%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN325+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 : n002.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 11:05:30 AM UTC 2026
% Result : Theorem 0.08s 0.18s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 1
% Syntax : Number of formulae : 31 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 193 ( 44 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 365 ( 83 ~; 54 |; 5 &; 208 @)
% ( 0 <=>; 15 =>; 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 : 6 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 0 ^; 34 !; 5 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_big_f,type,
big_f: $i > $i > $o ).
thf(tp_big_g,type,
big_g: $i > $o ).
thf(tp_sK1_SY2,type,
sK1_SY2: $i > $i ).
thf(1,conjecture,
? [X: $i] :
! [Y: $i] :
( ( ( ( big_f @ X @ X )
=> ( big_f @ Y @ Y ) )
=> ( ( big_f @ X @ Y )
& ( big_g @ X ) ) )
=> ( big_g @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_9_2) ).
thf(2,negated_conjecture,
( ( ? [X: $i] :
! [Y: $i] :
( ( ( ( big_f @ X @ X )
=> ( big_f @ Y @ Y ) )
=> ( ( big_f @ X @ Y )
& ( big_g @ X ) ) )
=> ( big_g @ Y ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [X: $i] :
! [Y: $i] :
( ( ( ( big_f @ X @ X )
=> ( big_f @ Y @ Y ) )
=> ( ( big_f @ X @ Y )
& ( big_g @ X ) ) )
=> ( big_g @ Y ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ? [X: $i] :
! [Y: $i] :
( ( ( ( big_f @ X @ X )
=> ( big_f @ Y @ Y ) )
=> ( ( big_f @ X @ Y )
& ( big_g @ X ) ) )
=> ( big_g @ Y ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ~ ? [X: $i] :
! [Y: $i] :
( ( ( ( big_f @ X @ X )
=> ( big_f @ Y @ Y ) )
=> ( ( big_f @ X @ Y )
& ( big_g @ X ) ) )
=> ( big_g @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] :
( ~ ( ~ ( ~ ( big_f @ SX0 @ SX0 )
| ( big_f @ SX1 @ SX1 ) )
| ~ ( ~ ( big_f @ SX0 @ SX1 )
| ~ ( big_g @ SX0 ) ) )
| ( big_g @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ! [SX0: $i] :
~ ! [SX1: $i] :
( ~ ( ~ ( ~ ( big_f @ SX0 @ SX0 )
| ( big_f @ SX1 @ SX1 ) )
| ~ ( ~ ( big_f @ SX0 @ SX1 )
| ~ ( big_g @ SX0 ) ) )
| ( big_g @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
( ~ ( ~ ( ~ ( big_f @ SX0 @ SX0 )
| ( big_f @ SX1 @ SX1 ) )
| ~ ( ~ ( big_f @ SX0 @ SX1 )
| ~ ( big_g @ SX0 ) ) )
| ( big_g @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7]) ).
thf(9,plain,
! [SV1: $i] :
( ( ~ ! [SY2: $i] :
( ~ ( ~ ( ~ ( big_f @ SV1 @ SV1 )
| ( big_f @ SY2 @ SY2 ) )
| ~ ( ~ ( big_f @ SV1 @ SY2 )
| ~ ( big_g @ SV1 ) ) )
| ( big_g @ SY2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: $i] :
( ( ! [SY2: $i] :
( ~ ( ~ ( ~ ( big_f @ SV1 @ SV1 )
| ( big_f @ SY2 @ SY2 ) )
| ~ ( ~ ( big_f @ SV1 @ SY2 )
| ~ ( big_g @ SV1 ) ) )
| ( big_g @ SY2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(11,plain,
! [SV1: $i] :
( ( ~ ( ~ ( ~ ( big_f @ SV1 @ SV1 )
| ( big_f @ ( sK1_SY2 @ SV1 ) @ ( sK1_SY2 @ SV1 ) ) )
| ~ ( ~ ( big_f @ SV1 @ ( sK1_SY2 @ SV1 ) )
| ~ ( big_g @ SV1 ) ) )
| ( big_g @ ( sK1_SY2 @ SV1 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(12,plain,
! [SV1: $i] :
( ( ~ ( ~ ( ~ ( big_f @ SV1 @ SV1 )
| ( big_f @ ( sK1_SY2 @ SV1 ) @ ( sK1_SY2 @ SV1 ) ) )
| ~ ( ~ ( big_f @ SV1 @ ( sK1_SY2 @ SV1 ) )
| ~ ( big_g @ SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(13,plain,
! [SV1: $i] :
( ( big_g @ ( sK1_SY2 @ SV1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(14,plain,
! [SV1: $i] :
( ( ~ ( ~ ( big_f @ SV1 @ SV1 )
| ( big_f @ ( sK1_SY2 @ SV1 ) @ ( sK1_SY2 @ SV1 ) ) )
| ~ ( ~ ( big_f @ SV1 @ ( sK1_SY2 @ SV1 ) )
| ~ ( big_g @ SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ( big_f @ SV1 @ SV1 )
| ( big_f @ ( sK1_SY2 @ SV1 ) @ ( sK1_SY2 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( ~ ( big_f @ SV1 @ ( sK1_SY2 @ SV1 ) )
| ~ ( big_g @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(16,plain,
! [SV1: $i] :
( ( ( ~ ( big_f @ SV1 @ SV1 )
| ( big_f @ ( sK1_SY2 @ SV1 ) @ ( sK1_SY2 @ SV1 ) ) )
= $false )
| ( ( ~ ( ~ ( big_f @ SV1 @ ( sK1_SY2 @ SV1 ) )
| ~ ( big_g @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(17,plain,
! [SV1: $i] :
( ( ( ~ ( big_f @ SV1 @ SV1 ) )
= $false )
| ( ( ~ ( ~ ( big_f @ SV1 @ ( sK1_SY2 @ SV1 ) )
| ~ ( big_g @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(18,plain,
! [SV1: $i] :
( ( ( big_f @ ( sK1_SY2 @ SV1 ) @ ( sK1_SY2 @ SV1 ) )
= $false )
| ( ( ~ ( ~ ( big_f @ SV1 @ ( sK1_SY2 @ SV1 ) )
| ~ ( big_g @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(19,plain,
! [SV1: $i] :
( ( ( big_f @ SV1 @ SV1 )
= $true )
| ( ( ~ ( ~ ( big_f @ SV1 @ ( sK1_SY2 @ SV1 ) )
| ~ ( big_g @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(20,plain,
! [SV1: $i] :
( ( ( ~ ( big_f @ SV1 @ ( sK1_SY2 @ SV1 ) )
| ~ ( big_g @ SV1 ) )
= $false )
| ( ( big_f @ ( sK1_SY2 @ SV1 ) @ ( sK1_SY2 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(21,plain,
! [SV1: $i] :
( ( ( ~ ( big_f @ SV1 @ ( sK1_SY2 @ SV1 ) )
| ~ ( big_g @ SV1 ) )
= $false )
| ( ( big_f @ SV1 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(22,plain,
! [SV1: $i] :
( ( ( ~ ( big_f @ SV1 @ ( sK1_SY2 @ SV1 ) ) )
= $false )
| ( ( big_f @ ( sK1_SY2 @ SV1 ) @ ( sK1_SY2 @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(23,plain,
! [SV1: $i] :
( ( ( ~ ( big_g @ SV1 ) )
= $false )
| ( ( big_f @ ( sK1_SY2 @ SV1 ) @ ( sK1_SY2 @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV1: $i] :
( ( ( ~ ( big_f @ SV1 @ ( sK1_SY2 @ SV1 ) ) )
= $false )
| ( ( big_f @ SV1 @ SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV1: $i] :
( ( ( ~ ( big_g @ SV1 ) )
= $false )
| ( ( big_f @ SV1 @ SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV1: $i] :
( ( ( big_f @ SV1 @ ( sK1_SY2 @ SV1 ) )
= $true )
| ( ( big_f @ ( sK1_SY2 @ SV1 ) @ ( sK1_SY2 @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(27,plain,
! [SV1: $i] :
( ( ( big_g @ SV1 )
= $true )
| ( ( big_f @ ( sK1_SY2 @ SV1 ) @ ( sK1_SY2 @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(28,plain,
! [SV1: $i] :
( ( ( big_f @ SV1 @ ( sK1_SY2 @ SV1 ) )
= $true )
| ( ( big_f @ SV1 @ SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
! [SV1: $i] :
( ( ( big_g @ SV1 )
= $true )
| ( ( big_f @ SV1 @ SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(30,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[13,29,28,27,26]) ).
thf(31,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN325+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
% 0.08/0.15 % Computer : n002.cluster.edu
% 0.08/0.15 % Model : x86_64 x86_64
% 0.08/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.15 % Memory : 8046.5625MB
% 0.08/0.15 % OS : Linux 6.8.0-71-generic
% 0.08/0.15 % CPULimit : 300
% 0.08/0.15 % WCLimit : 300
% 0.08/0.15 % DateTime : Tue Oct 6 17:21:12 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18
% 0.08/0.18 No.of.Axioms: 0
% 0.08/0.18
% 0.08/0.18 Length.of.Defs: 0
% 0.08/0.18
% 0.08/0.18 Contains.Choice.Funs: false
% 0.08/0.18
% 0.08/0.18 ********************************
% 0.08/0.18 * All subproblems solved! *
% 0.08/0.18 ********************************
% 0.08/0.18 % 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:30,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.18
% 0.08/0.18 %**** Beginning of derivation protocol ****
% 0.08/0.18 % SZS output start CNFRefutation
% See solution above
% 0.08/0.18
% 0.08/0.18 %**** End of derivation protocol ****
% 0.08/0.18 %**** no. of clauses in derivation: 31 ****
% 0.08/0.18 %**** clause counter: 30 ****
% 0.08/0.18
% 0.08/0.18 % 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:30,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------