| ( ( ~ ( ~ ( g @ sK1_SX0 )
| ( f @ sK1_SX0 ) ) )
= $true )
| ( ( ! [SX0: ( b > $o ) > $o] :
( ~ ( SX0 @ f )
| ( SX0 @ g ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(32,plain,
( ( ( f @ sK1_SX0 )
= $true )
| ( ( ~ ( ~ ( g @ sK1_SX0 )
| ( f @ sK1_SX0 ) ) )
= $true )
| ( ( ! [SX0: ( b > $o ) > $o] :
( ~ ( SX0 @ f )
| ( SX0 @ g ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(33,plain,
( ( ( ~ ( g @ sK1_SX0 )
| ( f @ sK1_SX0 ) )
= $false )
| ( ( g @ sK1_SX0 )
= $false )
| ( ( ! [SX0: ( b > $o ) > $o] :
( ~ ( SX0 @ f )
| ( SX0 @ g ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(34,plain,
( ( ( ~ ( g @ sK1_SX0 )
| ( f @ sK1_SX0 ) )
= $false )
| ( ( f @ sK1_SX0 )
= $true )
| ( ( ! [SX0: ( b > $o ) > $o] :
( ~ ( SX0 @ f )
| ( SX0 @ g ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(36,plain,
( ( ( f @ sK1_SX0 )
= $false )
| ( ( g @ sK1_SX0 )
= $false )
| ( ( ! [SX0: ( b > $o ) > $o] :
( ~ ( SX0 @ f )
| ( SX0 @ g ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(37,plain,
( ( ( ~ ( g @ sK1_SX0 ) )
= $false )
| ( ( f @ sK1_SX0 )
= $true )
| ( ( ! [SX0: ( b > $o ) > $o] :
( ~ ( SX0 @ f )
| ( SX0 @ g ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(40,plain,
! [SV2: ( b > $o ) > $o] :
( ( ( ~ ( SV2 @ f )
| ( SV2 @ g ) )
= $true )
| ( ( g @ sK1_SX0 )
= $false )
| ( ( f @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(41,plain,
( ( ( g @ sK1_SX0 )
= $true )
| ( ( f @ sK1_SX0 )
= $true )
| ( ( ! [SX0: ( b > $o ) > $o] :
( ~ ( SX0 @ f )
| ( SX0 @ g ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(44,plain,
! [SV2: ( b > $o ) > $o] :
( ( ( ~ ( SV2 @ f ) )
= $true )
| ( ( SV2 @ g )
= $true )
| ( ( g @ sK1_SX0 )
= $false )
| ( ( f @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV5: ( b > $o ) > $o] :
( ( ( ~ ( SV5 @ f )
| ( SV5 @ g ) )
= $true )
| ( ( f @ sK1_SX0 )
= $true )
| ( ( g @ sK1_SX0 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(48,plain,
! [SV2: ( b > $o ) > $o] :
( ( ( SV2 @ f )
= $false )
| ( ( SV2 @ g )
= $true )
| ( ( g @ sK1_SX0 )
= $false )
| ( ( f @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV5: ( b > $o ) > $o] :
( ( ( ~ ( SV5 @ f ) )
= $true )
| ( ( SV5 @ g )
= $true )
| ( ( f @ sK1_SX0 )
= $true )
| ( ( g @ sK1_SX0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(52,plain,
! [SV5: ( b > $o ) > $o] :
( ( ( SV5 @ f )
= $false )
| ( ( SV5 @ g )
= $true )
| ( ( f @ sK1_SX0 )
= $true )
| ( ( g @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(53,plain,
( ( ( f = f )
= $false )
| ( ( g = f )
= $true )
| ( ( g @ sK1_SX0 )
= $false )
| ( ( f @ sK1_SX0 )
= $false ) ),
inference(replace_leibnizEQ,[status(thm)],[48:[bind(SV2,$thf( ^ [SV6: b > $o] : ( SV6 = f ) ))]]) ).
thf(54,plain,
( ( ( g = f )
= $true )
| ( ( g @ sK1_SX0 )
= $false )
| ( ( f @ sK1_SX0 )
= $false ) ),
inference(sim,[status(thm)],[53]) ).
thf(57,plain,
( ( ( f = f )
= $false )
| ( ( g = f )
= $true )
| ( ( f @ sK1_SX0 )
= $true )
| ( ( g @ sK1_SX0 )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[52:[bind(SV5,$thf( ^ [SV9: b > $o] : ( SV9 = f ) ))]]) ).
thf(58,plain,
( ( ( g = f )
= $true )
| ( ( f @ sK1_SX0 )
= $true )
| ( ( g @ sK1_SX0 )
= $true ) ),
inference(sim,[status(thm)],[57]) ).
thf(59,plain,
! [SV10: b] :
( ( ( f @ sK1_SX0 )
= $false )
| ( ( g @ sK1_SX0 )
= $false )
| ( ( ( g @ SV10 )
= ( f @ SV10 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV11: b] :
( ( ( g @ sK1_SX0 )
= $true )
| ( ( f @ sK1_SX0 )
= $true )
| ( ( ( g @ SV11 )
= ( f @ SV11 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[58]) ).
thf(61,plain,
! [SV10: b] :
( ( ( g @ SV10 )
= $true )
| ( ( f @ SV10 )
= $false )
| ( ( g @ sK1_SX0 )
= $false )
| ( ( f @ sK1_SX0 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[59]) ).
thf(62,plain,
! [SV10: b] :
( ( ( g @ SV10 )
= $false )
| ( ( f @ SV10 )
= $true )
| ( ( g @ sK1_SX0 )
= $false )
| ( ( f @ sK1_SX0 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[59]) ).
thf(63,plain,
! [SV11: b] :
( ( ( g @ SV11 )
= $true )
| ( ( f @ SV11 )
= $false )
| ( ( f @ sK1_SX0 )
= $true )
| ( ( g @ sK1_SX0 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[60]) ).
thf(64,plain,
! [SV11: b] :
( ( ( g @ SV11 )
= $false )
| ( ( f @ SV11 )
= $true )
| ( ( f @ sK1_SX0 )
= $true )
| ( ( g @ sK1_SX0 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[60]) ).
thf(65,plain,
( ( ( f @ sK2_E )
= $true )
| ( ( g @ sK2_E )
= $true ) ),
inference(extuni,[status(esa)],[13]) ).
thf(66,plain,
( ( ( f @ sK2_E )
= $false )
| ( ( g @ sK2_E )
= $false ) ),
inference(extuni,[status(esa)],[13]) ).
thf(67,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[13,66,65,64,63,62,61,58,54,52,48,28,27]) ).
thf(68,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO359^5 : 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 : n008.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 17:36:24 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.23
% 0.07/0.23 No.of.Axioms: 0
% 0.07/0.23
% 0.07/0.23 Length.of.Defs: 0
% 0.07/0.23
% 0.07/0.23 Contains.Choice.Funs: false
% 0.07/0.23 .
% 0.07/0.23
% 0.07/0.23 ********************************
% 0.07/0.23 * All subproblems solved! *
% 0.07/0.23 ********************************
% 0.07/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:2,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:67,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.07/0.23
% 0.07/0.23 %**** Beginning of derivation protocol ****
% 0.07/0.23 % SZS output start CNFRefutation
% See solution above
% 0.07/0.23
% 0.07/0.23 %**** End of derivation protocol ****
% 0.07/0.23 %**** no. of clauses in derivation: 57 ****
% 0.07/0.23 %**** clause counter: 67 ****
% 0.07/0.23
% 0.07/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:2,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:67,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------