%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN318+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 : n004.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 11:05:28 AM UTC 2026
% Result : Theorem 0.11s 0.21s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 1
% Syntax : Number of formulae : 27 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 157 ( 31 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 202 ( 51 ~; 43 |; 0 &; 83 @)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 52 ( 0 ^; 47 !; 5 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_big_f,type,
big_f: $i > $o ).
thf(tp_big_g,type,
big_g: $i > $o ).
thf(tp_p,type,
p: $o ).
thf(tp_sK1_SY4,type,
sK1_SY4: $i > $i ).
thf(1,conjecture,
? [Y: $i] :
( ! [X: $i] :
( ( big_f @ X )
=> ( ( big_f @ Y )
=> ( big_g @ X ) ) )
=> ( p
=> ! [X: $i] :
( ( big_f @ X )
=> ( big_g @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_2_4) ).
thf(2,negated_conjecture,
( ( ? [Y: $i] :
( ! [X: $i] :
( ( big_f @ X )
=> ( ( big_f @ Y )
=> ( big_g @ X ) ) )
=> ( p
=> ! [X: $i] :
( ( big_f @ X )
=> ( big_g @ Y ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [Y: $i] :
( ! [X: $i] :
( ( big_f @ X )
=> ( ( big_f @ Y )
=> ( big_g @ X ) ) )
=> ( p
=> ! [X: $i] :
( ( big_f @ X )
=> ( big_g @ Y ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ? [Y: $i] :
( ! [X: $i] :
( ( big_f @ X )
=> ( ( big_f @ Y )
=> ( big_g @ X ) ) )
=> ( p
=> ! [X: $i] :
( ( big_f @ X )
=> ( big_g @ Y ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ~ ? [Y: $i] :
( ! [X: $i] :
( ( big_f @ X )
=> ( ( big_f @ Y )
=> ( big_g @ X ) ) )
=> ( p
=> ! [X: $i] :
( ( big_f @ X )
=> ( big_g @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( big_f @ SX1 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX1 ) )
| ~ p
| ! [SX1: $i] :
( ~ ( big_f @ SX1 )
| ( big_g @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( big_f @ SX1 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX1 ) )
| ~ p
| ! [SX1: $i] :
( ~ ( big_f @ SX1 )
| ( big_g @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( big_f @ SX1 )
| ~ ( big_f @ SX0 )
| ( big_g @ SX1 ) )
| ~ p
| ! [SX1: $i] :
( ~ ( big_f @ SX1 )
| ( big_g @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7]) ).
thf(9,plain,
! [SV1: $i] :
( ( ~ ( ~ ! [SY3: $i] :
( ~ ( big_f @ SY3 )
| ~ ( big_f @ SV1 )
| ( big_g @ SY3 ) )
| ~ p
| ! [SY4: $i] :
( ~ ( big_f @ SY4 )
| ( big_g @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: $i] :
( ( ~ ! [SY3: $i] :
( ~ ( big_f @ SY3 )
| ~ ( big_f @ SV1 )
| ( big_g @ SY3 ) )
| ~ p
| ! [SY4: $i] :
( ~ ( big_f @ SY4 )
| ( big_g @ SV1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(11,plain,
! [SV1: $i] :
( ( ~ ! [SY3: $i] :
( ~ ( big_f @ SY3 )
| ~ ( big_f @ SV1 )
| ( big_g @ SY3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[10]) ).
thf(12,plain,
! [SV1: $i] :
( ( ~ p
| ! [SY4: $i] :
( ~ ( big_f @ SY4 )
| ( big_g @ SV1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[10]) ).
thf(13,plain,
! [SV1: $i] :
( ( ! [SY3: $i] :
( ~ ( big_f @ SY3 )
| ~ ( big_f @ SV1 )
| ( big_g @ SY3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ p ) = $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: $i] :
( ( ! [SY4: $i] :
( ~ ( big_f @ SY4 )
| ( big_g @ SV1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(16,plain,
! [SV1: $i,SV2: $i] :
( ( ~ ( big_f @ SV2 )
| ~ ( big_f @ SV1 )
| ( big_g @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(17,plain,
p = $true,
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: $i] :
( ( ~ ( big_f @ ( sK1_SY4 @ SV1 ) )
| ( big_g @ SV1 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(19,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( big_f @ SV2 ) )
= $true )
| ( ( ~ ( big_f @ SV1 )
| ( big_g @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(20,plain,
! [SV1: $i] :
( ( ~ ( big_f @ ( sK1_SY4 @ SV1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(21,plain,
! [SV1: $i] :
( ( big_g @ SV1 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV1: $i,SV2: $i] :
( ( ( big_f @ SV2 )
= $false )
| ( ( ~ ( big_f @ SV1 )
| ( big_g @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV1: $i] :
( ( big_f @ ( sK1_SY4 @ SV1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( big_f @ SV1 ) )
= $true )
| ( ( big_g @ SV2 )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(25,plain,
! [SV2: $i,SV1: $i] :
( ( ( big_f @ SV1 )
= $false )
| ( ( big_g @ SV2 )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(26,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[17,25,23,21]) ).
thf(27,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN318+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % 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 : n004.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 17:18:24 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
% 0.11/0.21
% 0.11/0.21 No.of.Axioms: 0
% 0.11/0.21
% 0.11/0.21 Length.of.Defs: 0
% 0.11/0.21
% 0.11/0.21 Contains.Choice.Funs: false
% 0.11/0.21
% 0.11/0.21 ********************************
% 0.11/0.21 * All subproblems solved! *
% 0.11/0.21 ********************************
% 0.11/0.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,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:26,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.21
% 0.11/0.21 %**** Beginning of derivation protocol ****
% 0.11/0.21 % SZS output start CNFRefutation
% See solution above
% 0.11/0.21
% 0.11/0.21 %**** End of derivation protocol ****
% 0.11/0.21 %**** no. of clauses in derivation: 27 ****
% 0.11/0.21 %**** clause counter: 26 ****
% 0.11/0.21
% 0.11/0.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,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:26,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------