TSTP Solution File: MSC005-1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : MSC005-1 : 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 : n020.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 22:50:19 EDT 2022
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 63 ( 35 unt; 4 typ; 0 def)
% Number of atoms : 295 ( 78 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 528 ( 66 ~; 80 |; 0 &; 382 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 85 ( 0 ^ 85 !; 0 ?; 85 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_falsity,type,
falsity: $i ).
thf(tp_truth,type,
truth: $i ).
thf(tp_value,type,
value: $i > $i > $o ).
thf(tp_xor,type,
xor: $i > $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ~ ( value @ X @ falsity )
| ~ ( value @ Y @ falsity )
| ( value @ ( xor @ X @ Y ) @ falsity ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_xor_false) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ~ ( value @ X @ falsity )
| ~ ( value @ Y @ truth )
| ( value @ ( xor @ X @ Y ) @ truth ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_xor_true) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ~ ( value @ X @ truth )
| ~ ( value @ Y @ falsity )
| ( value @ ( xor @ X @ Y ) @ truth ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',true_xor_false) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ~ ( value @ X @ truth )
| ~ ( value @ Y @ truth )
| ( value @ ( xor @ X @ Y ) @ falsity ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',true_xor_true) ).
thf(5,axiom,
value @ falsity @ falsity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_is_false) ).
thf(6,axiom,
value @ truth @ truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',true_is_true) ).
thf(7,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(8,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,negated_conjecture,
! [Value: $i] :
~ ( value @ ( xor @ ( xor @ ( xor @ ( xor @ truth @ falsity ) @ falsity ) @ truth ) @ falsity ) @ Value ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',evaluate_expression) ).
thf(10,plain,
$false = $false,
inference(unfold_def,[status(thm)],[8]) ).
thf(11,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( value @ X @ falsity )
| ~ ( value @ Y @ falsity )
| ( value @ ( xor @ X @ Y ) @ falsity ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( value @ X @ falsity )
| ~ ( value @ Y @ truth )
| ( value @ ( xor @ X @ Y ) @ truth ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( value @ X @ truth )
| ~ ( value @ Y @ falsity )
| ( value @ ( xor @ X @ Y ) @ truth ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( value @ X @ truth )
| ~ ( value @ Y @ truth )
| ( value @ ( xor @ X @ Y ) @ falsity ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(15,plain,
( ( value @ falsity @ falsity )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(16,plain,
( ( value @ truth @ truth )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(17,plain,
( ( ! [Value: $i] :
~ ( value @ ( xor @ ( xor @ ( xor @ ( xor @ truth @ falsity ) @ falsity ) @ truth ) @ falsity ) @ Value ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(18,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [X: $i] :
( ~ ( value @ X @ falsity )
| ! [Y: $i] :
( ~ ( value @ Y @ falsity )
| ( value @ ( xor @ X @ Y ) @ falsity ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(20,plain,
( ( ! [X: $i] :
( ~ ( value @ X @ falsity )
| ! [Y: $i] :
( ~ ( value @ Y @ truth )
| ( value @ ( xor @ X @ Y ) @ truth ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(21,plain,
( ( ! [X: $i] :
( ~ ( value @ X @ truth )
| ! [Y: $i] :
( ~ ( value @ Y @ falsity )
| ( value @ ( xor @ X @ Y ) @ truth ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(22,plain,
( ( ! [X: $i] :
( ~ ( value @ X @ truth )
| ! [Y: $i] :
( ~ ( value @ Y @ truth )
| ( value @ ( xor @ X @ Y ) @ falsity ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(23,plain,
( ( ! [Value: $i] :
~ ( value @ ( xor @ ( xor @ ( xor @ ( xor @ truth @ falsity ) @ falsity ) @ truth ) @ falsity ) @ Value ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(24,plain,
( ( value @ truth @ truth )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(25,plain,
( ( value @ falsity @ falsity )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(26,plain,
( ( ! [X: $i] :
( ~ ( value @ X @ truth )
| ! [Y: $i] :
( ~ ( value @ Y @ truth )
| ( value @ ( xor @ X @ Y ) @ falsity ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(27,plain,
( ( ! [X: $i] :
( ~ ( value @ X @ truth )
| ! [Y: $i] :
( ~ ( value @ Y @ falsity )
| ( value @ ( xor @ X @ Y ) @ truth ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(28,plain,
( ( ! [X: $i] :
( ~ ( value @ X @ falsity )
| ! [Y: $i] :
( ~ ( value @ Y @ truth )
| ( value @ ( xor @ X @ Y ) @ truth ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(29,plain,
( ( ! [X: $i] :
( ~ ( value @ X @ falsity )
| ! [Y: $i] :
( ~ ( value @ Y @ falsity )
| ( value @ ( xor @ X @ Y ) @ falsity ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(30,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(31,plain,
! [SV1: $i] :
( ( ~ ( value @ ( xor @ ( xor @ ( xor @ ( xor @ truth @ falsity ) @ falsity ) @ truth ) @ falsity ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(32,plain,
! [SV2: $i] :
( ( ~ ( value @ SV2 @ truth )
| ! [SY9: $i] :
( ~ ( value @ SY9 @ truth )
| ( value @ ( xor @ SV2 @ SY9 ) @ falsity ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(33,plain,
! [SV3: $i] :
( ( ~ ( value @ SV3 @ truth )
| ! [SY10: $i] :
( ~ ( value @ SY10 @ falsity )
| ( value @ ( xor @ SV3 @ SY10 ) @ truth ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(34,plain,
! [SV4: $i] :
( ( ~ ( value @ SV4 @ falsity )
| ! [SY11: $i] :
( ~ ( value @ SY11 @ truth )
| ( value @ ( xor @ SV4 @ SY11 ) @ truth ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV5: $i] :
( ( ~ ( value @ SV5 @ falsity )
| ! [SY12: $i] :
( ~ ( value @ SY12 @ falsity )
| ( value @ ( xor @ SV5 @ SY12 ) @ falsity ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(36,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV1: $i] :
( ( value @ ( xor @ ( xor @ ( xor @ ( xor @ truth @ falsity ) @ falsity ) @ truth ) @ falsity ) @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV2: $i] :
( ( ( ~ ( value @ SV2 @ truth ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( value @ SY9 @ truth )
| ( value @ ( xor @ SV2 @ SY9 ) @ falsity ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(39,plain,
! [SV3: $i] :
( ( ( ~ ( value @ SV3 @ truth ) )
= $true )
| ( ( ! [SY10: $i] :
( ~ ( value @ SY10 @ falsity )
| ( value @ ( xor @ SV3 @ SY10 ) @ truth ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV4: $i] :
( ( ( ~ ( value @ SV4 @ falsity ) )
= $true )
| ( ( ! [SY11: $i] :
( ~ ( value @ SY11 @ truth )
| ( value @ ( xor @ SV4 @ SY11 ) @ truth ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV5: $i] :
( ( ( ~ ( value @ SV5 @ falsity ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( value @ SY12 @ falsity )
| ( value @ ( xor @ SV5 @ SY12 ) @ falsity ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(42,plain,
! [SV2: $i] :
( ( ( value @ SV2 @ truth )
= $false )
| ( ( ! [SY9: $i] :
( ~ ( value @ SY9 @ truth )
| ( value @ ( xor @ SV2 @ SY9 ) @ falsity ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV3: $i] :
( ( ( value @ SV3 @ truth )
= $false )
| ( ( ! [SY10: $i] :
( ~ ( value @ SY10 @ falsity )
| ( value @ ( xor @ SV3 @ SY10 ) @ truth ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV4: $i] :
( ( ( value @ SV4 @ falsity )
= $false )
| ( ( ! [SY11: $i] :
( ~ ( value @ SY11 @ truth )
| ( value @ ( xor @ SV4 @ SY11 ) @ truth ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV5: $i] :
( ( ( value @ SV5 @ falsity )
= $false )
| ( ( ! [SY12: $i] :
( ~ ( value @ SY12 @ falsity )
| ( value @ ( xor @ SV5 @ SY12 ) @ falsity ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV2: $i,SV6: $i] :
( ( ( ~ ( value @ SV6 @ truth )
| ( value @ ( xor @ SV2 @ SV6 ) @ falsity ) )
= $true )
| ( ( value @ SV2 @ truth )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( value @ SV7 @ falsity )
| ( value @ ( xor @ SV3 @ SV7 ) @ truth ) )
= $true )
| ( ( value @ SV3 @ truth )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( value @ SV8 @ truth )
| ( value @ ( xor @ SV4 @ SV8 ) @ truth ) )
= $true )
| ( ( value @ SV4 @ falsity )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV5: $i,SV9: $i] :
( ( ( ~ ( value @ SV9 @ falsity )
| ( value @ ( xor @ SV5 @ SV9 ) @ falsity ) )
= $true )
| ( ( value @ SV5 @ falsity )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV2: $i,SV6: $i] :
( ( ( ~ ( value @ SV6 @ truth ) )
= $true )
| ( ( value @ ( xor @ SV2 @ SV6 ) @ falsity )
= $true )
| ( ( value @ SV2 @ truth )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( value @ SV7 @ falsity ) )
= $true )
| ( ( value @ ( xor @ SV3 @ SV7 ) @ truth )
= $true )
| ( ( value @ SV3 @ truth )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( value @ SV8 @ truth ) )
= $true )
| ( ( value @ ( xor @ SV4 @ SV8 ) @ truth )
= $true )
| ( ( value @ SV4 @ falsity )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV5: $i,SV9: $i] :
( ( ( ~ ( value @ SV9 @ falsity ) )
= $true )
| ( ( value @ ( xor @ SV5 @ SV9 ) @ falsity )
= $true )
| ( ( value @ SV5 @ falsity )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV2: $i,SV6: $i] :
( ( ( value @ SV6 @ truth )
= $false )
| ( ( value @ ( xor @ SV2 @ SV6 ) @ falsity )
= $true )
| ( ( value @ SV2 @ truth )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV3: $i,SV7: $i] :
( ( ( value @ SV7 @ falsity )
= $false )
| ( ( value @ ( xor @ SV3 @ SV7 ) @ truth )
= $true )
| ( ( value @ SV3 @ truth )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV4: $i,SV8: $i] :
( ( ( value @ SV8 @ truth )
= $false )
| ( ( value @ ( xor @ SV4 @ SV8 ) @ truth )
= $true )
| ( ( value @ SV4 @ falsity )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV5: $i,SV9: $i] :
( ( ( value @ SV9 @ falsity )
= $false )
| ( ( value @ ( xor @ SV5 @ SV9 ) @ falsity )
= $true )
| ( ( value @ SV5 @ falsity )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(58,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,57,56,55,54,37,36,25]) ).
thf(59,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MSC005-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n020.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 : Fri Jul 1 16:27:30 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 7
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.36 (rf:0,axioms:7,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:9,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.13/0.40
% 0.13/0.40 ********************************
% 0.13/0.40 * All subproblems solved! *
% 0.13/0.40 ********************************
% 0.13/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:7,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:58,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.40
% 0.13/0.40 %**** Beginning of derivation protocol ****
% 0.13/0.40 % SZS output start CNFRefutation
% See solution above
% 0.13/0.40
% 0.13/0.40 %**** End of derivation protocol ****
% 0.13/0.40 %**** no. of clauses in derivation: 59 ****
% 0.13/0.40 %**** clause counter: 58 ****
% 0.13/0.40
% 0.13/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:7,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:58,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------