%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN366+1 : TPTP v9.3.1. Released v2.0.0.
% 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 : n001.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 11:05:38 AM UTC 2026
% Result : Theorem 0.09s 0.21s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 44 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 203 ( 50 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 321 ( 60 ~; 40 |; 3 &; 202 @)
% ( 10 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 82 ( 0 ^; 77 !; 5 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_big_r,type,
big_r: $i > $i > $o ).
thf(tp_sK1_Y,type,
sK1_Y: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(1,conjecture,
( ( ! [U: $i,V: $i] :
( ( big_r @ U @ U )
<=> ( big_r @ U @ V ) )
& ! [W: $i,Z: $i] :
( ( big_r @ W @ W )
<=> ( big_r @ Z @ W ) ) )
=> ( ? [X: $i] : ( big_r @ X @ X )
=> ! [Y: $i] : ( big_r @ Y @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2117) ).
thf(2,negated_conjecture,
( ( ( ! [U: $i,V: $i] :
( ( big_r @ U @ U )
<=> ( big_r @ U @ V ) )
& ! [W: $i,Z: $i] :
( ( big_r @ W @ W )
<=> ( big_r @ Z @ W ) ) )
=> ( ? [X: $i] : ( big_r @ X @ X )
=> ! [Y: $i] : ( big_r @ Y @ Y ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [U: $i,V: $i] :
( ( big_r @ U @ U )
<=> ( big_r @ U @ V ) )
& ! [W: $i,Z: $i] :
( ( big_r @ W @ W )
<=> ( big_r @ Z @ W ) ) )
=> ( ? [X: $i] : ( big_r @ X @ X )
=> ! [Y: $i] : ( big_r @ Y @ Y ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [U: $i,V: $i] :
( ( big_r @ U @ U )
<=> ( big_r @ U @ V ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [W: $i,Z: $i] :
( ( big_r @ W @ W )
<=> ( big_r @ Z @ W ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ? [X: $i] : ( big_r @ X @ X ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [Y: $i] : ( big_r @ Y @ Y ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ! [Y: $i] : ( big_r @ Y @ Y ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ? [X: $i] : ( big_r @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( ! [W: $i,Z: $i] :
( ( big_r @ W @ W )
<=> ( big_r @ Z @ W ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(11,plain,
( ( ! [U: $i,V: $i] :
( ( big_r @ U @ U )
<=> ( big_r @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(12,plain,
( ( ~ ! [Y: $i] : ( big_r @ Y @ Y ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ~ ! [SX0: $i] :
~ ( big_r @ SX0 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(14,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( big_r @ SX0 @ SX0 )
| ( big_r @ SX0 @ SX1 ) )
| ~ ( ~ ( big_r @ SX0 @ SX1 )
| ( big_r @ SX0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( big_r @ SX0 @ SX0 )
| ( big_r @ SX1 @ SX0 ) )
| ~ ( ~ ( big_r @ SX1 @ SX0 )
| ( big_r @ SX0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(16,plain,
( ( ! [Y: $i] : ( big_r @ Y @ Y ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(17,plain,
( ( ! [SX0: $i] :
~ ( big_r @ SX0 @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(18,plain,
! [SV1: $i] :
( ( ! [SY6: $i] :
~ ( ~ ( ~ ( big_r @ SV1 @ SV1 )
| ( big_r @ SV1 @ SY6 ) )
| ~ ( ~ ( big_r @ SV1 @ SY6 )
| ( big_r @ SV1 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(19,plain,
! [SV2: $i] :
( ( ! [SY7: $i] :
~ ( ~ ( ~ ( big_r @ SV2 @ SV2 )
| ( big_r @ SY7 @ SV2 ) )
| ~ ( ~ ( big_r @ SY7 @ SV2 )
| ( big_r @ SV2 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
( ( big_r @ sK1_Y @ sK1_Y )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(21,plain,
( ( ~ ( big_r @ sK2_SX0 @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(22,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ( ~ ( ~ ( big_r @ SV1 @ SV1 )
| ( big_r @ SV1 @ SV3 ) )
| ~ ( ~ ( big_r @ SV1 @ SV3 )
| ( big_r @ SV1 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV4: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( big_r @ SV2 @ SV2 )
| ( big_r @ SV4 @ SV2 ) )
| ~ ( ~ ( big_r @ SV4 @ SV2 )
| ( big_r @ SV2 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( big_r @ sK2_SX0 @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ( ~ ( big_r @ SV1 @ SV1 )
| ( big_r @ SV1 @ SV3 ) )
| ~ ( ~ ( big_r @ SV1 @ SV3 )
| ( big_r @ SV1 @ SV1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV4: $i,SV2: $i] :
( ( ~ ( ~ ( big_r @ SV2 @ SV2 )
| ( big_r @ SV4 @ SV2 ) )
| ~ ( ~ ( big_r @ SV4 @ SV2 )
| ( big_r @ SV2 @ SV2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ( ~ ( big_r @ SV1 @ SV1 )
| ( big_r @ SV1 @ SV3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(28,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ( ~ ( big_r @ SV1 @ SV3 )
| ( big_r @ SV1 @ SV1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(29,plain,
! [SV4: $i,SV2: $i] :
( ( ~ ( ~ ( big_r @ SV2 @ SV2 )
| ( big_r @ SV4 @ SV2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
! [SV2: $i,SV4: $i] :
( ( ~ ( ~ ( big_r @ SV4 @ SV2 )
| ( big_r @ SV2 @ SV2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(31,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ( big_r @ SV1 @ SV1 )
| ( big_r @ SV1 @ SV3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(32,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ( big_r @ SV1 @ SV3 )
| ( big_r @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(33,plain,
! [SV4: $i,SV2: $i] :
( ( ~ ( big_r @ SV2 @ SV2 )
| ( big_r @ SV4 @ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(34,plain,
! [SV2: $i,SV4: $i] :
( ( ~ ( big_r @ SV4 @ SV2 )
| ( big_r @ SV2 @ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(35,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( big_r @ SV1 @ SV1 ) )
= $true )
| ( ( big_r @ SV1 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( big_r @ SV1 @ SV3 ) )
= $true )
| ( ( big_r @ SV1 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( big_r @ SV2 @ SV2 ) )
= $true )
| ( ( big_r @ SV4 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( big_r @ SV4 @ SV2 ) )
= $true )
| ( ( big_r @ SV2 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV3: $i,SV1: $i] :
( ( ( big_r @ SV1 @ SV1 )
= $false )
| ( ( big_r @ SV1 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV3: $i,SV1: $i] :
( ( ( big_r @ SV1 @ SV3 )
= $false )
| ( ( big_r @ SV1 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV4: $i,SV2: $i] :
( ( ( big_r @ SV2 @ SV2 )
= $false )
| ( ( big_r @ SV4 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV2: $i,SV4: $i] :
( ( ( big_r @ SV4 @ SV2 )
= $false )
| ( ( big_r @ SV2 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,42,41,40,39,24]) ).
thf(44,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN366+1 : TPTP v9.3.1. Released v2.0.0.
% 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
% 0.09/0.17 % Computer : n001.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 17:25:39 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.21
% 0.09/0.21 No.of.Axioms: 0
% 0.09/0.21
% 0.09/0.21 Length.of.Defs: 0
% 0.09/0.21
% 0.09/0.21 Contains.Choice.Funs: false
% 0.09/0.21
% 0.09/0.21 ********************************
% 0.09/0.21 * All subproblems solved! *
% 0.09/0.21 ********************************
% 0.09/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:43,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.21
% 0.09/0.21 %**** Beginning of derivation protocol ****
% 0.09/0.21 % SZS output start CNFRefutation
% See solution above
% 0.09/0.21
% 0.09/0.21 %**** End of derivation protocol ****
% 0.09/0.21 %**** no. of clauses in derivation: 44 ****
% 0.09/0.21 %**** clause counter: 43 ****
% 0.09/0.21
% 0.09/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:43,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------