%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN369+1 : TPTP v9.3.1. Released v2.0.0.
% 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 : n026.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 11:05:39 AM UTC 2026
% Result : Theorem 0.09s 0.20s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 18 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 79 ( 4 ~; 10 |; 0 &; 62 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 0 ^; 39 !; 5 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_big_p,type,
big_p: $i > $i > $o ).
thf(tp_sK1_Y,type,
sK1_Y: $i > $i ).
thf(1,conjecture,
( ! [U: $i,V: $i,W: $i] :
( ( big_p @ U @ V )
| ( big_p @ V @ W ) )
=> ? [X: $i] :
! [Y: $i] : ( big_p @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2120) ).
thf(2,negated_conjecture,
( ( ! [U: $i,V: $i,W: $i] :
( ( big_p @ U @ V )
| ( big_p @ V @ W ) )
=> ? [X: $i] :
! [Y: $i] : ( big_p @ X @ Y ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( big_p @ U @ V )
| ( big_p @ V @ W ) )
=> ? [X: $i] :
! [Y: $i] : ( big_p @ X @ Y ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( big_p @ U @ V )
| ( big_p @ V @ W ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ? [X: $i] :
! [Y: $i] : ( big_p @ X @ Y ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ? [X: $i] :
! [Y: $i] : ( big_p @ X @ Y ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [X: $i] :
~ ( big_p @ X @ ( sK1_Y @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [U: $i,V: $i] :
( ( big_p @ U @ V )
| ! [W: $i] : ( big_p @ V @ W ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [U: $i,V: $i] :
( ( big_p @ U @ V )
| ! [W: $i] : ( big_p @ V @ W ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [X: $i] :
~ ( big_p @ X @ ( sK1_Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
! [SV1: $i] :
( ( ! [SY5: $i] :
( ( big_p @ SV1 @ SY5 )
| ! [W: $i] : ( big_p @ SY5 @ W ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV2: $i] :
( ( ~ ( big_p @ SV2 @ ( sK1_Y @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
! [SV3: $i,SV1: $i] :
( ( ( big_p @ SV1 @ SV3 )
| ! [SY7: $i] : ( big_p @ SV3 @ SY7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV2: $i] :
( ( big_p @ SV2 @ ( sK1_Y @ SV2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV3: $i,SV1: $i] :
( ( ( big_p @ SV1 @ SV3 )
= $true )
| ( ( ! [SY7: $i] : ( big_p @ SV3 @ SY7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[13]) ).
thf(16,plain,
! [SV1: $i,SV4: $i,SV3: $i] :
( ( ( big_p @ SV3 @ SV4 )
= $true )
| ( ( big_p @ SV1 @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(17,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,16]) ).
thf(18,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN369+1 : TPTP v9.3.1. Released v2.0.0.
% 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
% 0.09/0.17 % Computer : n026.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 17:22:17 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.20
% 0.09/0.20 No.of.Axioms: 0
% 0.09/0.20
% 0.09/0.20 Length.of.Defs: 0
% 0.09/0.20
% 0.09/0.20 Contains.Choice.Funs: false
% 0.09/0.20
% 0.09/0.20 ********************************
% 0.09/0.20 * All subproblems solved! *
% 0.09/0.20 ********************************
% 0.09/0.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:17,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.09/0.20
% 0.09/0.20 %**** Beginning of derivation protocol ****
% 0.09/0.20 % SZS output start CNFRefutation
% See solution above
% 0.09/0.20
% 0.09/0.20 %**** End of derivation protocol ****
% 0.09/0.20 %**** no. of clauses in derivation: 18 ****
% 0.09/0.20 %**** clause counter: 17 ****
% 0.09/0.20
% 0.09/0.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:17,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------