TSTP Solution File: SET846-2 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET846-2 : 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 : n010.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 : Tue Jul 19 03:05:35 EDT 2022
% Result : Unsatisfiable 0.20s 0.40s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 49 ( 32 unt; 8 typ; 0 def)
% Number of atoms : 145 ( 40 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 502 ( 26 ~; 24 |; 0 &; 452 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 82 ( 0 ^ 82 !; 0 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Union,type,
c_Union: $i > $i > $i ).
thf(tp_c_Zorn_OTFin,type,
c_Zorn_OTFin: $i > $i > $i ).
thf(tp_c_Zorn_Osucc,type,
c_Zorn_Osucc: $i > $i > $i > $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_set,type,
tc_set: $i > $i ).
thf(tp_v_S,type,
v_S: $i ).
thf(1,axiom,
! [V_Y: $i,V_S: $i,T_a: $i] :
( ~ ( c_lessequals @ V_Y @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ ( tc_set @ T_a ) ) ) )
| ( c_in @ ( c_Union @ V_Y @ ( tc_set @ T_a ) ) @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).
thf(2,axiom,
! [V_x: $i,V_S: $i,T_a: $i] :
( ~ ( c_in @ V_x @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_in @ ( c_Zorn_Osucc @ V_S @ V_x @ T_a ) @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin_OsuccI_0) ).
thf(3,axiom,
! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_set @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(4,axiom,
! [V_B: $i,V_A: $i,T_a: $i] :
( ~ ( c_in @ V_B @ V_A @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_B @ ( c_Union @ V_A @ T_a ) @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__upper_0) ).
thf(5,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(6,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,negated_conjecture,
~ ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ t_a ) @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(8,plain,
$false = $false,
inference(unfold_def,[status(thm)],[6]) ).
thf(9,plain,
( ( ! [V_Y: $i,V_S: $i,T_a: $i] :
( ~ ( c_lessequals @ V_Y @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ ( tc_set @ T_a ) ) ) )
| ( c_in @ ( c_Union @ V_Y @ ( tc_set @ T_a ) ) @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i] :
( ~ ( c_in @ V_x @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_in @ ( c_Zorn_Osucc @ V_S @ V_x @ T_a ) @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_set @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] :
( ~ ( c_in @ V_B @ V_A @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_B @ ( c_Union @ V_A @ T_a ) @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ~ ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ t_a ) @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(15,plain,
( ( ~ ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ t_a ) @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(16,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] :
( ~ ( c_in @ V_B @ V_A @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_B @ ( c_Union @ V_A @ T_a ) @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_set @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(18,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i] :
( ~ ( c_in @ V_x @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_in @ ( c_Zorn_Osucc @ V_S @ V_x @ T_a ) @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [V_Y: $i,V_S: $i,T_a: $i] :
( ~ ( c_lessequals @ V_Y @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ ( tc_set @ T_a ) ) ) )
| ( c_in @ ( c_Union @ V_Y @ ( tc_set @ T_a ) ) @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(20,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(21,plain,
( ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ t_a ) @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(22,plain,
! [SV1: $i] :
( ( ! [SY11: $i,SY12: $i] :
( ~ ( c_in @ SV1 @ SY11 @ ( tc_set @ SY12 ) )
| ( c_lessequals @ SV1 @ ( c_Union @ SY11 @ SY12 ) @ ( tc_set @ SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(23,plain,
! [SV2: $i] :
( ( ! [SY13: $i] : ( c_lessequals @ SV2 @ SV2 @ ( tc_set @ SY13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(24,plain,
! [SV3: $i] :
( ( ! [SY14: $i,SY15: $i] :
( ~ ( c_in @ SV3 @ ( c_Zorn_OTFin @ SY14 @ SY15 ) @ ( tc_set @ ( tc_set @ SY15 ) ) )
| ( c_in @ ( c_Zorn_Osucc @ SY14 @ SV3 @ SY15 ) @ ( c_Zorn_OTFin @ SY14 @ SY15 ) @ ( tc_set @ ( tc_set @ SY15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(25,plain,
! [SV4: $i] :
( ( ! [SY16: $i,SY17: $i] :
( ~ ( c_lessequals @ SV4 @ ( c_Zorn_OTFin @ SY16 @ SY17 ) @ ( tc_set @ ( tc_set @ ( tc_set @ SY17 ) ) ) )
| ( c_in @ ( c_Union @ SV4 @ ( tc_set @ SY17 ) ) @ ( c_Zorn_OTFin @ SY16 @ SY17 ) @ ( tc_set @ ( tc_set @ SY17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(26,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(27,plain,
! [SV5: $i,SV1: $i] :
( ( ! [SY18: $i] :
( ~ ( c_in @ SV1 @ SV5 @ ( tc_set @ SY18 ) )
| ( c_lessequals @ SV1 @ ( c_Union @ SV5 @ SY18 ) @ ( tc_set @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV6: $i,SV2: $i] :
( ( c_lessequals @ SV2 @ SV2 @ ( tc_set @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV7: $i,SV3: $i] :
( ( ! [SY19: $i] :
( ~ ( c_in @ SV3 @ ( c_Zorn_OTFin @ SV7 @ SY19 ) @ ( tc_set @ ( tc_set @ SY19 ) ) )
| ( c_in @ ( c_Zorn_Osucc @ SV7 @ SV3 @ SY19 ) @ ( c_Zorn_OTFin @ SV7 @ SY19 ) @ ( tc_set @ ( tc_set @ SY19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV8: $i,SV4: $i] :
( ( ! [SY20: $i] :
( ~ ( c_lessequals @ SV4 @ ( c_Zorn_OTFin @ SV8 @ SY20 ) @ ( tc_set @ ( tc_set @ ( tc_set @ SY20 ) ) ) )
| ( c_in @ ( c_Union @ SV4 @ ( tc_set @ SY20 ) ) @ ( c_Zorn_OTFin @ SV8 @ SY20 ) @ ( tc_set @ ( tc_set @ SY20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(31,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ~ ( c_in @ SV1 @ SV5 @ ( tc_set @ SV9 ) )
| ( c_lessequals @ SV1 @ ( c_Union @ SV5 @ SV9 ) @ ( tc_set @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ~ ( c_in @ SV3 @ ( c_Zorn_OTFin @ SV7 @ SV10 ) @ ( tc_set @ ( tc_set @ SV10 ) ) )
| ( c_in @ ( c_Zorn_Osucc @ SV7 @ SV3 @ SV10 ) @ ( c_Zorn_OTFin @ SV7 @ SV10 ) @ ( tc_set @ ( tc_set @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV11: $i,SV8: $i,SV4: $i] :
( ( ~ ( c_lessequals @ SV4 @ ( c_Zorn_OTFin @ SV8 @ SV11 ) @ ( tc_set @ ( tc_set @ ( tc_set @ SV11 ) ) ) )
| ( c_in @ ( c_Union @ SV4 @ ( tc_set @ SV11 ) ) @ ( c_Zorn_OTFin @ SV8 @ SV11 ) @ ( tc_set @ ( tc_set @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( ~ ( c_in @ SV1 @ SV5 @ ( tc_set @ SV9 ) ) )
= $true )
| ( ( c_lessequals @ SV1 @ ( c_Union @ SV5 @ SV9 ) @ ( tc_set @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( ~ ( c_in @ SV3 @ ( c_Zorn_OTFin @ SV7 @ SV10 ) @ ( tc_set @ ( tc_set @ SV10 ) ) ) )
= $true )
| ( ( c_in @ ( c_Zorn_Osucc @ SV7 @ SV3 @ SV10 ) @ ( c_Zorn_OTFin @ SV7 @ SV10 ) @ ( tc_set @ ( tc_set @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV11: $i,SV8: $i,SV4: $i] :
( ( ( ~ ( c_lessequals @ SV4 @ ( c_Zorn_OTFin @ SV8 @ SV11 ) @ ( tc_set @ ( tc_set @ ( tc_set @ SV11 ) ) ) ) )
= $true )
| ( ( c_in @ ( c_Union @ SV4 @ ( tc_set @ SV11 ) ) @ ( c_Zorn_OTFin @ SV8 @ SV11 ) @ ( tc_set @ ( tc_set @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV9: $i,SV5: $i,SV1: $i] :
( ( ( c_in @ SV1 @ SV5 @ ( tc_set @ SV9 ) )
= $false )
| ( ( c_lessequals @ SV1 @ ( c_Union @ SV5 @ SV9 ) @ ( tc_set @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ( c_in @ SV3 @ ( c_Zorn_OTFin @ SV7 @ SV10 ) @ ( tc_set @ ( tc_set @ SV10 ) ) )
= $false )
| ( ( c_in @ ( c_Zorn_Osucc @ SV7 @ SV3 @ SV10 ) @ ( c_Zorn_OTFin @ SV7 @ SV10 ) @ ( tc_set @ ( tc_set @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV11: $i,SV8: $i,SV4: $i] :
( ( ( c_lessequals @ SV4 @ ( c_Zorn_OTFin @ SV8 @ SV11 ) @ ( tc_set @ ( tc_set @ ( tc_set @ SV11 ) ) ) )
= $false )
| ( ( c_in @ ( c_Union @ SV4 @ ( tc_set @ SV11 ) ) @ ( c_Zorn_OTFin @ SV8 @ SV11 ) @ ( tc_set @ ( tc_set @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(40,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,39,38,37,28,26]) ).
thf(41,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET846-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n010.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 : Mon Jul 11 04:05:15 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 5
% 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:5,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:7,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.20/0.40
% 0.20/0.40 ********************************
% 0.20/0.40 * All subproblems solved! *
% 0.20/0.40 ********************************
% 0.20/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:40,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.40
% 0.20/0.40 %**** Beginning of derivation protocol ****
% 0.20/0.40 % SZS output start CNFRefutation
% See solution above
% 0.20/0.40
% 0.20/0.40 %**** End of derivation protocol ****
% 0.20/0.40 %**** no. of clauses in derivation: 41 ****
% 0.20/0.40 %**** clause counter: 40 ****
% 0.20/0.40
% 0.20/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:40,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------