%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO374^5 : 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 11:08:09 AM UTC 2026
% Result : Theorem 0.10s 0.24s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 68 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 193 ( 98 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 367 ( 68 ~; 50 |; 0 &; 230 @)
% ( 10 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 86 ( 0 ^; 86 !; 0 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cM,type,
cM: $i > $i ).
thf(tp_cN,type,
cN: $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: ( $i > $i ) > $o ).
thf(tp_sK2_E,type,
sK2_E: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: ( $i > $i ) > $o ).
thf(tp_sK4_E,type,
sK4_E: $i ).
thf(1,conjecture,
( ! [Xx: $i,Xp: $i > $o] :
( ( Xp @ ( cM @ Xx ) )
<=> ( Xp @ ( cN @ Xx ) ) )
=> ! [Xq: ( $i > $i ) > $o] :
( ( Xq @ cM )
<=> ( Xq @ cN ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEXT_A_LEIB2) ).
thf(2,negated_conjecture,
( ( ! [Xx: $i,Xp: $i > $o] :
( ( Xp @ ( cM @ Xx ) )
<=> ( Xp @ ( cN @ Xx ) ) )
=> ! [Xq: ( $i > $i ) > $o] :
( ( Xq @ cM )
<=> ( Xq @ cN ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i,Xp: $i > $o] :
( ( Xp @ ( cM @ Xx ) )
<=> ( Xp @ ( cN @ Xx ) ) )
=> ! [Xq: ( $i > $i ) > $o] :
( ( Xq @ cM )
<=> ( Xq @ cN ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx: $i,Xp: $i > $o] :
( ( Xp @ ( cM @ Xx ) )
<=> ( Xp @ ( cN @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xq: ( $i > $i ) > $o] :
( ( Xq @ cM )
<=> ( Xq @ cN ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xq: ( $i > $i ) > $o] :
( ( Xq @ cM )
=> ( Xq @ cN ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(7,plain,
( ( ! [Xq: ( $i > $i ) > $o] :
( ( Xq @ cN )
=> ( Xq @ cM ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(8,plain,
( ( ~ ! [Xq: ( $i > $i ) > $o] :
( ( Xq @ cM )
=> ( Xq @ cN ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [Xq: ( $i > $i ) > $o] :
( ( Xq @ cN )
=> ( Xq @ cM ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [Xx: $i,Xp: $i > $o] :
( ( Xp @ ( cM @ Xx ) )
<=> ( Xp @ ( cN @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(11,plain,
( ( ~ ! [Xq: ( $i > $i ) > $o] :
( ( Xq @ cM )
=> ( Xq @ cN ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ~ ! [SX0: ( $i > $i ) > $o] :
( ~ ( SX0 @ cM )
| ( SX0 @ cN ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
~ ( ~ ( ~ ( SX1 @ ( cM @ SX0 ) )
| ( SX1 @ ( cN @ SX0 ) ) )
| ~ ( ~ ( SX1 @ ( cN @ SX0 ) )
| ( SX1 @ ( cM @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(14,plain,
( ( ! [SX0: ( $i > $i ) > $o] :
( ~ ( SX0 @ cM )
| ( SX0 @ cN ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: $i] :
( ( ! [SY3: $i > $o] :
~ ( ~ ( ~ ( SY3 @ ( cM @ SV1 ) )
| ( SY3 @ ( cN @ SV1 ) ) )
| ~ ( ~ ( SY3 @ ( cN @ SV1 ) )
| ( SY3 @ ( cM @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( sK1_SX0 @ cM )
| ( sK1_SX0 @ cN ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(17,plain,
! [SV1: $i,SV2: $i > $o] :
( ( ~ ( ~ ( ~ ( SV2 @ ( cM @ SV1 ) )
| ( SV2 @ ( cN @ SV1 ) ) )
| ~ ( ~ ( SV2 @ ( cN @ SV1 ) )
| ( SV2 @ ( cM @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ( sK1_SX0 @ cM ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( sK1_SX0 @ cN )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV1: $i,SV2: $i > $o] :
( ( ~ ( ~ ( SV2 @ ( cM @ SV1 ) )
| ( SV2 @ ( cN @ SV1 ) ) )
| ~ ( ~ ( SV2 @ ( cN @ SV1 ) )
| ( SV2 @ ( cM @ SV1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( sK1_SX0 @ cM )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV1: $i,SV2: $i > $o] :
( ( ~ ( ~ ( SV2 @ ( cM @ SV1 ) )
| ( SV2 @ ( cN @ SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(23,plain,
! [SV1: $i,SV2: $i > $o] :
( ( ~ ( ~ ( SV2 @ ( cN @ SV1 ) )
| ( SV2 @ ( cM @ SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV1: $i,SV2: $i > $o] :
( ( ~ ( SV2 @ ( cM @ SV1 ) )
| ( SV2 @ ( cN @ SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(25,plain,
! [SV1: $i,SV2: $i > $o] :
( ( ~ ( SV2 @ ( cN @ SV1 ) )
| ( SV2 @ ( cM @ SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(26,plain,
! [SV1: $i,SV2: $i > $o] :
( ( ( ~ ( SV2 @ ( cM @ SV1 ) ) )
= $true )
| ( ( SV2 @ ( cN @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV1: $i,SV2: $i > $o] :
( ( ( ~ ( SV2 @ ( cN @ SV1 ) ) )
= $true )
| ( ( SV2 @ ( cM @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV1: $i,SV2: $i > $o] :
( ( ( SV2 @ ( cM @ SV1 ) )
= $false )
| ( ( SV2 @ ( cN @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV1: $i,SV2: $i > $o] :
( ( ( SV2 @ ( cN @ SV1 ) )
= $false )
| ( ( SV2 @ ( cM @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(30,plain,
! [SV1: $i] :
( ( ( ( cM @ SV1 )
= ( cM @ SV1 ) )
= $false )
| ( ( ( cN @ SV1 )
= ( cM @ SV1 ) )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[28:[bind(SV2,$thf( ^ [SV3: $i] : ( SV3 = ( cM @ SV1 ) ) ))]]) ).
thf(31,plain,
! [SV1: $i] :
( ( ( cN @ SV1 )
= ( cM @ SV1 ) )
= $true ),
inference(sim,[status(thm)],[30]) ).
thf(32,plain,
! [SV1: $i] :
( ( ( ( cN @ SV1 )
= ( cN @ SV1 ) )
= $false )
| ( ( ( cM @ SV1 )
= ( cN @ SV1 ) )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[29:[bind(SV2,$thf( ^ [SV4: $i] : ( SV4 = ( cN @ SV1 ) ) ))]]) ).
thf(33,plain,
! [SV1: $i] :
( ( ( cM @ SV1 )
= ( cN @ SV1 ) )
= $true ),
inference(sim,[status(thm)],[32]) ).
thf(34,plain,
( ( ( sK1_SX0 @ cM )
= ( sK1_SX0 @ cN ) )
= $false ),
inference(res,[status(thm)],[21,19]) ).
thf(35,plain,
( ( ( cM @ sK2_E )
= ( cN @ sK2_E ) )
= $false ),
inference(extuni,[status(esa)],[34]) ).
thf(36,plain,
! [SV5: $i] :
( ( ( cN @ SV5 )
= ( cM @ SV5 ) )
= $true ),
inference(rename,[status(thm)],[31]) ).
thf(38,plain,
! [SV6: $i] :
( ( ( cM @ SV6 )
= ( cN @ SV6 ) )
= $true ),
inference(rename,[status(thm)],[33]) ).
thf(40,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,38,36,35,21]) ).
thf(41,plain,
( ( ! [Xx: $i,Xp: $i > $o] :
( ( Xp @ ( cM @ Xx ) )
<=> ( Xp @ ( cN @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(42,plain,
( ( ~ ! [Xq: ( $i > $i ) > $o] :
( ( Xq @ cN )
=> ( Xq @ cM ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(43,plain,
( ( ~ ! [SX0: ( $i > $i ) > $o] :
( ~ ( SX0 @ cN )
| ( SX0 @ cM ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(44,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
~ ( ~ ( ~ ( SX1 @ ( cM @ SX0 ) )
| ( SX1 @ ( cN @ SX0 ) ) )
| ~ ( ~ ( SX1 @ ( cN @ SX0 ) )
| ( SX1 @ ( cM @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(45,plain,
( ( ! [SX0: ( $i > $i ) > $o] :
( ~ ( SX0 @ cN )
| ( SX0 @ cM ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV7: $i] :
( ( ! [SY4: $i > $o] :
~ ( ~ ( ~ ( SY4 @ ( cM @ SV7 ) )
| ( SY4 @ ( cN @ SV7 ) ) )
| ~ ( ~ ( SY4 @ ( cN @ SV7 ) )
| ( SY4 @ ( cM @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(47,plain,
( ( ~ ( sK3_SX0 @ cN )
| ( sK3_SX0 @ cM ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[45]) ).
thf(48,plain,
! [SV7: $i,SV8: $i > $o] :
( ( ~ ( ~ ( ~ ( SV8 @ ( cM @ SV7 ) )
| ( SV8 @ ( cN @ SV7 ) ) )
| ~ ( ~ ( SV8 @ ( cN @ SV7 ) )
| ( SV8 @ ( cM @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(49,plain,
( ( ~ ( sK3_SX0 @ cN ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(50,plain,
( ( sK3_SX0 @ cM )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(51,plain,
! [SV7: $i,SV8: $i > $o] :
( ( ~ ( ~ ( SV8 @ ( cM @ SV7 ) )
| ( SV8 @ ( cN @ SV7 ) ) )
| ~ ( ~ ( SV8 @ ( cN @ SV7 ) )
| ( SV8 @ ( cM @ SV7 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(52,plain,
( ( sK3_SX0 @ cN )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(53,plain,
! [SV7: $i,SV8: $i > $o] :
( ( ~ ( ~ ( SV8 @ ( cM @ SV7 ) )
| ( SV8 @ ( cN @ SV7 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(54,plain,
! [SV7: $i,SV8: $i > $o] :
( ( ~ ( ~ ( SV8 @ ( cN @ SV7 ) )
| ( SV8 @ ( cM @ SV7 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(55,plain,
! [SV7: $i,SV8: $i > $o] :
( ( ~ ( SV8 @ ( cM @ SV7 ) )
| ( SV8 @ ( cN @ SV7 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(56,plain,
! [SV7: $i,SV8: $i > $o] :
( ( ~ ( SV8 @ ( cN @ SV7 ) )
| ( SV8 @ ( cM @ SV7 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(57,plain,
! [SV7: $i,SV8: $i > $o] :
( ( ( ~ ( SV8 @ ( cM @ SV7 ) ) )
= $true )
| ( ( SV8 @ ( cN @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV7: $i,SV8: $i > $o] :
( ( ( ~ ( SV8 @ ( cN @ SV7 ) ) )
= $true )
| ( ( SV8 @ ( cM @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(59,plain,
! [SV7: $i,SV8: $i > $o] :
( ( ( SV8 @ ( cM @ SV7 ) )
= $false )
| ( ( SV8 @ ( cN @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(60,plain,
! [SV7: $i,SV8: $i > $o] :
( ( ( SV8 @ ( cN @ SV7 ) )
= $false )
| ( ( SV8 @ ( cM @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(61,plain,
! [SV7: $i] :
( ( ( ( cM @ SV7 )
= ( cM @ SV7 ) )
= $false )
| ( ( ( cN @ SV7 )
= ( cM @ SV7 ) )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[59:[bind(SV8,$thf( ^ [SV9: $i] : ( SV9 = ( cM @ SV7 ) ) ))]]) ).
thf(62,plain,
! [SV7: $i] :
( ( ( cN @ SV7 )
= ( cM @ SV7 ) )
= $true ),
inference(sim,[status(thm)],[61]) ).
thf(63,plain,
! [SV7: $i] :
( ( ( ( cN @ SV7 )
= ( cN @ SV7 ) )
= $false )
| ( ( ( cM @ SV7 )
= ( cN @ SV7 ) )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[60:[bind(SV8,$thf( ^ [SV10: $i] : ( SV10 = ( cN @ SV7 ) ) ))]]) ).
thf(64,plain,
! [SV7: $i] :
( ( ( cM @ SV7 )
= ( cN @ SV7 ) )
= $true ),
inference(sim,[status(thm)],[63]) ).
thf(65,plain,
( ( ( sK3_SX0 @ cN )
= ( sK3_SX0 @ cM ) )
= $false ),
inference(res,[status(thm)],[52,50]) ).
thf(66,plain,
( ( ( cN @ sK4_E )
= ( cM @ sK4_E ) )
= $false ),
inference(extuni,[status(esa)],[65]) ).
thf(67,plain,
! [SV11: $i] :
( ( ( cN @ SV11 )
= ( cM @ SV11 ) )
= $true ),
inference(rename,[status(thm)],[62]) ).
thf(69,plain,
! [SV12: $i] :
( ( ( cM @ SV12 )
= ( cN @ SV12 ) )
= $true ),
inference(rename,[status(thm)],[64]) ).
thf(71,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[50,69,67,66,52]) ).
thf(72,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[71,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO374^5 : 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
% 0.10/0.17 % Computer : n004.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 17:39:05 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.24
% 0.10/0.24 No.of.Axioms: 0
% 0.10/0.24
% 0.10/0.24 Length.of.Defs: 0
% 0.10/0.24
% 0.10/0.24 Contains.Choice.Funs: false
% 0.10/0.24 .
% 0.10/0.24
% 0.10/0.24 ********************************
% 0.10/0.24 * All subproblems solved! *
% 0.10/0.24 ********************************
% 0.10/0.24 % 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:71,loop_count:5,foatp_calls:3,translation:fof_full)
% 0.10/0.24
% 0.10/0.24 %**** Beginning of derivation protocol ****
% 0.10/0.24 % SZS output start CNFRefutation
% See solution above
% 0.10/0.24
% 0.10/0.24 %**** End of derivation protocol ****
% 0.10/0.24 %**** no. of clauses in derivation: 68 ****
% 0.10/0.24 %**** clause counter: 71 ****
% 0.10/0.24
% 0.10/0.24 % 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:71,loop_count:5,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------