%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO363^5 : 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 : n009.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 0.11s 0.19s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 28 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 85 ( 50 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 132 ( 7 ~; 3 |; 3 &; 110 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 ^; 34 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_f,type,
f: ( a > a ) > a > a ).
thf(tp_g,type,
g: ( a > a ) > a > a ).
thf(tp_h,type,
h: a > a ).
thf(tp_j,type,
j: a > a ).
thf(tp_sK1_SX0,type,
sK1_SX0: ( a > a ) > $o ).
thf(tp_sK2_E,type,
sK2_E: a ).
thf(tp_sK3_E,type,
sK3_E: a ).
thf(1,conjecture,
( ( ! [X: a > a,Y: a] :
( ( f @ X @ Y )
= ( g @ X @ Y ) )
& ! [Z: a] :
( ( h @ Z )
= ( j @ Z ) ) )
=> ! [Xq: ( a > a ) > $o] :
( ( Xq @ ( f @ h ) )
=> ( Xq @ ( g @ j ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEDEC2_pme) ).
thf(2,negated_conjecture,
( ( ( ! [X: a > a,Y: a] :
( ( f @ X @ Y )
= ( g @ X @ Y ) )
& ! [Z: a] :
( ( h @ Z )
= ( j @ Z ) ) )
=> ! [Xq: ( a > a ) > $o] :
( ( Xq @ ( f @ h ) )
=> ( Xq @ ( g @ j ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [X: a > a,Y: a] :
( ( f @ X @ Y )
= ( g @ X @ Y ) )
& ! [Z: a] :
( ( h @ Z )
= ( j @ Z ) ) )
=> ! [Xq: ( a > a ) > $o] :
( ( Xq @ ( f @ h ) )
=> ( Xq @ ( g @ j ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [X: a > a,Y: a] :
( ( f @ X @ Y )
= ( g @ X @ Y ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Z: a] :
( ( h @ Z )
= ( j @ Z ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xq: ( a > a ) > $o] :
( ( Xq @ ( f @ h ) )
=> ( Xq @ ( g @ j ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [Xq: ( a > a ) > $o] :
( ( Xq @ ( f @ h ) )
=> ( Xq @ ( g @ j ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [Z: a] :
( ( h @ Z )
= ( j @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [X: a > a,Y: a] :
( ( f @ X @ Y )
= ( g @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(10,plain,
( ( ~ ! [Xq: ( a > a ) > $o] :
( ( Xq @ ( f @ h ) )
=> ( Xq @ ( g @ j ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ! [SX0: ( a > a ) > $o] :
( ~ ( SX0 @ ( f @ h ) )
| ( SX0 @ ( g @ j ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
! [SV1: a] :
( ( ( h @ SV1 )
= ( j @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(13,plain,
! [SV2: a > a] :
( ( ! [SY4: a] :
( ( f @ SV2 @ SY4 )
= ( g @ SV2 @ SY4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(14,plain,
( ( ! [SX0: ( a > a ) > $o] :
( ~ ( SX0 @ ( f @ h ) )
| ( SX0 @ ( g @ j ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(15,plain,
! [SV3: a,SV2: a > a] :
( ( ( f @ SV2 @ SV3 )
= ( g @ SV2 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( sK1_SX0 @ ( f @ h ) )
| ( sK1_SX0 @ ( g @ j ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(17,plain,
( ( ~ ( sK1_SX0 @ ( f @ h ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(18,plain,
( ( sK1_SX0 @ ( g @ j ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( sK1_SX0 @ ( f @ h ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(20,plain,
! [SV4: a] :
( ( ( h @ SV4 )
= ( j @ SV4 ) )
= $true ),
inference(rename,[status(thm)],[12]) ).
thf(21,plain,
! [SV5: a,SV6: a > a] :
( ( ( f @ SV6 @ SV5 )
= ( g @ SV6 @ SV5 ) )
= $true ),
inference(rename,[status(thm)],[15]) ).
thf(24,plain,
( ( ( sK1_SX0 @ ( f @ h ) )
= ( sK1_SX0 @ ( g @ j ) ) )
= $false ),
inference(res,[status(thm)],[19,18]) ).
thf(25,plain,
( ( ( f @ h @ sK2_E )
= ( g @ j @ sK2_E ) )
= $false ),
inference(extuni,[status(esa)],[24]) ).
thf(26,plain,
! [SV5: a,SV6: a > a] :
( ( ( ( f @ h @ sK2_E )
= ( g @ j @ sK2_E ) )
= ( ( f @ SV6 @ SV5 )
= ( g @ SV6 @ SV5 ) ) )
= $false ),
inference(res,[status(thm)],[25,21]) ).
thf(32,plain,
( ( ( j @ sK3_E )
= ( h @ sK3_E ) )
= $false ),
inference(extuni,[status(esa)],[26:[bind(SV5,$thf( sK2_E )),bind(SV6,$thf( h ))]]) ).
thf(37,plain,
! [SV4: a] :
( ( ( ( j @ sK3_E )
= ( h @ sK3_E ) )
= ( ( h @ SV4 )
= ( j @ SV4 ) ) )
= $false ),
inference(res,[status(thm)],[32,20]) ).
thf(39,plain,
$false = $true,
inference(extuni,[status(esa)],[37:[bind(SV4,$thf( sK3_E ))]]) ).
thf(40,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO363^5 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.15 % Computer : n009.cluster.edu
% 0.11/0.15 % Model : x86_64 x86_64
% 0.11/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.15 % Memory : 8046.5625MB
% 0.11/0.15 % OS : Linux 6.8.0-71-generic
% 0.11/0.15 % CPULimit : 300
% 0.11/0.15 % WCLimit : 300
% 0.11/0.15 % DateTime : Tue Oct 6 17:35:47 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.19
% 0.11/0.19 No.of.Axioms: 0
% 0.11/0.19
% 0.11/0.19 Length.of.Defs: 0
% 0.11/0.19
% 0.11/0.19 Contains.Choice.Funs: false
% 0.11/0.19 .
% 0.11/0.19
% 0.11/0.19 ********************************
% 0.11/0.19 * All subproblems solved! *
% 0.11/0.19 ********************************
% 0.11/0.19 % 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:39,loop_count:6,foatp_calls:2,translation:fof_full)
% 0.11/0.19
% 0.11/0.19 %**** Beginning of derivation protocol ****
% 0.11/0.19 % SZS output start CNFRefutation
% See solution above
% 0.11/0.19
% 0.11/0.19 %**** End of derivation protocol ****
% 0.11/0.19 %**** no. of clauses in derivation: 28 ****
% 0.11/0.19 %**** clause counter: 39 ****
% 0.11/0.19
% 0.11/0.19 % 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:39,loop_count:6,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------