TSTP Solution File: SYN940+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN940+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n004.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 08:30:42 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 26 unt; 6 typ; 0 def)
% Number of atoms : 329 ( 72 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 468 ( 118 ~; 98 |; 25 &; 208 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 96 ( 0 ^ 82 !; 14 ?; 96 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_f,type,
f: $i > $i ).
thf(tp_p,type,
p: $i > $o ).
thf(tp_q,type,
q: $i > $o ).
thf(tp_r,type,
r: $i > $o ).
thf(tp_sK1_B,type,
sK1_B: $i ).
thf(tp_sK2_SY5,type,
sK2_SY5: $i ).
thf(1,conjecture,
! [B: $i,C: $i] :
( ! [Z: $i] : ( q @ ( f @ Z ) )
=> ? [X: $i,Y: $i] :
( ( ( p @ ( f @ Y ) )
=> ( ( p @ X )
& ( ( r @ Y )
=> ( ( r @ B )
& ( r @ C ) ) ) ) )
& ( q @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(2,negated_conjecture,
( ( ! [B: $i,C: $i] :
( ! [Z: $i] : ( q @ ( f @ Z ) )
=> ? [X: $i,Y: $i] :
( ( ( p @ ( f @ Y ) )
=> ( ( p @ X )
& ( ( r @ Y )
=> ( ( r @ B )
& ( r @ C ) ) ) ) )
& ( q @ X ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [B: $i,C: $i] :
( ! [Z: $i] : ( q @ ( f @ Z ) )
=> ? [X: $i,Y: $i] :
( ( ( p @ ( f @ Y ) )
=> ( ( p @ X )
& ( ( r @ Y )
=> ( ( r @ B )
& ( r @ C ) ) ) ) )
& ( q @ X ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY5: $i] :
( ! [Z: $i] : ( q @ ( f @ Z ) )
=> ? [SY7: $i,SY8: $i] :
( ( ( p @ ( f @ SY8 ) )
=> ( ( p @ SY7 )
& ( ( r @ SY8 )
=> ( ( r @ sK1_B )
& ( r @ SY5 ) ) ) ) )
& ( q @ SY7 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [Z: $i] : ( q @ ( f @ Z ) )
=> ? [SY10: $i,SY11: $i] :
( ( ( p @ ( f @ SY11 ) )
=> ( ( p @ SY10 )
& ( ( r @ SY11 )
=> ( ( r @ sK1_B )
& ( r @ sK2_SY5 ) ) ) ) )
& ( q @ SY10 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [Z: $i] : ( q @ ( f @ Z ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ? [SY10: $i,SY11: $i] :
( ( ( p @ ( f @ SY11 ) )
=> ( ( p @ SY10 )
& ( ( r @ SY11 )
=> ( ( r @ sK1_B )
& ( r @ sK2_SY5 ) ) ) ) )
& ( q @ SY10 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ? [SY10: $i,SY11: $i] :
( ( ( p @ ( f @ SY11 ) )
=> ( ( p @ SY10 )
& ( ( r @ SY11 )
=> ( ( r @ sK1_B )
& ( r @ sK2_SY5 ) ) ) ) )
& ( q @ SY10 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ( ! [SY11: $i] : ( p @ ( f @ SY11 ) )
| ! [SY10: $i] :
~ ( q @ SY10 ) )
& ! [SY10: $i] :
( ! [SY11: $i] : ( r @ SY11 )
| ~ ( p @ SY10 )
| ~ ( q @ SY10 ) )
& ! [SY10: $i] :
( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 )
| ~ ( p @ SY10 )
| ~ ( q @ SY10 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [Z: $i] : ( q @ ( f @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(11,plain,
( ( ( ! [SY11: $i] : ( p @ ( f @ SY11 ) )
| ! [SY10: $i] :
~ ( q @ SY10 ) )
& ! [SY10: $i] :
( ! [SY11: $i] : ( r @ SY11 )
| ~ ( p @ SY10 )
| ~ ( q @ SY10 ) )
& ! [SY10: $i] :
( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 )
| ~ ( p @ SY10 )
| ~ ( q @ SY10 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( ~ ( ! [SX0: $i] : ( p @ ( f @ SX0 ) )
| ! [SX0: $i] :
~ ( q @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] : ( r @ SX1 )
| ~ ( p @ SX0 )
| ~ ( q @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 )
| ~ ( p @ SX0 )
| ~ ( q @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(13,plain,
! [SV1: $i] :
( ( q @ ( f @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(14,plain,
( ( ~ ( ! [SX0: $i] : ( p @ ( f @ SX0 ) )
| ! [SX0: $i] :
~ ( q @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] : ( r @ SX1 )
| ~ ( p @ SX0 )
| ~ ( q @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 )
| ~ ( p @ SX0 )
| ~ ( q @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( ! [SX0: $i] : ( p @ ( f @ SX0 ) )
| ! [SX0: $i] :
~ ( q @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(16,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] : ( r @ SX1 )
| ~ ( p @ SX0 )
| ~ ( q @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 )
| ~ ( p @ SX0 )
| ~ ( q @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ! [SX0: $i] : ( p @ ( f @ SX0 ) )
| ! [SX0: $i] :
~ ( q @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] : ( r @ SX1 )
| ~ ( p @ SX0 )
| ~ ( q @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 )
| ~ ( p @ SX0 )
| ~ ( q @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( ( ! [SX0: $i] : ( p @ ( f @ SX0 ) ) )
= $true )
| ( ( ! [SX0: $i] :
~ ( q @ SX0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] : ( r @ SX1 )
| ~ ( p @ SX0 )
| ~ ( q @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 )
| ~ ( p @ SX0 )
| ~ ( q @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(21,plain,
! [SV2: $i] :
( ( ( p @ ( f @ SV2 ) )
= $true )
| ( ( ! [SX0: $i] :
~ ( q @ SX0 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(22,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] : ( r @ SX1 )
| ~ ( p @ SX0 )
| ~ ( q @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(23,plain,
( ( ~ ! [SX0: $i] :
( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 )
| ~ ( p @ SX0 )
| ~ ( q @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV2: $i,SV3: $i] :
( ( ( ~ ( q @ SV3 ) )
= $true )
| ( ( p @ ( f @ SV2 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] : ( r @ SX1 )
| ~ ( p @ SX0 )
| ~ ( q @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(26,plain,
( ( ! [SX0: $i] :
( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 )
| ~ ( p @ SX0 )
| ~ ( q @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(27,plain,
! [SV2: $i,SV3: $i] :
( ( ( q @ SV3 )
= $false )
| ( ( p @ ( f @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV4: $i] :
( ( ! [SX1: $i] : ( r @ SX1 )
| ~ ( p @ SV4 )
| ~ ( q @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV5: $i] :
( ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 )
| ~ ( p @ SV5 )
| ~ ( q @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV4: $i] :
( ( ( ! [SX1: $i] : ( r @ SX1 )
| ~ ( p @ SV4 ) )
= $true )
| ( ( ~ ( q @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(31,plain,
! [SV5: $i] :
( ( ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 )
| ~ ( p @ SV5 ) )
= $true )
| ( ( ~ ( q @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV4: $i] :
( ( ( ! [SX1: $i] : ( r @ SX1 ) )
= $true )
| ( ( ~ ( p @ SV4 ) )
= $true )
| ( ( ~ ( q @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV5: $i] :
( ( ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 ) )
= $true )
| ( ( ~ ( p @ SV5 ) )
= $true )
| ( ( ~ ( q @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV4: $i,SV6: $i] :
( ( ( r @ SV6 )
= $true )
| ( ( ~ ( p @ SV4 ) )
= $true )
| ( ( ~ ( q @ SV4 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV5: $i] :
( ( ( ~ ( r @ sK1_B ) )
= $true )
| ( ( ~ ( r @ sK2_SY5 ) )
= $true )
| ( ( ~ ( p @ SV5 ) )
= $true )
| ( ( ~ ( q @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV6: $i,SV4: $i] :
( ( ( p @ SV4 )
= $false )
| ( ( r @ SV6 )
= $true )
| ( ( ~ ( q @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV5: $i] :
( ( ( r @ sK1_B )
= $false )
| ( ( ~ ( r @ sK2_SY5 ) )
= $true )
| ( ( ~ ( p @ SV5 ) )
= $true )
| ( ( ~ ( q @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV6: $i,SV4: $i] :
( ( ( q @ SV4 )
= $false )
| ( ( r @ SV6 )
= $true )
| ( ( p @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV5: $i] :
( ( ( r @ sK2_SY5 )
= $false )
| ( ( r @ sK1_B )
= $false )
| ( ( ~ ( p @ SV5 ) )
= $true )
| ( ( ~ ( q @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV5: $i] :
( ( ( p @ SV5 )
= $false )
| ( ( r @ sK1_B )
= $false )
| ( ( r @ sK2_SY5 )
= $false )
| ( ( ~ ( q @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(41,plain,
! [SV5: $i] :
( ( ( q @ SV5 )
= $false )
| ( ( r @ sK2_SY5 )
= $false )
| ( ( r @ sK1_B )
= $false )
| ( ( p @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(42,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[13,41,38,27]) ).
thf(43,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN940+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n004.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 06:24:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 0
% 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: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)..
% 0.19/0.38
% 0.19/0.38 ********************************
% 0.19/0.38 * All subproblems solved! *
% 0.19/0.38 ********************************
% 0.19/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:42,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.38
% 0.19/0.38 %**** Beginning of derivation protocol ****
% 0.19/0.38 % SZS output start CNFRefutation
% See solution above
% 0.19/0.38
% 0.19/0.38 %**** End of derivation protocol ****
% 0.19/0.38 %**** no. of clauses in derivation: 43 ****
% 0.19/0.38 %**** clause counter: 42 ****
% 0.19/0.38
% 0.19/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:42,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------