%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO370^5 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 11:08:09 AM UTC 2026
% Result : Theorem 0.07s 0.20s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 98 ( 27 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 71 ( 24 ~; 6 |; 0 &; 38 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 8 ( 8 ^; 0 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cA,type,
cA: $i > $o ).
thf(tp_cP,type,
cP: ( $i > $o ) > $o ).
thf(tp_sK1_E,type,
sK1_E: $i ).
thf(1,conjecture,
( ( cP @ cA )
=> ( cP
@ ^ [Xx: $i] :
~ ~ ( cA @ Xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTRIVEXT3) ).
thf(2,negated_conjecture,
( ( ( cP @ cA )
=> ( cP
@ ^ [Xx: $i] :
~ ~ ( cA @ Xx ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( cP @ cA )
=> ( cP
@ ^ [Xx: $i] :
~ ~ ( cA @ Xx ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( cP @ cA )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( cP
@ ^ [Xx: $i] :
~ ~ ( cA @ Xx ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ( cP
@ ^ [Xx: $i] :
~ ~ ( cA @ Xx ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( cP @ cA )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ( cP
@ ^ [Xx: $i] :
~ ~ ( cA @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( cP
@ ^ [Xx: $i] :
~ ~ ( cA @ Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8]) ).
thf(10,plain,
( ( ( cP
@ ^ [Xx: $i] :
~ ~ ( cA @ Xx ) )
= ( cP @ cA ) )
= $false ),
inference(res,[status(thm)],[9,7]) ).
thf(11,plain,
( ( ( ~ ~ ( cA @ sK1_E ) )
= $true )
| ( ( cA @ sK1_E )
= $true ) ),
inference(extuni,[status(esa)],[10]) ).
thf(12,plain,
( ( ( ~ ~ ( cA @ sK1_E ) )
= $false )
| ( ( cA @ sK1_E )
= $false ) ),
inference(extuni,[status(esa)],[10]) ).
thf(13,plain,
( ( ( ~ ( cA @ sK1_E ) )
= $true )
| ( ( cA @ sK1_E )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[12]) ).
thf(14,plain,
( ( ( ~ ( cA @ sK1_E ) )
= $false )
| ( ( cA @ sK1_E )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(15,plain,
( ( ( cA @ sK1_E )
= $false )
| ( ( cA @ sK1_E )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ( cA @ sK1_E )
= $true )
| ( ( cA @ sK1_E )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( cA @ sK1_E )
= $false ),
inference(sim,[status(thm)],[15]) ).
thf(18,plain,
( ( cA @ sK1_E )
= $true ),
inference(sim,[status(thm)],[16]) ).
thf(20,plain,
( ( ( cA @ sK1_E )
= ( cA @ sK1_E ) )
= $false ),
inference(res,[status(thm)],[18,17]) ).
thf(22,plain,
$false = $true,
inference(extuni,[status(esa)],[20]) ).
thf(23,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO370^5 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n013.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % 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 17:38:32 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.20
% 0.07/0.20 No.of.Axioms: 0
% 0.07/0.20
% 0.07/0.20 Length.of.Defs: 0
% 0.07/0.20
% 0.07/0.20 Contains.Choice.Funs: false
% 0.07/0.20
% 0.07/0.20 ********************************
% 0.07/0.20 * All subproblems solved! *
% 0.07/0.20 ********************************
% 0.07/0.20 % SZS status Theorem for /export/starexec/sandbox2/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:22,loop_count:4,foatp_calls:1,translation:fof_full)
% 0.07/0.20
% 0.07/0.20 %**** Beginning of derivation protocol ****
% 0.07/0.20 % SZS output start CNFRefutation
% See solution above
% 0.07/0.20
% 0.07/0.20 %**** End of derivation protocol ****
% 0.07/0.20 %**** no. of clauses in derivation: 21 ****
% 0.07/0.20 %**** clause counter: 22 ****
% 0.07/0.20
% 0.07/0.20 % SZS status Theorem for /export/starexec/sandbox2/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:22,loop_count:4,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------