TSTP Solution File: SYN058+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN058+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 : n013.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 08:23:07 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 67 ( 28 unt; 10 typ; 0 def)
% Number of atoms : 305 ( 79 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 300 ( 92 ~; 64 |; 12 &; 118 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 43 ( 0 ^ 39 !; 4 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_big_f,type,
big_f: $i > $o ).
thf(tp_big_g,type,
big_g: $i > $o ).
thf(tp_big_p,type,
big_p: $i > $o ).
thf(tp_big_q,type,
big_q: $i > $o ).
thf(tp_big_r,type,
big_r: $i > $o ).
thf(tp_big_s,type,
big_s: $i > $o ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_X1,type,
sK2_X1: $i ).
thf(tp_sK3_X,type,
sK3_X: $i ).
thf(tp_sK4_REN,type,
sK4_REN: $o ).
thf(1,axiom,
( ? [X: $i] : ( big_s @ X )
=> ! [X1: $i] :
( ( big_f @ X1 )
=> ( big_g @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel28_3) ).
thf(2,axiom,
( ! [X: $i] :
( ( big_q @ X )
| ( big_r @ X ) )
=> ? [X1: $i] :
( ( big_q @ X1 )
& ( big_s @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel28_2) ).
thf(3,axiom,
! [X: $i] :
( ( big_p @ X )
=> ! [Z: $i] : ( big_q @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel28_1) ).
thf(4,conjecture,
! [X: $i] :
( ( ( big_p @ X )
& ( big_f @ X ) )
=> ( big_g @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel28) ).
thf(5,negated_conjecture,
( ( ! [X: $i] :
( ( ( big_p @ X )
& ( big_f @ X ) )
=> ( big_g @ X ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( ! [X: $i] :
( ( ( big_p @ X )
& ( big_f @ X ) )
=> ( big_g @ X ) ) )
= $false ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ? [X: $i] : ( big_s @ X )
=> ! [X1: $i] :
( ( big_f @ X1 )
=> ( big_g @ X1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ! [X: $i] :
( ( big_q @ X )
| ( big_r @ X ) )
=> ? [X1: $i] :
( ( big_q @ X1 )
& ( big_s @ X1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( ! [X: $i] :
( ( big_p @ X )
=> ! [Z: $i] : ( big_q @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(10,plain,
( ( ( ( big_p @ sK1_X )
& ( big_f @ sK1_X ) )
=> ( big_g @ sK1_X ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(11,plain,
( ( big_p @ sK1_X )
= $true ),
inference(standard_cnf,[status(thm)],[10]) ).
thf(12,plain,
( ( big_f @ sK1_X )
= $true ),
inference(standard_cnf,[status(thm)],[10]) ).
thf(13,plain,
( ( big_g @ sK1_X )
= $false ),
inference(standard_cnf,[status(thm)],[10]) ).
thf(14,plain,
( ( ~ ( big_g @ sK1_X ) )
= $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [X: $i] :
~ ( big_s @ X )
| ! [X1: $i] :
( ~ ( big_f @ X1 )
| ( big_g @ X1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(16,plain,
( ( ( sK4_REN
| ( ( big_q @ sK2_X1 )
& ( big_s @ sK2_X1 ) ) )
& ( sK4_REN
=> ( ~ ( big_q @ sK3_X )
& ~ ( big_r @ sK3_X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(17,plain,
( ( ! [X: $i] :
~ ( big_p @ X )
| ! [Z: $i] : ( big_q @ Z ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(18,plain,
( ( ! [X: $i] :
~ ( big_p @ X )
| ! [Z: $i] : ( big_q @ Z ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(19,plain,
( ( ( sK4_REN
| ( ( big_q @ sK2_X1 )
& ( big_s @ sK2_X1 ) ) )
& ( sK4_REN
=> ( ~ ( big_q @ sK3_X )
& ~ ( big_r @ sK3_X ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(20,plain,
( ( ! [X: $i] :
~ ( big_s @ X )
| ! [X1: $i] :
( ~ ( big_f @ X1 )
| ( big_g @ X1 ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(21,plain,
( ( big_f @ sK1_X )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(22,plain,
( ( big_p @ sK1_X )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(23,plain,
( ( ~ ( big_g @ sK1_X ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(24,plain,
( ( ~ ( ~ ( sK4_REN
| ~ ( ~ ( big_q @ sK2_X1 )
| ~ ( big_s @ sK2_X1 ) ) )
| ~ ( ~ sK4_REN
| ~ ( ~ ~ ( big_q @ sK3_X )
| ~ ~ ( big_r @ sK3_X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(25,plain,
( ( ( ! [X: $i] :
~ ( big_p @ X ) )
= $true )
| ( ( ! [Z: $i] : ( big_q @ Z ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(26,plain,
( ( ( ! [X: $i] :
~ ( big_s @ X ) )
= $true )
| ( ( ! [X1: $i] :
( ~ ( big_f @ X1 )
| ( big_g @ X1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(27,plain,
( ( big_g @ sK1_X )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( ~ ( sK4_REN
| ~ ( ~ ( big_q @ sK2_X1 )
| ~ ( big_s @ sK2_X1 ) ) )
| ~ ( ~ sK4_REN
| ~ ( ~ ~ ( big_q @ sK3_X )
| ~ ~ ( big_r @ sK3_X ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV1: $i] :
( ( ( ~ ( big_p @ SV1 ) )
= $true )
| ( ( ! [Z: $i] : ( big_q @ Z ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV2: $i] :
( ( ( ~ ( big_s @ SV2 ) )
= $true )
| ( ( ! [X1: $i] :
( ~ ( big_f @ X1 )
| ( big_g @ X1 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(31,plain,
( ( ~ ( sK4_REN
| ~ ( ~ ( big_q @ sK2_X1 )
| ~ ( big_s @ sK2_X1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(32,plain,
( ( ~ ( ~ sK4_REN
| ~ ( ~ ~ ( big_q @ sK3_X )
| ~ ~ ( big_r @ sK3_X ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(33,plain,
! [SV1: $i] :
( ( ( big_p @ SV1 )
= $false )
| ( ( ! [Z: $i] : ( big_q @ Z ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV2: $i] :
( ( ( big_s @ SV2 )
= $false )
| ( ( ! [X1: $i] :
( ~ ( big_f @ X1 )
| ( big_g @ X1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(35,plain,
( ( sK4_REN
| ~ ( ~ ( big_q @ sK2_X1 )
| ~ ( big_s @ sK2_X1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(36,plain,
( ( ~ sK4_REN
| ~ ( ~ ~ ( big_q @ sK3_X )
| ~ ~ ( big_r @ sK3_X ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(37,plain,
! [SV1: $i,SV3: $i] :
( ( ( big_q @ SV3 )
= $true )
| ( ( big_p @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( big_f @ SV4 )
| ( big_g @ SV4 ) )
= $true )
| ( ( big_s @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(39,plain,
( ( sK4_REN = $true )
| ( ( ~ ( ~ ( big_q @ sK2_X1 )
| ~ ( big_s @ sK2_X1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(40,plain,
( ( ( ~ sK4_REN )
= $true )
| ( ( ~ ( ~ ~ ( big_q @ sK3_X )
| ~ ~ ( big_r @ sK3_X ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( big_f @ SV4 ) )
= $true )
| ( ( big_g @ SV4 )
= $true )
| ( ( big_s @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(42,plain,
( ( ( ~ ( big_q @ sK2_X1 )
| ~ ( big_s @ sK2_X1 ) )
= $false )
| ( sK4_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(43,plain,
( ( sK4_REN = $false )
| ( ( ~ ( ~ ~ ( big_q @ sK3_X )
| ~ ~ ( big_r @ sK3_X ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV2: $i,SV4: $i] :
( ( ( big_f @ SV4 )
= $false )
| ( ( big_g @ SV4 )
= $true )
| ( ( big_s @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(45,plain,
( ( ( ~ ( big_q @ sK2_X1 ) )
= $false )
| ( sK4_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(46,plain,
( ( ( ~ ( big_s @ sK2_X1 ) )
= $false )
| ( sK4_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(47,plain,
( ( ( ~ ~ ( big_q @ sK3_X )
| ~ ~ ( big_r @ sK3_X ) )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(48,plain,
( ( ( big_q @ sK2_X1 )
= $true )
| ( sK4_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(49,plain,
( ( ( big_s @ sK2_X1 )
= $true )
| ( sK4_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(50,plain,
( ( ( ~ ~ ( big_q @ sK3_X ) )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(51,plain,
( ( ( ~ ~ ( big_r @ sK3_X ) )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(52,plain,
( ( ( ~ ( big_q @ sK3_X ) )
= $true )
| ( sK4_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(53,plain,
( ( ( ~ ( big_r @ sK3_X ) )
= $true )
| ( sK4_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(54,plain,
( ( ( big_q @ sK3_X )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(55,plain,
( ( ( big_r @ sK3_X )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(56,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,55,54,49,48,44,37,27,22]) ).
thf(57,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN058+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 12 04:59:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 3
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.35 (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:5,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.13/0.38
% 0.13/0.38 ********************************
% 0.13/0.38 * All subproblems solved! *
% 0.13/0.38 ********************************
% 0.13/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,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:56,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.38
% 0.13/0.38 %**** Beginning of derivation protocol ****
% 0.13/0.38 % SZS output start CNFRefutation
% See solution above
% 0.13/0.38
% 0.13/0.38 %**** End of derivation protocol ****
% 0.13/0.38 %**** no. of clauses in derivation: 57 ****
% 0.13/0.38 %**** clause counter: 56 ****
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,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:56,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------