TSTP Solution File: SYN323+1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN323+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 08:25:07 EDT 2022
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 42 ( 31 unt; 2 typ; 0 def)
% Number of atoms : 222 ( 46 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 443 ( 97 ~; 64 |; 6 &; 256 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 116 ( 0 ^ 112 !; 4 ?; 116 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_big_f,type,
big_f: $i > $i > $o ).
thf(tp_big_g,type,
big_g: $i > $i > $o ).
thf(1,conjecture,
? [Y: $i] :
( ! [X: $i] :
( ( ( big_f @ X @ Y )
=> ( big_f @ Y @ X ) )
=> ( big_g @ X @ Y ) )
=> ~ ! [X: $i] :
( ( ( big_f @ X @ Y )
=> ( big_f @ Y @ X ) )
=> ~ ( big_g @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_4_2) ).
thf(2,negated_conjecture,
( ( ? [Y: $i] :
( ! [X: $i] :
( ( ( big_f @ X @ Y )
=> ( big_f @ Y @ X ) )
=> ( big_g @ X @ Y ) )
=> ~ ! [X: $i] :
( ( ( big_f @ X @ Y )
=> ( big_f @ Y @ X ) )
=> ~ ( big_g @ X @ Y ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [Y: $i] :
( ! [X: $i] :
( ( ( big_f @ X @ Y )
=> ( big_f @ Y @ X ) )
=> ( big_g @ X @ Y ) )
=> ~ ! [X: $i] :
( ( ( big_f @ X @ Y )
=> ( big_f @ Y @ X ) )
=> ~ ( big_g @ X @ Y ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ? [Y: $i] :
( ! [X: $i] :
( ( ( big_f @ X @ Y )
=> ( big_f @ Y @ X ) )
=> ( big_g @ X @ Y ) )
=> ~ ! [X: $i] :
( ( ( big_f @ X @ Y )
=> ( big_f @ Y @ X ) )
=> ~ ( big_g @ X @ Y ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Y: $i,X: $i] :
( ( big_f @ X @ Y )
| ( big_g @ X @ Y ) )
& ! [Y: $i,X: $i] :
( ~ ( big_f @ Y @ X )
| ( big_g @ X @ Y ) )
& ! [Y: $i,X: $i] :
( ( big_f @ X @ Y )
| ~ ( big_g @ X @ Y ) )
& ! [Y: $i,X: $i] :
( ~ ( big_f @ Y @ X )
| ~ ( big_g @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [Y: $i,X: $i] :
( ( big_f @ X @ Y )
| ( big_g @ X @ Y ) )
& ! [Y: $i,X: $i] :
( ~ ( big_f @ Y @ X )
| ( big_g @ X @ Y ) )
& ! [Y: $i,X: $i] :
( ( big_f @ X @ Y )
| ~ ( big_g @ X @ Y ) )
& ! [Y: $i,X: $i] :
( ~ ( big_f @ Y @ X )
| ~ ( big_g @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( big_f @ SX1 @ SX0 )
| ( big_g @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_f @ SX0 @ SX1 )
| ( big_g @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( big_f @ SX1 @ SX0 )
| ~ ( big_g @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_f @ SX0 @ SX1 )
| ~ ( big_g @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( big_f @ SX1 @ SX0 )
| ( big_g @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_f @ SX0 @ SX1 )
| ( big_g @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( big_f @ SX1 @ SX0 )
| ~ ( big_g @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_f @ SX0 @ SX1 )
| ~ ( big_g @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7]) ).
thf(9,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( big_f @ SX1 @ SX0 )
| ( big_g @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_f @ SX0 @ SX1 )
| ( big_g @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[8]) ).
thf(10,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( big_f @ SX1 @ SX0 )
| ~ ( big_g @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_f @ SX0 @ SX1 )
| ~ ( big_g @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( big_f @ SX1 @ SX0 )
| ( big_g @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_f @ SX0 @ SX1 )
| ( big_g @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( big_f @ SX1 @ SX0 )
| ~ ( big_g @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_f @ SX0 @ SX1 )
| ~ ( big_g @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( big_f @ SX1 @ SX0 )
| ( big_g @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_f @ SX0 @ SX1 )
| ( big_g @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( big_f @ SX1 @ SX0 )
| ~ ( big_g @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_f @ SX0 @ SX1 )
| ~ ( big_g @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( big_f @ SX1 @ SX0 )
| ( big_g @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_f @ SX0 @ SX1 )
| ( big_g @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( big_f @ SX1 @ SX0 )
| ~ ( big_g @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_f @ SX0 @ SX1 )
| ~ ( big_g @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(19,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( big_f @ SX1 @ SX0 )
| ( big_g @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(20,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_f @ SX0 @ SX1 )
| ( big_g @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(21,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( big_f @ SX1 @ SX0 )
| ~ ( big_g @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(22,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_f @ SX0 @ SX1 )
| ~ ( big_g @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(23,plain,
! [SV1: $i] :
( ( ! [SY3: $i] :
( ( big_f @ SY3 @ SV1 )
| ( big_g @ SY3 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV2: $i] :
( ( ! [SY4: $i] :
( ~ ( big_f @ SV2 @ SY4 )
| ( big_g @ SY4 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV3: $i] :
( ( ! [SY5: $i] :
( ( big_f @ SY5 @ SV3 )
| ~ ( big_g @ SY5 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV4: $i] :
( ( ! [SY6: $i] :
( ~ ( big_f @ SV4 @ SY6 )
| ~ ( big_g @ SY6 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV1: $i,SV5: $i] :
( ( ( big_f @ SV5 @ SV1 )
| ( big_g @ SV5 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV6: $i,SV2: $i] :
( ( ~ ( big_f @ SV2 @ SV6 )
| ( big_g @ SV6 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV3: $i,SV7: $i] :
( ( ( big_f @ SV7 @ SV3 )
| ~ ( big_g @ SV7 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ( big_f @ SV4 @ SV8 )
| ~ ( big_g @ SV8 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV1: $i,SV5: $i] :
( ( ( big_f @ SV5 @ SV1 )
= $true )
| ( ( big_g @ SV5 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV6: $i,SV2: $i] :
( ( ( ~ ( big_f @ SV2 @ SV6 ) )
= $true )
| ( ( big_g @ SV6 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV3: $i,SV7: $i] :
( ( ( big_f @ SV7 @ SV3 )
= $true )
| ( ( ~ ( big_g @ SV7 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( big_f @ SV4 @ SV8 ) )
= $true )
| ( ( ~ ( big_g @ SV8 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV6: $i,SV2: $i] :
( ( ( big_f @ SV2 @ SV6 )
= $false )
| ( ( big_g @ SV6 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV3: $i,SV7: $i] :
( ( ( big_g @ SV7 @ SV3 )
= $false )
| ( ( big_f @ SV7 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV8: $i,SV4: $i] :
( ( ( big_f @ SV4 @ SV8 )
= $false )
| ( ( ~ ( big_g @ SV8 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV4: $i,SV8: $i] :
( ( ( big_g @ SV8 @ SV4 )
= $false )
| ( ( big_f @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(39,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[31,38,36,35]) ).
thf(40,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN323+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 11 19:37:34 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35
% 0.14/0.35 No.of.Axioms: 0
% 0.14/0.35
% 0.14/0.35 Length.of.Defs: 0
% 0.14/0.35
% 0.14/0.35 Contains.Choice.Funs: false
% 0.14/0.35 (rf:0,axioms:0,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.14/0.39
% 0.14/0.39 ********************************
% 0.14/0.39 * All subproblems solved! *
% 0.14/0.39 ********************************
% 0.14/0.39 % SZS status Theorem for /export/starexec/sandbox/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:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:39,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.14/0.39
% 0.14/0.39 %**** Beginning of derivation protocol ****
% 0.14/0.39 % SZS output start CNFRefutation
% See solution above
% 0.14/0.39
% 0.14/0.39 %**** End of derivation protocol ****
% 0.14/0.39 %**** no. of clauses in derivation: 40 ****
% 0.14/0.39 %**** clause counter: 39 ****
% 0.14/0.39
% 0.14/0.39 % SZS status Theorem for /export/starexec/sandbox/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:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:39,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------