TSTP Solution File: LCL431-2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LCL431-2 : 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 : n029.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 12:23:11 EDT 2022
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 40 ( 25 unt; 10 typ; 0 def)
% Number of atoms : 96 ( 33 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 275 ( 12 ~; 10 |; 0 &; 253 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 50 ( 0 ^ 50 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_PropLog_Ohyps,type,
c_PropLog_Ohyps: $i > $i > $i > $i ).
thf(tp_c_PropLog_Osat,type,
c_PropLog_Osat: $i > $i > $i > $o ).
thf(tp_c_PropLog_Othms,type,
c_PropLog_Othms: $i > $i > $i ).
thf(tp_c_emptyset,type,
c_emptyset: $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_minus,type,
c_minus: $i > $i > $i > $i ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_PropLog_Opl,type,
tc_PropLog_Opl: $i > $i ).
thf(tp_tc_set,type,
tc_set: $i > $i ).
thf(tp_v_p,type,
v_p: $i ).
thf(1,axiom,
! [V_A: $i,T_a: $i] :
( ( c_minus @ V_A @ V_A @ ( tc_set @ T_a ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
thf(2,axiom,
! [V_p: $i,T_a: $i,V_U: $i,V_t0: $i] :
( ~ ( c_PropLog_Osat @ c_emptyset @ V_p @ T_a )
| ( c_in @ V_p @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ V_p @ V_U @ T_a ) @ ( c_PropLog_Ohyps @ V_p @ V_t0 @ T_a ) @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Ocompleteness__0__lemma__dest_0) ).
thf(3,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(4,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,negated_conjecture,
~ ( c_in @ v_p @ ( c_PropLog_Othms @ c_emptyset @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(6,negated_conjecture,
c_PropLog_Osat @ c_emptyset @ v_p @ t_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(7,plain,
$false = $false,
inference(unfold_def,[status(thm)],[4]) ).
thf(8,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_minus @ V_A @ V_A @ ( tc_set @ T_a ) )
= c_emptyset ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( ! [V_p: $i,T_a: $i,V_U: $i,V_t0: $i] :
( ~ ( c_PropLog_Osat @ c_emptyset @ V_p @ T_a )
| ( c_in @ V_p @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ V_p @ V_U @ T_a ) @ ( c_PropLog_Ohyps @ V_p @ V_t0 @ T_a ) @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
( ( ~ ( c_in @ v_p @ ( c_PropLog_Othms @ c_emptyset @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(11,plain,
( ( c_PropLog_Osat @ c_emptyset @ v_p @ t_a )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(12,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [V_p: $i,T_a: $i] :
( ~ ( c_PropLog_Osat @ c_emptyset @ V_p @ T_a )
| ! [V_U: $i,V_t0: $i] : ( c_in @ V_p @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ V_p @ V_U @ T_a ) @ ( c_PropLog_Ohyps @ V_p @ V_t0 @ T_a ) @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(14,plain,
( ( c_PropLog_Osat @ c_emptyset @ v_p @ t_a )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
( ( ~ ( c_in @ v_p @ ( c_PropLog_Othms @ c_emptyset @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ! [V_p: $i,T_a: $i] :
( ~ ( c_PropLog_Osat @ c_emptyset @ V_p @ T_a )
| ! [V_U: $i,V_t0: $i] : ( c_in @ V_p @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ V_p @ V_U @ T_a ) @ ( c_PropLog_Ohyps @ V_p @ V_t0 @ T_a ) @ ( tc_set @ ( tc_PropLog_Opl @ T_a ) ) ) @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(17,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_minus @ V_A @ V_A @ ( tc_set @ T_a ) )
= c_emptyset ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(18,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(19,plain,
( ( c_in @ v_p @ ( c_PropLog_Othms @ c_emptyset @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(20,plain,
! [SV1: $i] :
( ( ! [SY6: $i] :
( ~ ( c_PropLog_Osat @ c_emptyset @ SV1 @ SY6 )
| ! [SY7: $i,SY8: $i] : ( c_in @ SV1 @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ SV1 @ SY7 @ SY6 ) @ ( c_PropLog_Ohyps @ SV1 @ SY8 @ SY6 ) @ ( tc_set @ ( tc_PropLog_Opl @ SY6 ) ) ) @ SY6 ) @ ( tc_PropLog_Opl @ SY6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(21,plain,
! [SV2: $i] :
( ( ! [SY9: $i] :
( ( c_minus @ SV2 @ SV2 @ ( tc_set @ SY9 ) )
= c_emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(22,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ( c_PropLog_Osat @ c_emptyset @ SV1 @ SV3 )
| ! [SY10: $i,SY11: $i] : ( c_in @ SV1 @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ SV1 @ SY10 @ SV3 ) @ ( c_PropLog_Ohyps @ SV1 @ SY11 @ SV3 ) @ ( tc_set @ ( tc_PropLog_Opl @ SV3 ) ) ) @ SV3 ) @ ( tc_PropLog_Opl @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV4: $i,SV2: $i] :
( ( ( c_minus @ SV2 @ SV2 @ ( tc_set @ SV4 ) )
= c_emptyset )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( c_PropLog_Osat @ c_emptyset @ SV1 @ SV3 ) )
= $true )
| ( ( ! [SY10: $i,SY11: $i] : ( c_in @ SV1 @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ SV1 @ SY10 @ SV3 ) @ ( c_PropLog_Ohyps @ SV1 @ SY11 @ SV3 ) @ ( tc_set @ ( tc_PropLog_Opl @ SV3 ) ) ) @ SV3 ) @ ( tc_PropLog_Opl @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV3: $i,SV1: $i] :
( ( ( c_PropLog_Osat @ c_emptyset @ SV1 @ SV3 )
= $false )
| ( ( ! [SY10: $i,SY11: $i] : ( c_in @ SV1 @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ SV1 @ SY10 @ SV3 ) @ ( c_PropLog_Ohyps @ SV1 @ SY11 @ SV3 ) @ ( tc_set @ ( tc_PropLog_Opl @ SV3 ) ) ) @ SV3 ) @ ( tc_PropLog_Opl @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(27,plain,
! [SV3: $i,SV5: $i,SV1: $i] :
( ( ( ! [SY12: $i] : ( c_in @ SV1 @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ SV1 @ SV5 @ SV3 ) @ ( c_PropLog_Ohyps @ SV1 @ SY12 @ SV3 ) @ ( tc_set @ ( tc_PropLog_Opl @ SV3 ) ) ) @ SV3 ) @ ( tc_PropLog_Opl @ SV3 ) ) )
= $true )
| ( ( c_PropLog_Osat @ c_emptyset @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(28,plain,
! [SV6: $i,SV3: $i,SV5: $i,SV1: $i] :
( ( ( c_in @ SV1 @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ SV1 @ SV5 @ SV3 ) @ ( c_PropLog_Ohyps @ SV1 @ SV6 @ SV3 ) @ ( tc_set @ ( tc_PropLog_Opl @ SV3 ) ) ) @ SV3 ) @ ( tc_PropLog_Opl @ SV3 ) )
= $true )
| ( ( c_PropLog_Osat @ c_emptyset @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(29,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,28,24,22,19]) ).
thf(30,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL431-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n029.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 : Sun Jul 3 13:43:11 EDT 2022
% 0.13/0.33 % 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).
% 0.13/0.38
% 0.13/0.38 ********************************
% 0.13/0.38 * All subproblems solved! *
% 0.13/0.38 ********************************
% 0.13/0.38 % SZS status Unsatisfiable 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:29,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: 30 ****
% 0.13/0.38 %**** clause counter: 29 ****
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable 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:29,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------