TSTP Solution File: MSC012+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : MSC012+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n015.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 : Sun Jul 17 22:50:24 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 27 unt; 5 typ; 0 def)
% Number of atoms : 270 ( 72 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 317 ( 54 ~; 64 |; 10 &; 185 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 78 ( 0 ^ 74 !; 4 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_goal,type,
goal: $o ).
thf(tp_less,type,
less: $i > $i > $o ).
thf(tp_p,type,
p: $i > $o ).
thf(tp_sK1_B,type,
sK1_B: $i > $i ).
thf(tp_sK2_B,type,
sK2_B: $i > $i ).
thf(1,axiom,
! [A: $i] :
? [B: $i] : ( less @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',serial_less) ).
thf(2,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( less @ A @ B )
& ( less @ B @ C ) )
=> ( less @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_less) ).
thf(3,axiom,
! [A: $i] :
( ( p @ A )
| ? [B: $i] :
( ( less @ A @ B )
& ( p @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_to_left) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( p @ A )
& ( less @ A @ B )
& ( p @ B ) )
=> goal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_to_right) ).
thf(5,conjecture,
goal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_to_be_proved) ).
thf(6,negated_conjecture,
goal = $false,
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
goal = $false,
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [A: $i] :
? [B: $i] : ( less @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( less @ A @ B )
& ( less @ B @ C ) )
=> ( less @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
( ( ! [A: $i] :
( ( p @ A )
| ? [B: $i] :
( ( less @ A @ B )
& ( p @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ( ( p @ A )
& ( less @ A @ B )
& ( p @ B ) )
=> goal ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(12,plain,
( ( ~ goal )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [A: $i] : ( less @ A @ ( sK1_B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(14,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ C )
| ( less @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(15,plain,
( ( ! [A: $i] :
( ( ( less @ A @ ( sK2_B @ A ) )
& ( p @ ( sK2_B @ A ) ) )
| ( p @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
( ~ ( less @ A @ B )
| ~ ( p @ A )
| ~ ( p @ B ) )
| goal )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ~ ( less @ A @ B )
| ~ ( p @ A )
| ~ ( p @ B ) )
| goal )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(18,plain,
( ( ! [A: $i] :
( ( ( less @ A @ ( sK2_B @ A ) )
& ( p @ ( sK2_B @ A ) ) )
| ( p @ A ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ C )
| ( less @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(20,plain,
( ( ! [A: $i] : ( less @ A @ ( sK1_B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( ~ goal )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(22,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( less @ SX0 @ ( sK2_B @ SX0 ) )
| ~ ( p @ ( sK2_B @ SX0 ) ) )
| ( p @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(23,plain,
( ( ( ! [A: $i,B: $i] :
( ~ ( less @ A @ B )
| ~ ( p @ A )
| ~ ( p @ B ) ) )
= $true )
| ( goal = $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(24,plain,
! [SV1: $i] :
( ( ! [SY9: $i,SY10: $i] :
( ~ ( less @ SV1 @ SY9 )
| ~ ( less @ SY9 @ SY10 )
| ( less @ SV1 @ SY10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(25,plain,
! [SV2: $i] :
( ( less @ SV2 @ ( sK1_B @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(26,plain,
goal = $false,
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV3: $i] :
( ( ~ ( ~ ( less @ SV3 @ ( sK2_B @ SV3 ) )
| ~ ( p @ ( sK2_B @ SV3 ) ) )
| ( p @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV4: $i] :
( ( ( ! [SY11: $i] :
( ~ ( less @ SV4 @ SY11 )
| ~ ( p @ SV4 )
| ~ ( p @ SY11 ) ) )
= $true )
| ( goal = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV5: $i,SV1: $i] :
( ( ! [SY12: $i] :
( ~ ( less @ SV1 @ SV5 )
| ~ ( less @ SV5 @ SY12 )
| ( less @ SV1 @ SY12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ( less @ SV3 @ ( sK2_B @ SV3 ) )
| ~ ( p @ ( sK2_B @ SV3 ) ) ) )
= $true )
| ( ( p @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV6: $i,SV4: $i] :
( ( ( ~ ( less @ SV4 @ SV6 )
| ~ ( p @ SV4 )
| ~ ( p @ SV6 ) )
= $true )
| ( goal = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV7: $i,SV5: $i,SV1: $i] :
( ( ~ ( less @ SV1 @ SV5 )
| ~ ( less @ SV5 @ SV7 )
| ( less @ SV1 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV3: $i] :
( ( ( ~ ( less @ SV3 @ ( sK2_B @ SV3 ) )
| ~ ( p @ ( sK2_B @ SV3 ) ) )
= $false )
| ( ( p @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV6: $i,SV4: $i] :
( ( ( ~ ( less @ SV4 @ SV6 )
| ~ ( p @ SV4 ) )
= $true )
| ( ( ~ ( p @ SV6 ) )
= $true )
| ( goal = $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV7: $i,SV5: $i,SV1: $i] :
( ( ( ~ ( less @ SV1 @ SV5 )
| ~ ( less @ SV5 @ SV7 ) )
= $true )
| ( ( less @ SV1 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV3: $i] :
( ( ( ~ ( less @ SV3 @ ( sK2_B @ SV3 ) ) )
= $false )
| ( ( p @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV3: $i] :
( ( ( ~ ( p @ ( sK2_B @ SV3 ) ) )
= $false )
| ( ( p @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(38,plain,
! [SV6: $i,SV4: $i] :
( ( ( ~ ( less @ SV4 @ SV6 ) )
= $true )
| ( ( ~ ( p @ SV4 ) )
= $true )
| ( ( ~ ( p @ SV6 ) )
= $true )
| ( goal = $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV7: $i,SV5: $i,SV1: $i] :
( ( ( ~ ( less @ SV1 @ SV5 ) )
= $true )
| ( ( ~ ( less @ SV5 @ SV7 ) )
= $true )
| ( ( less @ SV1 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV3: $i] :
( ( ( less @ SV3 @ ( sK2_B @ SV3 ) )
= $true )
| ( ( p @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(41,plain,
! [SV3: $i] :
( ( ( p @ ( sK2_B @ SV3 ) )
= $true )
| ( ( p @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(42,plain,
! [SV6: $i,SV4: $i] :
( ( ( less @ SV4 @ SV6 )
= $false )
| ( ( ~ ( p @ SV4 ) )
= $true )
| ( ( ~ ( p @ SV6 ) )
= $true )
| ( goal = $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV7: $i,SV5: $i,SV1: $i] :
( ( ( less @ SV1 @ SV5 )
= $false )
| ( ( ~ ( less @ SV5 @ SV7 ) )
= $true )
| ( ( less @ SV1 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV6: $i,SV4: $i] :
( ( ( p @ SV4 )
= $false )
| ( ( less @ SV4 @ SV6 )
= $false )
| ( ( ~ ( p @ SV6 ) )
= $true )
| ( goal = $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV1: $i,SV7: $i,SV5: $i] :
( ( ( less @ SV5 @ SV7 )
= $false )
| ( ( less @ SV1 @ SV5 )
= $false )
| ( ( less @ SV1 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV4: $i,SV6: $i] :
( ( ( p @ SV6 )
= $false )
| ( ( less @ SV4 @ SV6 )
= $false )
| ( ( p @ SV4 )
= $false )
| ( goal = $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(47,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,46,45,41,40,26]) ).
thf(48,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MSC012+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jul 1 16:53:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 4
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.34 (rf:0,axioms:4,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:6,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.13/0.37
% 0.13/0.37 ********************************
% 0.13/0.37 * All subproblems solved! *
% 0.13/0.37 ********************************
% 0.13/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:47,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.37
% 0.13/0.37 %**** Beginning of derivation protocol ****
% 0.13/0.37 % SZS output start CNFRefutation
% See solution above
% 0.13/0.37
% 0.13/0.37 %**** End of derivation protocol ****
% 0.13/0.37 %**** no. of clauses in derivation: 48 ****
% 0.13/0.37 %**** clause counter: 47 ****
% 0.13/0.37
% 0.13/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:47,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------