%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO365^5 : 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 : 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 11:08:08 AM UTC 2026
% Result : Theorem 0.10s 0.14s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 16 unt; 0 typ; 2 def)
% Number of atoms : 104 ( 31 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 49 ( 22 ~; 6 |; 0 &; 12 @)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cA,type,
cA: $o ).
thf(tp_cC,type,
cC: $o > $o ).
thf(tp_cEXT2,type,
cEXT2: $o ).
thf(tp_cEXT_eq_0,type,
cEXT_eq_0: $o ).
thf(cEXT2,definition,
( cEXT2
= ( ( cC @ cA )
=> ( cC
@ ~ ~ cA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEXT2_def) ).
thf(cEXT_eq_0,definition,
( cEXT_eq_0
= ( ! [Xp: $o,Xq: $o] :
( ( Xp
<=> Xq )
=> ( Xp = Xq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEXT_eq_0_def) ).
thf(1,conjecture,
( cEXT_eq_0
=> cEXT2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEXT2A) ).
thf(2,negated_conjecture,
( ( cEXT_eq_0
=> cEXT2 )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xp: $o,Xq: $o] :
( ( Xp
<=> Xq )
=> ( Xp = Xq ) )
=> ( ( cC @ cA )
=> ( cC
@ ~ ~ cA ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cEXT2,cEXT_eq_0]) ).
thf(5,plain,
( ( cC @ cA )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( cC
@ ~ ~ cA )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ( cC
@ ~ ~ cA ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(9,plain,
( ( cC @ cA )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(11,plain,
( ( ~ ( cC
@ ~ ~ cA ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(13,plain,
( ( cC
@ ~ ~ cA )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(821,plain,
( ( ( cC
@ ~ ~ cA )
= ( cC @ cA ) )
= $false ),
inference(res,[status(thm)],[13,9]) ).
thf(822,plain,
( ( ( ~ ~ cA )
= $true )
| ( cA = $true ) ),
inference(extuni,[status(esa)],[821]) ).
thf(823,plain,
( ( ( ~ ~ cA )
= $false )
| ( cA = $false ) ),
inference(extuni,[status(esa)],[821]) ).
thf(824,plain,
( ( ( ~ cA ) = $true )
| ( cA = $false ) ),
inference(extcnf_not_neg,[status(thm)],[823]) ).
thf(825,plain,
( ( ( ~ cA ) = $false )
| ( cA = $true ) ),
inference(extcnf_not_pos,[status(thm)],[822]) ).
thf(826,plain,
( ( cA = $false )
| ( cA = $false ) ),
inference(extcnf_not_pos,[status(thm)],[824]) ).
thf(827,plain,
( ( cA = $true )
| ( cA = $true ) ),
inference(extcnf_not_neg,[status(thm)],[825]) ).
thf(828,plain,
cA = $false,
inference(sim,[status(thm)],[826]) ).
thf(829,plain,
cA = $true,
inference(sim,[status(thm)],[827]) ).
thf(831,plain,
( ( cA = cA )
= $false ),
inference(res,[status(thm)],[829,828]) ).
thf(833,plain,
$false = $true,
inference(extuni,[status(esa)],[831]) ).
thf(834,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[833]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO365^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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
% 0.00/0.09 % Computer : n012.cluster.edu
% 0.00/0.09 % Model : x86_64 x86_64
% 0.00/0.09 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.09 % Memory : 8046.5625MB
% 0.00/0.09 % OS : Linux 6.8.0-71-generic
% 0.00/0.09 % CPULimit : 300
% 0.00/0.09 % WCLimit : 300
% 0.00/0.09 % DateTime : Tue Oct 6 17:35:15 UTC 2026
% 0.00/0.09 % CPUTime :
% 0.00/0.09 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: 292
% 0.10/0.14
% 0.10/0.14 Contains.Choice.Funs: false
% 0.10/0.14 ...........
% 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:0,axioms:2,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:833,loop_count:4,foatp_calls:2,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: 21 ****
% 0.10/0.14 %**** clause counter: 833 ****
% 0.10/0.14
% 0.10/0.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:833,loop_count:4,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------