%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO379^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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 : n007.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 11:08:10 AM UTC 2026
% Result : Theorem 0.07s 0.21s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 177 ( 109 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 170 ( 40 ~; 41 |; 3 &; 86 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 12 ^; 53 !; 7 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c,type,
c: $i ).
thf(tp_cQDP0,type,
cQDP0: $i > $o ).
thf(tp_cQDP1,type,
cQDP1: ( $i > $o ) > $o ).
thf(tp_sK1_SV2,type,
sK1_SV2: ( $i > $o ) > $i ).
thf(cQDP0,definition,
( cQDP0
= ( ^ [Xz: $i] : ( Xz = c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cQDP0_def) ).
thf(cQDP1,definition,
( cQDP1
= ( ^ [Xz: $i > $o] :
( ( Xz = cQDP0 )
& ? [Xt: $i] : ( Xz @ Xt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cQDP1_def) ).
thf(1,conjecture,
? [Xs: $i > $o] : ( cQDP1 @ Xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cQDTHM1) ).
thf(2,negated_conjecture,
( ( ? [Xs: $i > $o] : ( cQDP1 @ Xs ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [SY0: $i > $o] :
( ( SY0
= ( ^ [Xz: $i] : ( Xz = c ) ) )
& ? [SY1: $i] : ( SY0 @ SY1 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cQDP0,cQDP1]) ).
thf(4,plain,
( ( ~ ? [SY0: $i > $o] :
( ( SY0
= ( ^ [Xz: $i] : ( Xz = c ) ) )
& ? [SY1: $i] : ( SY0 @ SY1 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: $i > $o] :
( ( SY0
!= ( ^ [Xz: $i] : ( Xz = c ) ) )
| ! [SY1: $i] :
~ ( SY0 @ SY1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY0: $i > $o] :
( ( SY0
!= ( ^ [Xz: $i] : ( Xz = c ) ) )
| ! [SY1: $i] :
~ ( SY0 @ SY1 ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
! [SV1: $i > $o] :
( ( ( SV1
!= ( ^ [Xz: $i] : ( Xz = c ) ) )
| ! [SY6: $i] :
~ ( SV1 @ SY6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6]) ).
thf(8,plain,
! [SV1: $i > $o] :
( ( ( SV1
!= ( ^ [Xz: $i] : ( Xz = c ) ) )
= $true )
| ( ( ! [SY6: $i] :
~ ( SV1 @ SY6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7]) ).
thf(9,plain,
! [SV1: $i > $o] :
( ( ( SV1
= ( ^ [Xz: $i] : ( Xz = c ) ) )
= $false )
| ( ( ! [SY6: $i] :
~ ( SV1 @ SY6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: $i > $o] :
( ( ( ! [SV2: $i] :
( ( SV1 @ SV2 )
= ( SV2 = c ) ) )
= $false )
| ( ( ! [SY6: $i] :
~ ( SV1 @ SY6 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[9]) ).
thf(11,plain,
! [SV1: $i > $o] :
( ( ( SV1
= ( ^ [Xz: $i] : ( Xz = c ) ) )
= $false )
| ( ( ! [SY6: $i] :
~ ( SV1 @ SY6 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i > $o] :
( ( ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= ( ( sK1_SV2 @ SV1 )
= c ) )
= $false )
| ( ( ! [SY6: $i] :
~ ( SV1 @ SY6 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(13,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV3 ) )
= $true )
| ( ( SV1
= ( ^ [Xz: $i] : ( Xz = c ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV1: $i > $o] :
( ( ( ~ ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
| ( ( sK1_SV2 @ SV1 )
= c ) )
| ~ ( ~ ( SV1 @ ( sK1_SV2 @ SV1 ) )
| ( ( sK1_SV2 @ SV1 )
!= c ) ) )
= $false )
| ( ( ! [SY6: $i] :
~ ( SV1 @ SY6 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: $i > $o] :
( ( ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= ( ( sK1_SV2 @ SV1 )
= c ) )
= $false )
| ( ( ! [SY6: $i] :
~ ( SV1 @ SY6 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[12]) ).
thf(16,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ SV3 )
= $false )
| ( ( SV1
= ( ^ [Xz: $i] : ( Xz = c ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV1: $i > $o] :
( ( ( ~ ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
| ( ( sK1_SV2 @ SV1 )
= c ) ) )
= $false )
| ( ( ! [SY6: $i] :
~ ( SV1 @ SY6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: $i > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK1_SV2 @ SV1 ) )
| ( ( sK1_SV2 @ SV1 )
!= c ) ) )
= $false )
| ( ( ! [SY6: $i] :
~ ( SV1 @ SY6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(19,plain,
! [SV4: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV4 ) )
= $true )
| ( ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= ( ( sK1_SV2 @ SV1 )
= c ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
! [SV1: $i > $o] :
( ( ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
| ( ( sK1_SV2 @ SV1 )
= c ) )
= $true )
| ( ( ! [SY6: $i] :
~ ( SV1 @ SY6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV1: $i > $o] :
( ( ( ~ ( SV1 @ ( sK1_SV2 @ SV1 ) )
| ( ( sK1_SV2 @ SV1 )
!= c ) )
= $true )
| ( ( ! [SY6: $i] :
~ ( SV1 @ SY6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV4: $i,SV1: $i > $o] :
( ( ( SV1 @ SV4 )
= $false )
| ( ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= ( ( sK1_SV2 @ SV1 )
= c ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ( sK1_SV2 @ SV1 )
= c )
= $true )
| ( ( ! [SY6: $i] :
~ ( SV1 @ SY6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV1: $i > $o] :
( ( ( ~ ( SV1 @ ( sK1_SV2 @ SV1 ) ) )
= $true )
| ( ( ( sK1_SV2 @ SV1 )
!= c )
= $true )
| ( ( ! [SY6: $i] :
~ ( SV1 @ SY6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV5: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV5 ) )
= $true )
| ( ( ( sK1_SV2 @ SV1 )
= c )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ( sK1_SV2 @ SV1 )
!= c )
= $true )
| ( ( ! [SY6: $i] :
~ ( SV1 @ SY6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV5: $i,SV1: $i > $o] :
( ( ( SV1 @ SV5 )
= $false )
| ( ( ( sK1_SV2 @ SV1 )
= c )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV1: $i > $o] :
( ( ( ( sK1_SV2 @ SV1 )
= c )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY6: $i] :
~ ( SV1 @ SY6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV6: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV6 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ( sK1_SV2 @ SV1 )
= c )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(30,plain,
! [SV6: $i,SV1: $i > $o] :
( ( ( SV1 @ SV6 )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ( sK1_SV2 @ SV1 )
= c )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(31,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,30,27,22]) ).
thf(32,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO379^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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
% 0.07/0.17 % Computer : n007.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 17:37:11 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.21
% 0.07/0.21 No.of.Axioms: 0
% 0.07/0.21
% 0.07/0.21 Length.of.Defs: 279
% 0.07/0.21
% 0.07/0.21 Contains.Choice.Funs: false
% 0.07/0.21
% 0.07/0.21 ********************************
% 0.07/0.21 * All subproblems solved! *
% 0.07/0.21 ********************************
% 0.07/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:31,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.21
% 0.07/0.21 %**** Beginning of derivation protocol ****
% 0.07/0.21 % SZS output start CNFRefutation
% See solution above
% 0.07/0.21
% 0.07/0.21 %**** End of derivation protocol ****
% 0.07/0.21 %**** no. of clauses in derivation: 32 ****
% 0.07/0.21 %**** clause counter: 31 ****
% 0.07/0.21
% 0.07/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:31,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------