%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN381+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 : n003.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 11:05:41 AM UTC 2026
% Result : Theorem 0.08s 0.20s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 29 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 138 ( 34 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 175 ( 13 ~; 24 |; 6 &; 121 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 0 ^; 50 !; 8 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_big_p,type,
big_p: $i > $o ).
thf(tp_big_q,type,
big_q: $i > $i > $o ).
thf(tp_sK1_Z,type,
sK1_Z: $i ).
thf(tp_sK2_U,type,
sK2_U: $i > $i ).
thf(1,conjecture,
( ( ! [X: $i] :
( ? [Y: $i] : ( big_q @ X @ Y )
=> ( big_p @ X ) )
& ! [V: $i] :
? [U: $i] : ( big_q @ U @ V )
& ! [W: $i,Z: $i] :
( ( big_q @ W @ Z )
=> ( ( big_q @ Z @ W )
| ( big_q @ Z @ Z ) ) ) )
=> ! [Z: $i] : ( big_p @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2133) ).
thf(2,negated_conjecture,
( ( ( ! [X: $i] :
( ? [Y: $i] : ( big_q @ X @ Y )
=> ( big_p @ X ) )
& ! [V: $i] :
? [U: $i] : ( big_q @ U @ V )
& ! [W: $i,Z: $i] :
( ( big_q @ W @ Z )
=> ( ( big_q @ Z @ W )
| ( big_q @ Z @ Z ) ) ) )
=> ! [Z: $i] : ( big_p @ Z ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [X: $i] :
( ? [Y: $i] : ( big_q @ X @ Y )
=> ( big_p @ X ) )
& ! [V: $i] :
? [U: $i] : ( big_q @ U @ V )
& ! [W: $i,Z: $i] :
( ( big_q @ W @ Z )
=> ( ( big_q @ Z @ W )
| ( big_q @ Z @ Z ) ) ) )
=> ! [Z: $i] : ( big_p @ Z ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [X: $i] :
( ? [Y: $i] : ( big_q @ X @ Y )
=> ( big_p @ X ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [V: $i] :
? [U: $i] : ( big_q @ U @ V ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [W: $i,Z: $i] :
( ( big_q @ W @ Z )
=> ( ( big_q @ Z @ W )
| ( big_q @ Z @ Z ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [Z: $i] : ( big_p @ Z ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ! [Z: $i] : ( big_p @ Z ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ~ ( big_p @ sK1_Z ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
~ ( big_q @ X @ Y )
| ( big_p @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(11,plain,
( ( ! [V: $i] : ( big_q @ ( sK2_U @ V ) @ V ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(12,plain,
( ( ! [W: $i,Z: $i] :
( ~ ( big_q @ W @ Z )
| ( big_q @ Z @ W )
| ( big_q @ Z @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(13,plain,
( ( ! [W: $i,Z: $i] :
( ~ ( big_q @ W @ Z )
| ( big_q @ Z @ W )
| ( big_q @ Z @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [V: $i] : ( big_q @ ( sK2_U @ V ) @ V ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
~ ( big_q @ X @ Y )
| ( big_p @ X ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ~ ( big_p @ sK1_Z ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(17,plain,
! [SV1: $i] :
( ( ! [SY7: $i] :
( ~ ( big_q @ SV1 @ SY7 )
| ( big_q @ SY7 @ SV1 )
| ( big_q @ SY7 @ SY7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(18,plain,
! [SV2: $i] :
( ( big_q @ ( sK2_U @ SV2 ) @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(19,plain,
! [SV3: $i] :
( ( ! [SY8: $i] :
~ ( big_q @ SV3 @ SY8 )
| ( big_p @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
( ( big_p @ sK1_Z )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(21,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( big_q @ SV1 @ SV4 )
| ( big_q @ SV4 @ SV1 )
| ( big_q @ SV4 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV3: $i] :
( ( ( ! [SY8: $i] :
~ ( big_q @ SV3 @ SY8 ) )
= $true )
| ( ( big_p @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( big_q @ SV1 @ SV4 ) )
= $true )
| ( ( ( big_q @ SV4 @ SV1 )
| ( big_q @ SV4 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(24,plain,
! [SV5: $i,SV3: $i] :
( ( ( ~ ( big_q @ SV3 @ SV5 ) )
= $true )
| ( ( big_p @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(25,plain,
! [SV4: $i,SV1: $i] :
( ( ( big_q @ SV1 @ SV4 )
= $false )
| ( ( ( big_q @ SV4 @ SV1 )
| ( big_q @ SV4 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV5: $i,SV3: $i] :
( ( ( big_q @ SV3 @ SV5 )
= $false )
| ( ( big_p @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV1: $i,SV4: $i] :
( ( ( big_q @ SV4 @ SV1 )
= $true )
| ( ( big_q @ SV4 @ SV4 )
= $true )
| ( ( big_q @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(28,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,27,26,20]) ).
thf(29,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN381+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
% 0.08/0.17 % Computer : n003.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 17:21:25 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.20
% 0.08/0.20 No.of.Axioms: 0
% 0.08/0.20
% 0.08/0.20 Length.of.Defs: 0
% 0.08/0.20
% 0.08/0.20 Contains.Choice.Funs: false
% 0.08/0.20
% 0.08/0.20 ********************************
% 0.08/0.20 * All subproblems solved! *
% 0.08/0.20 ********************************
% 0.08/0.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:28,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.08/0.20
% 0.08/0.20 %**** Beginning of derivation protocol ****
% 0.08/0.20 % SZS output start CNFRefutation
% See solution above
% 0.08/0.20
% 0.08/0.20 %**** End of derivation protocol ****
% 0.08/0.20 %**** no. of clauses in derivation: 29 ****
% 0.08/0.20 %**** clause counter: 28 ****
% 0.08/0.20
% 0.08/0.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:28,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------