TSTP Solution File: SYN066-1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN066-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n008.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 08:23:14 EDT 2022
% Result : Unsatisfiable 0.20s 0.39s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 55 ( 34 unt; 8 typ; 0 def)
% Number of atoms : 172 ( 48 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 275 ( 25 ~; 29 |; 0 &; 221 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 0 ^ 82 !; 0 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_big_p,type,
big_p: $i > $i > $o ).
thf(tp_big_q,type,
big_q: $i > $i > $o ).
thf(tp_big_r,type,
big_r: $i > $i > $o ).
thf(tp_f,type,
f: $i > $i > $i ).
thf(tp_g,type,
g: $i > $i ).
thf(tp_h,type,
h: $i > $i > $i ).
thf(tp_i,type,
i: $i > $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( big_q @ X @ Y )
| ( big_r @ Z @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( big_p @ X @ Y )
| ( big_q @ ( i @ X @ Y ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ~ ( big_p @ ( f @ X @ Y ) @ ( g @ X ) )
| ( big_q @ ( h @ X @ Y ) @ ( g @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
thf(4,axiom,
! [X: $i,Y: $i] : ( big_p @ ( f @ X @ Y ) @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
thf(5,axiom,
! [Y: $i,X: $i] :
( ~ ( big_p @ Y @ X )
| ( big_p @ ( f @ X @ Y ) @ ( g @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
thf(6,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(7,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,negated_conjecture,
! [Z: $i] :
~ ( big_r @ a @ Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
thf(9,plain,
$false = $false,
inference(unfold_def,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( big_q @ X @ Y )
| ( big_r @ Z @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [X: $i,Y: $i] :
( ( big_p @ X @ Y )
| ( big_q @ ( i @ X @ Y ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( big_p @ ( f @ X @ Y ) @ ( g @ X ) )
| ( big_q @ ( h @ X @ Y ) @ ( g @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [X: $i,Y: $i] : ( big_p @ ( f @ X @ Y ) @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,plain,
( ( ! [Y: $i,X: $i] :
( ~ ( big_p @ Y @ X )
| ( big_p @ ( f @ X @ Y ) @ ( g @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( ! [Z: $i] :
~ ( big_r @ a @ Z ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
~ ( big_q @ X @ Y )
| ! [Z: $i] : ( big_r @ Z @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(18,plain,
( ( ! [Z: $i] :
~ ( big_r @ a @ Z ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [Y: $i,X: $i] :
( ~ ( big_p @ Y @ X )
| ( big_p @ ( f @ X @ Y ) @ ( g @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(20,plain,
( ( ! [X: $i,Y: $i] : ( big_p @ ( f @ X @ Y ) @ X ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( big_p @ ( f @ X @ Y ) @ ( g @ X ) )
| ( big_q @ ( h @ X @ Y ) @ ( g @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(22,plain,
( ( ! [X: $i,Y: $i] :
( ( big_p @ X @ Y )
| ( big_q @ ( i @ X @ Y ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(23,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
~ ( big_q @ X @ Y )
| ! [Z: $i] : ( big_r @ Z @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(24,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(25,plain,
! [SV1: $i] :
( ( ~ ( big_r @ a @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(26,plain,
! [SV2: $i] :
( ( ! [SY12: $i] :
( ~ ( big_p @ SV2 @ SY12 )
| ( big_p @ ( f @ SY12 @ SV2 ) @ ( g @ SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(27,plain,
! [SV3: $i] :
( ( ! [SY13: $i] : ( big_p @ ( f @ SV3 @ SY13 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(28,plain,
! [SV4: $i] :
( ( ! [SY14: $i] :
( ~ ( big_p @ ( f @ SV4 @ SY14 ) @ ( g @ SV4 ) )
| ( big_q @ ( h @ SV4 @ SY14 ) @ ( g @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(29,plain,
! [SV5: $i] :
( ( ! [SY15: $i] :
( ( big_p @ SV5 @ SY15 )
| ( big_q @ ( i @ SV5 @ SY15 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(30,plain,
! [SV6: $i] :
( ( ! [SY16: $i] :
~ ( big_q @ SV6 @ SY16 )
| ! [Z: $i] : ( big_r @ Z @ Z ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(31,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(32,plain,
! [SV1: $i] :
( ( big_r @ a @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(33,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ( big_p @ SV2 @ SV7 )
| ( big_p @ ( f @ SV7 @ SV2 ) @ ( g @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(34,plain,
! [SV8: $i,SV3: $i] :
( ( big_p @ ( f @ SV3 @ SV8 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(35,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( big_p @ ( f @ SV4 @ SV9 ) @ ( g @ SV4 ) )
| ( big_q @ ( h @ SV4 @ SV9 ) @ ( g @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(36,plain,
! [SV10: $i,SV5: $i] :
( ( ( big_p @ SV5 @ SV10 )
| ( big_q @ ( i @ SV5 @ SV10 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(37,plain,
! [SV6: $i] :
( ( ( ! [SY16: $i] :
~ ( big_q @ SV6 @ SY16 ) )
= $true )
| ( ( ! [Z: $i] : ( big_r @ Z @ Z ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(38,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( big_p @ SV2 @ SV7 ) )
= $true )
| ( ( big_p @ ( f @ SV7 @ SV2 ) @ ( g @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( big_p @ ( f @ SV4 @ SV9 ) @ ( g @ SV4 ) ) )
= $true )
| ( ( big_q @ ( h @ SV4 @ SV9 ) @ ( g @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV10: $i,SV5: $i] :
( ( ( big_p @ SV5 @ SV10 )
= $true )
| ( ( big_q @ ( i @ SV5 @ SV10 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( big_q @ SV6 @ SV11 ) )
= $true )
| ( ( ! [Z: $i] : ( big_r @ Z @ Z ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV7: $i,SV2: $i] :
( ( ( big_p @ SV2 @ SV7 )
= $false )
| ( ( big_p @ ( f @ SV7 @ SV2 ) @ ( g @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV9: $i,SV4: $i] :
( ( ( big_p @ ( f @ SV4 @ SV9 ) @ ( g @ SV4 ) )
= $false )
| ( ( big_q @ ( h @ SV4 @ SV9 ) @ ( g @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV11: $i,SV6: $i] :
( ( ( big_q @ SV6 @ SV11 )
= $false )
| ( ( ! [Z: $i] : ( big_r @ Z @ Z ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV11: $i,SV6: $i,SV12: $i] :
( ( ( big_r @ SV12 @ SV12 )
= $true )
| ( ( big_q @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(46,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[31,45,43,42,40,34,32]) ).
thf(47,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN066-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jul 12 00:04:08 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 6
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.36 (rf:0,axioms:6,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:8,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.20/0.39
% 0.20/0.39 ********************************
% 0.20/0.39 * All subproblems solved! *
% 0.20/0.39 ********************************
% 0.20/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:46,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.39
% 0.20/0.39 %**** Beginning of derivation protocol ****
% 0.20/0.39 % SZS output start CNFRefutation
% See solution above
% 0.20/0.39
% 0.20/0.39 %**** End of derivation protocol ****
% 0.20/0.39 %**** no. of clauses in derivation: 47 ****
% 0.20/0.39 %**** clause counter: 46 ****
% 0.20/0.39
% 0.20/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:46,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------