%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN360+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/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 11:05:37 AM UTC 2026
% Result : Theorem 0.11s 0.22s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 22 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 87 ( 24 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 102 ( 8 ~; 7 |; 3 &; 77 @)
% ( 0 <=>; 7 =>; 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 : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 0 ^; 46 !; 8 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_big_p,type,
big_p: $i > $i > $o ).
thf(tp_big_q,type,
big_q: $i > $i > $o ).
thf(tp_sK1_Y,type,
sK1_Y: $i ).
thf(tp_sK2_SY7,type,
sK2_SY7: $i ).
thf(tp_sK3_Y,type,
sK3_Y: $i > $i ).
thf(1,conjecture,
( ( ! [X: $i] :
( ? [Y: $i] : ( big_p @ X @ Y )
=> ! [Y: $i] : ( big_q @ X @ Y ) )
& ! [Z: $i] :
? [Y: $i] : ( big_p @ Z @ Y ) )
=> ! [Y: $i,X: $i] : ( big_q @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2111) ).
thf(2,negated_conjecture,
( ( ( ! [X: $i] :
( ? [Y: $i] : ( big_p @ X @ Y )
=> ! [Y: $i] : ( big_q @ X @ Y ) )
& ! [Z: $i] :
? [Y: $i] : ( big_p @ Z @ Y ) )
=> ! [Y: $i,X: $i] : ( big_q @ X @ Y ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [X: $i] :
( ? [Y: $i] : ( big_p @ X @ Y )
=> ! [Y: $i] : ( big_q @ X @ Y ) )
& ! [Z: $i] :
? [Y: $i] : ( big_p @ Z @ Y ) )
=> ! [Y: $i,X: $i] : ( big_q @ X @ Y ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [X: $i] :
( ? [Y: $i] : ( big_p @ X @ Y )
=> ! [Y: $i] : ( big_q @ X @ Y ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Z: $i] :
? [Y: $i] : ( big_p @ Z @ Y ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Y: $i,X: $i] : ( big_q @ X @ Y ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [Y: $i,X: $i] : ( big_q @ X @ Y ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ( big_q @ sK2_SY7 @ sK1_Y ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
~ ( big_p @ X @ Y )
| ! [Y: $i] : ( big_q @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(10,plain,
( ( ! [Z: $i] : ( big_p @ Z @ ( sK3_Y @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(11,plain,
( ( ! [Z: $i] : ( big_p @ Z @ ( sK3_Y @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
~ ( big_p @ X @ Y )
| ! [Y: $i] : ( big_q @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ ( big_q @ sK2_SY7 @ sK1_Y ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
! [SV1: $i] :
( ( big_p @ SV1 @ ( sK3_Y @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
! [SV2: $i] :
( ( ! [SY8: $i] :
~ ( big_p @ SV2 @ SY8 )
| ! [SY9: $i] : ( big_q @ SV2 @ SY9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
( ( big_q @ sK2_SY7 @ sK1_Y )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV2: $i] :
( ( ( ! [SY8: $i] :
~ ( big_p @ SV2 @ SY8 ) )
= $true )
| ( ( ! [SY9: $i] : ( big_q @ SV2 @ SY9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(18,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( big_p @ SV2 @ SV3 ) )
= $true )
| ( ( ! [SY9: $i] : ( big_q @ SV2 @ SY9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(19,plain,
! [SV3: $i,SV2: $i] :
( ( ( big_p @ SV2 @ SV3 )
= $false )
| ( ( ! [SY9: $i] : ( big_q @ SV2 @ SY9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(20,plain,
! [SV3: $i,SV4: $i,SV2: $i] :
( ( ( big_q @ SV2 @ SV4 )
= $true )
| ( ( big_p @ SV2 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(21,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,20,16]) ).
thf(22,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN360+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.18 % Computer : n010.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Oct 6 17:19:43 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.22
% 0.11/0.22 No.of.Axioms: 0
% 0.11/0.22
% 0.11/0.22 Length.of.Defs: 0
% 0.11/0.22
% 0.11/0.22 Contains.Choice.Funs: false
% 0.11/0.22
% 0.11/0.22 ********************************
% 0.11/0.22 * All subproblems solved! *
% 0.11/0.22 ********************************
% 0.11/0.22 % SZS status Theorem for /export/starexec/sandbox2/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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:21,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.22
% 0.11/0.22 %**** Beginning of derivation protocol ****
% 0.11/0.22 % SZS output start CNFRefutation
% See solution above
% 0.11/0.22
% 0.11/0.22 %**** End of derivation protocol ****
% 0.11/0.22 %**** no. of clauses in derivation: 22 ****
% 0.11/0.22 %**** clause counter: 21 ****
% 0.11/0.22
% 0.11/0.22 % SZS status Theorem for /export/starexec/sandbox2/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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:21,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------