%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN340+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 : n016.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 11:05:32 AM UTC 2026
% Result : Theorem 0.09s 0.20s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 1
% Syntax : Number of formulae : 22 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 79 ( 20 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 275 ( 56 ~; 12 |; 0 &; 202 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-5 aty)
% Number of variables : 70 ( 0 ^; 55 !; 15 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_big_f,type,
big_f: $i > $i > $i > $i > $i > $o ).
thf(tp_sK1_SY4,type,
sK1_SY4: $i > $i ).
thf(1,conjecture,
? [X: $i] :
! [Y: $i] :
? [Z1: $i,Z2: $i] :
( ( big_f @ X @ Y @ Z1 @ Z2 @ Z1 )
=> ( big_f @ Z1 @ X @ Y @ Z1 @ Z2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_15_5) ).
thf(2,negated_conjecture,
( ( ? [X: $i] :
! [Y: $i] :
? [Z1: $i,Z2: $i] :
( ( big_f @ X @ Y @ Z1 @ Z2 @ Z1 )
=> ( big_f @ Z1 @ X @ Y @ Z1 @ Z2 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [X: $i] :
! [Y: $i] :
? [Z1: $i,Z2: $i] :
( ( big_f @ X @ Y @ Z1 @ Z2 @ Z1 )
=> ( big_f @ Z1 @ X @ Y @ Z1 @ Z2 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ? [X: $i] :
! [Y: $i] :
? [Z1: $i,Z2: $i] :
( ( big_f @ X @ Y @ Z1 @ Z2 @ Z1 )
=> ( big_f @ Z1 @ X @ Y @ Z1 @ Z2 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ~ ? [X: $i] :
! [Y: $i] :
? [Z1: $i,Z2: $i] :
( ( big_f @ X @ Y @ Z1 @ Z2 @ Z1 )
=> ( big_f @ Z1 @ X @ Y @ Z1 @ Z2 ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ( ~ ( big_f @ SX0 @ SX1 @ SX2 @ SX3 @ SX2 )
| ( big_f @ SX2 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ! [SX0: $i] :
~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ( ~ ( big_f @ SX0 @ SX1 @ SX2 @ SX3 @ SX2 )
| ( big_f @ SX2 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ( ~ ( big_f @ SX0 @ SX1 @ SX2 @ SX3 @ SX2 )
| ( big_f @ SX2 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7]) ).
thf(9,plain,
! [SV1: $i] :
( ( ~ ! [SY4: $i] :
~ ! [SY5: $i] :
~ ~ ! [SY6: $i] :
~ ( ~ ( big_f @ SV1 @ SY4 @ SY5 @ SY6 @ SY5 )
| ( big_f @ SY5 @ SV1 @ SY4 @ SY5 @ SY6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: $i] :
( ( ! [SY4: $i] :
~ ! [SY5: $i] :
~ ~ ! [SY6: $i] :
~ ( ~ ( big_f @ SV1 @ SY4 @ SY5 @ SY6 @ SY5 )
| ( big_f @ SY5 @ SV1 @ SY4 @ SY5 @ SY6 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(11,plain,
! [SV1: $i] :
( ( ~ ! [SY7: $i] :
~ ~ ! [SY8: $i] :
~ ( ~ ( big_f @ SV1 @ ( sK1_SY4 @ SV1 ) @ SY7 @ SY8 @ SY7 )
| ( big_f @ SY7 @ SV1 @ ( sK1_SY4 @ SV1 ) @ SY7 @ SY8 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY7: $i] :
~ ~ ! [SY8: $i] :
~ ( ~ ( big_f @ SV1 @ ( sK1_SY4 @ SV1 ) @ SY7 @ SY8 @ SY7 )
| ( big_f @ SY7 @ SV1 @ ( sK1_SY4 @ SV1 ) @ SY7 @ SY8 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[11]) ).
thf(13,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ~ ! [SY9: $i] :
~ ( ~ ( big_f @ SV1 @ ( sK1_SY4 @ SV1 ) @ SV2 @ SY9 @ SV2 )
| ( big_f @ SV2 @ SV1 @ ( sK1_SY4 @ SV1 ) @ SV2 @ SY9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(14,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ! [SY9: $i] :
~ ( ~ ( big_f @ SV1 @ ( sK1_SY4 @ SV1 ) @ SV2 @ SY9 @ SV2 )
| ( big_f @ SV2 @ SV1 @ ( sK1_SY4 @ SV1 ) @ SV2 @ SY9 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(15,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY9: $i] :
~ ( ~ ( big_f @ SV1 @ ( sK1_SY4 @ SV1 ) @ SV2 @ SY9 @ SV2 )
| ( big_f @ SV2 @ SV1 @ ( sK1_SY4 @ SV1 ) @ SV2 @ SY9 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(16,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ( ~ ( big_f @ SV1 @ ( sK1_SY4 @ SV1 ) @ SV2 @ SV3 @ SV2 )
| ( big_f @ SV2 @ SV1 @ ( sK1_SY4 @ SV1 ) @ SV2 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(17,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ( big_f @ SV1 @ ( sK1_SY4 @ SV1 ) @ SV2 @ SV3 @ SV2 )
| ( big_f @ SV2 @ SV1 @ ( sK1_SY4 @ SV1 ) @ SV2 @ SV3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(18,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ( big_f @ SV1 @ ( sK1_SY4 @ SV1 ) @ SV2 @ SV3 @ SV2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(19,plain,
! [SV3: $i,SV1: $i,SV2: $i] :
( ( big_f @ SV2 @ SV1 @ ( sK1_SY4 @ SV1 ) @ SV2 @ SV3 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( big_f @ SV1 @ ( sK1_SY4 @ SV1 ) @ SV2 @ SV3 @ SV2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(21,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,20]) ).
thf(22,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN340+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 : n016.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 17:23:44 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:1,axioms:0,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:21,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.20
% 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: 22 ****
% 0.09/0.20 %**** clause counter: 21 ****
% 0.09/0.20
% 0.09/0.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:0,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:21,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------