%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO308^5 : 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 : n012.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 11:08:02 AM UTC 2026
% Result : Theorem 0.10s 0.14s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 27 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 163 ( 39 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 177 ( 18 ~; 44 |; 0 &; 92 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 0 ^; 40 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cA,type,
cA: $i > $o ).
thf(tp_cB,type,
cB: $i > $o ).
thf(tp_sK1_Z1,type,
sK1_Z1: $i > $o ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(1,conjecture,
! [Z1: $i > $o] :
( ( ! [Z3: $i] :
( ( Z1 @ Z3 )
=> ( cA @ Z3 ) )
| ! [Z4: $i] :
( ( Z1 @ Z4 )
=> ( cB @ Z4 ) ) )
=> ! [Z5: $i] :
( ( Z1 @ Z5 )
=> ( ( cA @ Z5 )
| ( cB @ Z5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSET81_pme) ).
thf(2,negated_conjecture,
( ( ! [Z1: $i > $o] :
( ( ! [Z3: $i] :
( ( Z1 @ Z3 )
=> ( cA @ Z3 ) )
| ! [Z4: $i] :
( ( Z1 @ Z4 )
=> ( cB @ Z4 ) ) )
=> ! [Z5: $i] :
( ( Z1 @ Z5 )
=> ( ( cA @ Z5 )
| ( cB @ Z5 ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Z1: $i > $o] :
( ( ! [Z3: $i] :
( ( Z1 @ Z3 )
=> ( cA @ Z3 ) )
| ! [Z4: $i] :
( ( Z1 @ Z4 )
=> ( cB @ Z4 ) ) )
=> ! [Z5: $i] :
( ( Z1 @ Z5 )
=> ( ( cA @ Z5 )
| ( cB @ Z5 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ( ! [SY4: $i] :
( ( sK1_Z1 @ SY4 )
=> ( cA @ SY4 ) )
| ! [SY5: $i] :
( ( sK1_Z1 @ SY5 )
=> ( cB @ SY5 ) ) )
=> ! [SY6: $i] :
( ( sK1_Z1 @ SY6 )
=> ( ( cA @ SY6 )
| ( cB @ SY6 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY4: $i] :
( ( sK1_Z1 @ SY4 )
=> ( cA @ SY4 ) )
| ! [SY5: $i] :
( ( sK1_Z1 @ SY5 )
=> ( cB @ SY5 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [SY6: $i] :
( ( sK1_Z1 @ SY6 )
=> ( ( cA @ SY6 )
| ( cB @ SY6 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ! [SY6: $i] :
( ( sK1_Z1 @ SY6 )
=> ( ( cA @ SY6 )
| ( cB @ SY6 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY4: $i] :
( ( sK1_Z1 @ SY4 )
=> ( cA @ SY4 ) )
| ! [SY5: $i] :
( ( sK1_Z1 @ SY5 )
=> ( cB @ SY5 ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ~ ! [SY6: $i] :
( ( sK1_Z1 @ SY6 )
=> ( ( cA @ SY6 )
| ( cB @ SY6 ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [SX0: $i] :
( ~ ( sK1_Z1 @ SX0 )
| ( cA @ SX0 ) )
| ! [SX0: $i] :
( ~ ( sK1_Z1 @ SX0 )
| ( cB @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK1_Z1 @ SX0 )
| ( cA @ SX0 )
| ( cB @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
( ( ( ! [SX0: $i] :
( ~ ( sK1_Z1 @ SX0 )
| ( cA @ SX0 ) ) )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( sK1_Z1 @ SX0 )
| ( cB @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [SX0: $i] :
( ~ ( sK1_Z1 @ SX0 )
| ( cA @ SX0 )
| ( cB @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV1: $i] :
( ( ( ~ ( sK1_Z1 @ SV1 )
| ( cA @ SV1 ) )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( sK1_Z1 @ SX0 )
| ( cB @ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( sK1_Z1 @ sK2_SX0 )
| ( cA @ sK2_SX0 )
| ( cB @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(16,plain,
! [SV1: $i] :
( ( ( ~ ( sK1_Z1 @ SV1 ) )
= $true )
| ( ( cA @ SV1 )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( sK1_Z1 @ SX0 )
| ( cB @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( sK1_Z1 @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ( cA @ sK2_SX0 )
| ( cB @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(19,plain,
! [SV1: $i] :
( ( ( sK1_Z1 @ SV1 )
= $false )
| ( ( cA @ SV1 )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( sK1_Z1 @ SX0 )
| ( cB @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( sK1_Z1 @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( cA @ sK2_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(22,plain,
( ( cB @ sK2_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(23,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( sK1_Z1 @ SV2 )
| ( cB @ SV2 ) )
= $true )
| ( ( cA @ SV1 )
= $true )
| ( ( sK1_Z1 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( sK1_Z1 @ SV2 ) )
= $true )
| ( ( cB @ SV2 )
= $true )
| ( ( cA @ SV1 )
= $true )
| ( ( sK1_Z1 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(25,plain,
! [SV1: $i,SV2: $i] :
( ( ( sK1_Z1 @ SV2 )
= $false )
| ( ( cB @ SV2 )
= $true )
| ( ( cA @ SV1 )
= $true )
| ( ( sK1_Z1 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(26,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,25,22,21]) ).
thf(27,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO308^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Oct 6 17:34:01 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.14
% 0.10/0.14 No.of.Axioms: 0
% 0.10/0.14
% 0.10/0.14 Length.of.Defs: 0
% 0.10/0.14
% 0.10/0.14 Contains.Choice.Funs: false
% 0.10/0.14
% 0.10/0.14 ********************************
% 0.10/0.14 * All subproblems solved! *
% 0.10/0.14 ********************************
% 0.10/0.14 % 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:26,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.14
% 0.10/0.14 %**** Beginning of derivation protocol ****
% 0.10/0.14 % SZS output start CNFRefutation
% See solution above
% 0.10/0.14
% 0.10/0.14 %**** End of derivation protocol ****
% 0.10/0.14 %**** no. of clauses in derivation: 27 ****
% 0.10/0.14 %**** clause counter: 26 ****
% 0.10/0.14
% 0.10/0.14 % 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:26,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------