%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO236^5 : 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 : n005.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 11:07:54 AM UTC 2026
% Result : Theorem 0.09s 0.20s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 1
% Syntax : Number of formulae : 44 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 261 ( 172 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 232 ( 15 ~; 60 |; 0 &; 150 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 69 ( 0 ^; 69 !; 0 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_b,type,
b: $tType ).
thf(tp_f,type,
f: b > a ).
thf(tp_g,type,
g: b > a ).
thf(tp_sK1_SV2,type,
sK1_SV2: b ).
thf(tp_sK2_SV15,type,
sK2_SV15: b > b > b ).
thf(tp_sK3_E,type,
sK3_E: b > b > b ).
thf(tp_sK4_E,type,
sK4_E: b ).
thf(tp_sK5_SV19,type,
sK5_SV19: b > b > b ).
thf(tp_sK6_SV20,type,
sK6_SV20: b > b > b ).
thf(tp_sK7_E,type,
sK7_E: b > b > b ).
thf(1,conjecture,
( ( ! [Q: ( b > a ) > $o] :
( ( Q @ f )
=> ( Q @ g ) )
| ! [Xx: b] :
( ( f @ Xx )
= ( g @ Xx ) ) )
=> ( f = g ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM504) ).
thf(2,negated_conjecture,
( ( ( ! [Q: ( b > a ) > $o] :
( ( Q @ f )
=> ( Q @ g ) )
| ! [Xx: b] :
( ( f @ Xx )
= ( g @ Xx ) ) )
=> ( f = g ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [Q: ( b > a ) > $o] :
( ( Q @ f )
=> ( Q @ g ) )
| ! [Xx: b] :
( ( f @ Xx )
= ( g @ Xx ) ) )
=> ( f = g ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Q: ( b > a ) > $o] :
( ( Q @ f )
=> ( Q @ g ) )
| ! [Xx: b] :
( ( f @ Xx )
= ( g @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( f = g )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( f != g )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [Q: ( b > a ) > $o] :
( ~ ( Q @ f )
| ( Q @ g ) )
| ! [Xx: b] :
( ( f @ Xx )
= ( g @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(8,plain,
( ( ! [Q: ( b > a ) > $o] :
( ~ ( Q @ f )
| ( Q @ g ) )
| ! [Xx: b] :
( ( f @ Xx )
= ( g @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(9,plain,
( ( f != g )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( ( ! [Q: ( b > a ) > $o] :
( ~ ( Q @ f )
| ( Q @ g ) ) )
= $true )
| ( ( ! [Xx: b] :
( ( f @ Xx )
= ( g @ Xx ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8]) ).
thf(11,plain,
( ( f = g )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: ( b > a ) > $o] :
( ( ( ~ ( SV1 @ f )
| ( SV1 @ g ) )
= $true )
| ( ( ! [Xx: b] :
( ( f @ Xx )
= ( g @ Xx ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [SV2: b] :
( ( f @ SV2 )
= ( g @ SV2 ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[11]) ).
thf(14,plain,
( ( f = g )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[11]) ).
thf(15,plain,
! [SV1: ( b > a ) > $o] :
( ( ( ~ ( SV1 @ f ) )
= $true )
| ( ( SV1 @ g )
= $true )
| ( ( ! [Xx: b] :
( ( f @ Xx )
= ( g @ Xx ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(16,plain,
( ( ( f @ sK1_SV2 )
= ( g @ sK1_SV2 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(17,plain,
! [SV1: ( b > a ) > $o] :
( ( ( SV1 @ f )
= $false )
| ( ( SV1 @ g )
= $true )
| ( ( ! [Xx: b] :
( ( f @ Xx )
= ( g @ Xx ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
! [SV1: ( b > a ) > $o,SV3: b] :
( ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= $true )
| ( ( SV1 @ g )
= $true )
| ( ( SV1 @ f )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(19,plain,
! [SV3: b] :
( ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= $true )
| ( ( g = f )
= $true )
| ( ( f = f )
= $false ) ),
inference(replace_leibnizEQ,[status(thm)],[18:[bind(SV1,$thf( ^ [SV4: b > a] : ( SV4 = f ) ))]]) ).
thf(20,plain,
! [SV3: b] :
( ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= $true )
| ( ( g = f )
= $true ) ),
inference(sim,[status(thm)],[19]) ).
thf(23,plain,
! [SV8: ( b > a ) > $o,SV3: b] :
( ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= $true )
| ( ( ~ ( SV8 @ g ) )
= $true )
| ( ( ~ ( SV8 @ f ) )
= $false ) ),
inference(prim_subst,[status(thm)],[18:[bind(SV1,$thf( ^ [SV7: b > a] : ~ ( SV8 @ SV7 ) ))]]) ).
thf(25,plain,
! [SV3: b] :
( ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= $true )
| ( ( g = f )
= $true )
| ( ( f = f )
= $false ) ),
inference(prim_subst,[status(thm)],[18:[bind(SV1,$thf( ^ [SV6: b > a] : ( SV6 = f ) ))]]) ).
thf(26,plain,
! [SV3: b] :
( ( ( g = f )
= $true )
| ( ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= ( g = f ) )
= $false ) ),
inference(fac_restr,[status(thm)],[20]) ).
thf(27,plain,
! [SV3: b,SV11: b] :
( ( ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= ( g = f ) )
= $false )
| ( ( ( g @ SV11 )
= ( f @ SV11 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[26]) ).
thf(28,plain,
! [SV3: b,SV12: b] :
( ( ( ( g @ SV12 )
= ( f @ SV12 ) )
= $true )
| ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[20]) ).
thf(29,plain,
! [SV11: b,SV3: b] :
( ( ( ~ ( ( ( f @ SV3 )
= ( g @ SV3 ) )
| ( g = f ) )
| ~ ( ( ( f @ SV3 )
!= ( g @ SV3 ) )
| ( g != f ) ) )
= $false )
| ( ( ( g @ SV11 )
= ( f @ SV11 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[27]) ).
thf(31,plain,
! [SV11: b,SV3: b] :
( ( ( ~ ( ( ( f @ SV3 )
= ( g @ SV3 ) )
| ( g = f ) ) )
= $false )
| ( ( ( g @ SV11 )
= ( f @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV11: b,SV3: b] :
( ( ( ( ( f @ SV3 )
= ( g @ SV3 ) )
| ( g = f ) )
= $true )
| ( ( ( g @ SV11 )
= ( f @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(35,plain,
! [SV11: b,SV3: b] :
( ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= $true )
| ( ( g = f )
= $true )
| ( ( ( g @ SV11 )
= ( f @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV11: b,SV3: b] :
( ( ( ! [SV13: b] :
( ( g @ SV13 )
= ( f @ SV13 ) ) )
= $true )
| ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= $true )
| ( ( ( g @ SV11 )
= ( f @ SV11 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV11: b,SV3: b] :
( ( ( g = f )
= $true )
| ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= $true )
| ( ( ( g @ SV11 )
= ( f @ SV11 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV11: b,SV3: b,SV14: b] :
( ( ( ( g @ SV14 )
= ( f @ SV14 ) )
= $true )
| ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= $true )
| ( ( ( g @ SV11 )
= ( f @ SV11 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV11: b,SV3: b,SV16: b] :
( ( ( ( g @ SV11 )
= ( f @ SV11 ) )
= $true )
| ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= $true )
| ( ( ( g @ SV16 )
= ( f @ SV16 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[38]) ).
thf(46,plain,
( ( ( f @ sK4_E )
= ( g @ sK4_E ) )
= $false ),
inference(extuni,[status(esa)],[14]) ).
thf(48,plain,
! [SV3: b,SV18: b] :
( ( ( f = f )
= $false )
| ( ( ( g @ SV18 )
= ( f @ SV18 ) )
= $true )
| ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[25]) ).
thf(49,plain,
! [SV3: b,SV8: ( b > a ) > $o] :
( ( ( SV8 @ g )
= $false )
| ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= $true )
| ( ( ~ ( SV8 @ f ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(52,plain,
! [SV3: b,SV18: b] :
( ( ( ! [SV20: b] :
( ( f @ SV20 )
= ( f @ SV20 ) ) )
= $false )
| ( ( ( g @ SV18 )
= ( f @ SV18 ) )
= $true )
| ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[48]) ).
thf(53,plain,
! [SV3: b,SV18: b] :
( ( ( f = f )
= $false )
| ( ( ( g @ SV18 )
= ( f @ SV18 ) )
= $true )
| ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[48]) ).
thf(54,plain,
! [SV3: b,SV8: ( b > a ) > $o] :
( ( ( SV8 @ f )
= $true )
| ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= $true )
| ( ( SV8 @ g )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(56,plain,
! [SV18: b,SV3: b] :
( ( ( ( f @ ( sK6_SV20 @ SV3 @ SV18 ) )
= ( f @ ( sK6_SV20 @ SV3 @ SV18 ) ) )
= $false )
| ( ( ( g @ SV18 )
= ( f @ SV18 ) )
= $true )
| ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[52]) ).
thf(58,plain,
! [SV18: b,SV3: b] :
( ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= $true )
| ( ( ( g @ SV18 )
= ( f @ SV18 ) )
= $true ) ),
inference(extuni,[status(esa)],[56]) ).
thf(59,plain,
! [SV18: b,SV3: b] :
( ( ( ( f @ SV3 )
= ( g @ SV3 ) )
= $true )
| ( ( ( g @ SV18 )
= ( f @ SV18 ) )
= $true ) ),
inference(extuni,[status(esa)],[53]) ).
thf(60,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,59,58,54,46,45,40,28,20,18,16]) ).
thf(61,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO236^5 : 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
% 0.09/0.16 % Computer : n005.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Oct 6 17:33:14 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.20
% 0.09/0.20 No.of.Axioms: 0
% 0.09/0.20
% 0.09/0.20 Length.of.Defs: 0
% 0.09/0.20
% 0.09/0.20 Contains.Choice.Funs: false
% 0.09/0.20 .
% 0.09/0.20
% 0.09/0.20 ********************************
% 0.09/0.20 * All subproblems solved! *
% 0.09/0.20 ********************************
% 0.09/0.20 % SZS status Theorem for /export/starexec/sandbox/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:60,loop_count:0,foatp_calls:2,translation:fof_experiment)
% 0.09/0.20
% 0.09/0.20 %**** Beginning of derivation protocol ****
% 0.09/0.20 % SZS output start CNFRefutation
% See solution above
% 0.09/0.20
% 0.09/0.20 %**** End of derivation protocol ****
% 0.09/0.20 %**** no. of clauses in derivation: 44 ****
% 0.09/0.20 %**** clause counter: 60 ****
% 0.09/0.20
% 0.09/0.20 % SZS status Theorem for /export/starexec/sandbox/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:60,loop_count:0,foatp_calls:2,translation:fof_experiment)
%------------------------------------------------------------------------------