%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV258^5 : 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 : n010.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 10:49:50 AM UTC 2026
% Result : Theorem 0.10s 0.23s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 28 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 134 ( 46 equ; 0 cnn)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 101 ( 17 ~; 0 |; 34 &; 25 @)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 65 ( 20 ^; 40 !; 5 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_R,type,
sK1_R: a > $o ).
thf(tp_sK2_R,type,
sK2_R: a > $o ).
thf(tp_sK3_K,type,
sK3_K: ( a > $o ) > $o ).
thf(tp_sK4_R,type,
sK4_R: a > $o ).
thf(tp_sK5_Y,type,
sK5_Y: a > $o ).
thf(tp_sK6_Z,type,
sK6_Z: a > $o ).
thf(tp_sK7_S,type,
sK7_S: a > $o ).
thf(1,conjecture,
( ! [R: a > $o] :
( ( R
= ( ^ [Xx: a] : $false ) )
=> $true )
& ! [R: a > $o] :
( ( R
= ( ^ [Xx: a] : ~ $false ) )
=> $true )
& ! [K: ( a > $o ) > $o,R: a > $o] :
( ( ! [Xx: a > $o] :
( ( K @ Xx )
=> $true )
& ( R
= ( ^ [Xx: a] :
? [S: a > $o] :
( ( K @ S )
& ( S @ Xx ) ) ) ) )
=> $true )
& ! [Y: a > $o,Z: a > $o,S: a > $o] :
( ( $true
& $true
& ( S
= ( ^ [Xx: a] :
( ( Y @ Xx )
& ( Z @ Xx ) ) ) ) )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cDISCRETE_TOPOLOGY_pme) ).
thf(2,negated_conjecture,
( ( ! [R: a > $o] :
( ( R
= ( ^ [Xx: a] : $false ) )
=> $true )
& ! [R: a > $o] :
( ( R
= ( ^ [Xx: a] : ~ $false ) )
=> $true )
& ! [K: ( a > $o ) > $o,R: a > $o] :
( ( ! [Xx: a > $o] :
( ( K @ Xx )
=> $true )
& ( R
= ( ^ [Xx: a] :
? [S: a > $o] :
( ( K @ S )
& ( S @ Xx ) ) ) ) )
=> $true )
& ! [Y: a > $o,Z: a > $o,S: a > $o] :
( ( $true
& $true
& ( S
= ( ^ [Xx: a] :
( ( Y @ Xx )
& ( Z @ Xx ) ) ) ) )
=> $true ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [R: a > $o] :
( ( R
= ( ^ [Xx: a] : $false ) )
=> $true )
& ! [R: a > $o] :
( ( R
= ( ^ [Xx: a] : ~ $false ) )
=> $true )
& ! [K: ( a > $o ) > $o,R: a > $o] :
( ( ! [Xx: a > $o] :
( ( K @ Xx )
=> $true )
& ( R
= ( ^ [Xx: a] :
? [S: a > $o] :
( ( K @ S )
& ( S @ Xx ) ) ) ) )
=> $true )
& ! [Y: a > $o,Z: a > $o,S: a > $o] :
( ( $true
& $true
& ( S
= ( ^ [Xx: a] :
( ( Y @ Xx )
& ( Z @ Xx ) ) ) ) )
=> $true ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [R: a > $o] :
( ( R
= ( ^ [Xx: a] : $false ) )
=> $true ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(5,plain,
( ( ! [R: a > $o] :
( ( R
= ( ^ [Xx: a] : ~ $false ) )
=> $true ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(6,plain,
( ( ! [K: ( a > $o ) > $o,R: a > $o] :
( ( ! [Xx: a > $o] :
( ( K @ Xx )
=> $true )
& ( R
= ( ^ [Xx: a] :
? [S: a > $o] :
( ( K @ S )
& ( S @ Xx ) ) ) ) )
=> $true ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(7,plain,
( ( ! [Y: a > $o,Z: a > $o,S: a > $o] :
( ( $true
& $true
& ( S
= ( ^ [Xx: a] :
( ( Y @ Xx )
& ( Z @ Xx ) ) ) ) )
=> $true ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(8,plain,
( ( ~ ! [R: a > $o] :
( ( R
= ( ^ [Xx: a] : $false ) )
=> $true ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(9,plain,
( ( ~ ! [R: a > $o] :
( ( R
= ( ^ [Xx: a] : ~ $false ) )
=> $true ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(10,plain,
( ( ~ ! [K: ( a > $o ) > $o,R: a > $o] :
( ( ! [Xx: a > $o] :
( ( K @ Xx )
=> $true )
& ( R
= ( ^ [Xx: a] :
? [S: a > $o] :
( ( K @ S )
& ( S @ Xx ) ) ) ) )
=> $true ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(11,plain,
( ( ~ ! [Y: a > $o,Z: a > $o,S: a > $o] :
( ( $true
& $true
& ( S
= ( ^ [Xx: a] :
( ( Y @ Xx )
& ( Z @ Xx ) ) ) ) )
=> $true ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(12,plain,
( ( ~ $true ) = $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(13,plain,
( ( ~ $true ) = $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(14,plain,
( ( ~ $true ) = $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(15,plain,
( ( ~ $true ) = $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(16,plain,
( ( ~ $true ) = $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
$true = $false,
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(18,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[17]) ).
thf(19,plain,
( ( ~ $true ) = $true ),
inference(copy,[status(thm)],[13]) ).
thf(20,plain,
$true = $false,
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(21,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20]) ).
thf(22,plain,
( ( ~ $true ) = $true ),
inference(copy,[status(thm)],[14]) ).
thf(23,plain,
$true = $false,
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(24,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23]) ).
thf(25,plain,
( ( ~ $true ) = $true ),
inference(copy,[status(thm)],[15]) ).
thf(26,plain,
$true = $false,
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(27,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26]) ).
thf(28,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[27,18,21,24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV258^5 : 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 : n010.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 15:44:10 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
% 0.10/0.23
% 0.10/0.23 No.of.Axioms: 0
% 0.10/0.23
% 0.10/0.23 Length.of.Defs: 0
% 0.10/0.23
% 0.10/0.23 Contains.Choice.Funs: false
% 0.10/0.23
% 0.10/0.23 ********************************
% 0.10/0.23 * All subproblems solved! *
% 0.10/0.23 ********************************
% 0.10/0.23 % 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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:27,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.10/0.23
% 0.10/0.23 %**** Beginning of derivation protocol ****
% 0.10/0.23 % SZS output start CNFRefutation
% See solution above
% 0.10/0.23
% 0.10/0.23 %**** End of derivation protocol ****
% 0.10/0.23 %**** no. of clauses in derivation: 28 ****
% 0.10/0.23 %**** clause counter: 27 ****
% 0.10/0.23
% 0.10/0.23 % 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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:27,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------