TSTP Solution File: SEV097^5 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEV097^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n021.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 17:35:05 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 66 ( 40 unt; 9 typ; 0 def)
% Number of atoms : 333 ( 80 equ; 0 cnn)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 543 ( 73 ~; 70 |; 28 &; 354 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 166 ( 0 ^ 157 !; 9 ?; 166 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_b,type,
b: $tType ).
thf(tp_cR,type,
cR: a > a > $o ).
thf(tp_cS,type,
cS: b > b > $o ).
thf(tp_f,type,
f: a > b > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: a ).
thf(tp_sK2_Xw,type,
sK2_Xw: b > a ).
thf(tp_sK3_Xy,type,
sK3_Xy: a > b ).
thf(tp_z,type,
z: a ).
thf(1,conjecture,
( ( ! [Xu: a,Xv: a,Xw: a] :
( ( ( cR @ Xu @ Xv )
& ( cR @ Xw @ Xv ) )
=> ( cR @ Xu @ Xw ) )
& ! [Xx: a] : ( cR @ Xx @ Xx ) )
=> ( ( ! [Xx: a] :
? [Xy: b] : ( f @ Xx @ Xy )
& ! [Xx: a,Xy1: b,Xy2: b] :
( ( ( f @ Xx @ Xy1 )
& ( f @ Xx @ Xy2 ) )
=> ( cS @ Xy1 @ Xy2 ) )
& ! [Xx1: a,Xx2: a,Xy: b] :
( ( ( f @ Xx1 @ Xy )
& ( f @ Xx2 @ Xy ) )
=> ( cR @ Xx1 @ Xx2 ) ) )
=> ! [Xx: a] :
? [Xy: b] :
! [Xw: a] :
( ( f @ Xx @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx @ z ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM552C_pme) ).
thf(2,negated_conjecture,
( ( ( ! [Xu: a,Xv: a,Xw: a] :
( ( ( cR @ Xu @ Xv )
& ( cR @ Xw @ Xv ) )
=> ( cR @ Xu @ Xw ) )
& ! [Xx: a] : ( cR @ Xx @ Xx ) )
=> ( ( ! [Xx: a] :
? [Xy: b] : ( f @ Xx @ Xy )
& ! [Xx: a,Xy1: b,Xy2: b] :
( ( ( f @ Xx @ Xy1 )
& ( f @ Xx @ Xy2 ) )
=> ( cS @ Xy1 @ Xy2 ) )
& ! [Xx1: a,Xx2: a,Xy: b] :
( ( ( f @ Xx1 @ Xy )
& ( f @ Xx2 @ Xy ) )
=> ( cR @ Xx1 @ Xx2 ) ) )
=> ! [Xx: a] :
? [Xy: b] :
! [Xw: a] :
( ( f @ Xx @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx @ z ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [Xu: a,Xv: a,Xw: a] :
( ( ( cR @ Xu @ Xv )
& ( cR @ Xw @ Xv ) )
=> ( cR @ Xu @ Xw ) )
& ! [Xx: a] : ( cR @ Xx @ Xx ) )
=> ( ( ! [Xx: a] :
? [Xy: b] : ( f @ Xx @ Xy )
& ! [Xx: a,Xy1: b,Xy2: b] :
( ( ( f @ Xx @ Xy1 )
& ( f @ Xx @ Xy2 ) )
=> ( cS @ Xy1 @ Xy2 ) )
& ! [Xx1: a,Xx2: a,Xy: b] :
( ( ( f @ Xx1 @ Xy )
& ( f @ Xx2 @ Xy ) )
=> ( cR @ Xx1 @ Xx2 ) ) )
=> ! [Xx: a] :
? [Xy: b] :
! [Xw: a] :
( ( f @ Xx @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx @ z ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xu: a,Xv: a,Xw: a] :
( ( ( cR @ Xu @ Xv )
& ( cR @ Xw @ Xv ) )
=> ( cR @ Xu @ Xw ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: a] : ( cR @ Xx @ Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: a] :
? [Xy: b] : ( f @ Xx @ Xy ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [Xx: a,Xy1: b,Xy2: b] :
( ( ( f @ Xx @ Xy1 )
& ( f @ Xx @ Xy2 ) )
=> ( cS @ Xy1 @ Xy2 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [Xx1: a,Xx2: a,Xy: b] :
( ( ( f @ Xx1 @ Xy )
& ( f @ Xx2 @ Xy ) )
=> ( cR @ Xx1 @ Xx2 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ! [Xx: a] :
? [Xy: b] :
! [Xw: a] :
( ( f @ Xx @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx @ z ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ~ ! [Xx: a] :
? [Xy: b] :
! [Xw: a] :
( ( f @ Xx @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx @ z ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( ( ! [Xy: b] : ( f @ ( sK2_Xw @ Xy ) @ Xy )
| ~ ( cR @ sK1_Xx @ z ) )
& ! [SY17: b] :
~ ( f @ sK1_Xx @ SY17 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(12,plain,
( ( ! [Xu: a,Xv: a,Xw: a] :
( ~ ( cR @ Xu @ Xv )
| ~ ( cR @ Xw @ Xv )
| ( cR @ Xu @ Xw ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(13,plain,
( ( ! [Xx: a] : ( f @ Xx @ ( sK3_Xy @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(14,plain,
( ( ! [Xx: a,Xy1: b,Xy2: b] :
( ~ ( f @ Xx @ Xy1 )
| ~ ( f @ Xx @ Xy2 )
| ( cS @ Xy1 @ Xy2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(15,plain,
( ( ! [Xx1: a,Xx2: a] :
( ! [Xy: b] :
( ~ ( f @ Xx1 @ Xy )
| ~ ( f @ Xx2 @ Xy ) )
| ( cR @ Xx1 @ Xx2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(16,plain,
( ( ! [Xx1: a,Xx2: a] :
( ! [Xy: b] :
( ~ ( f @ Xx1 @ Xy )
| ~ ( f @ Xx2 @ Xy ) )
| ( cR @ Xx1 @ Xx2 ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [Xx: a,Xy1: b,Xy2: b] :
( ~ ( f @ Xx @ Xy1 )
| ~ ( f @ Xx @ Xy2 )
| ( cS @ Xy1 @ Xy2 ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(18,plain,
( ( ! [Xx: a] : ( f @ Xx @ ( sK3_Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(19,plain,
( ( ! [Xx: a] : ( cR @ Xx @ Xx ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(20,plain,
( ( ! [Xu: a,Xv: a,Xw: a] :
( ~ ( cR @ Xu @ Xv )
| ~ ( cR @ Xw @ Xv )
| ( cR @ Xu @ Xw ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(21,plain,
( ( ( ! [Xy: b] : ( f @ ( sK2_Xw @ Xy ) @ Xy )
| ~ ( cR @ sK1_Xx @ z ) )
& ! [SY17: b] :
~ ( f @ sK1_Xx @ SY17 ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(22,plain,
( ( ~ ( ~ ( ! [SX0: b] : ( f @ ( sK2_Xw @ SX0 ) @ SX0 )
| ~ ( cR @ sK1_Xx @ z ) )
| ~ ! [SX0: b] :
~ ( f @ sK1_Xx @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(23,plain,
! [SV1: a] :
( ( ! [SY18: a] :
( ! [SY19: b] :
( ~ ( f @ SV1 @ SY19 )
| ~ ( f @ SY18 @ SY19 ) )
| ( cR @ SV1 @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(24,plain,
! [SV2: a] :
( ( ! [SY20: b,SY21: b] :
( ~ ( f @ SV2 @ SY20 )
| ~ ( f @ SV2 @ SY21 )
| ( cS @ SY20 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(25,plain,
! [SV3: a] :
( ( f @ SV3 @ ( sK3_Xy @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(26,plain,
! [SV4: a] :
( ( cR @ SV4 @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(27,plain,
! [SV5: a] :
( ( ! [SY22: a,SY23: a] :
( ~ ( cR @ SV5 @ SY22 )
| ~ ( cR @ SY23 @ SY22 )
| ( cR @ SV5 @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(28,plain,
( ( ~ ( ! [SX0: b] : ( f @ ( sK2_Xw @ SX0 ) @ SX0 )
| ~ ( cR @ sK1_Xx @ z ) )
| ~ ! [SX0: b] :
~ ( f @ sK1_Xx @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(29,plain,
! [SV6: a,SV1: a] :
( ( ! [SY24: b] :
( ~ ( f @ SV1 @ SY24 )
| ~ ( f @ SV6 @ SY24 ) )
| ( cR @ SV1 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(30,plain,
! [SV7: b,SV2: a] :
( ( ! [SY25: b] :
( ~ ( f @ SV2 @ SV7 )
| ~ ( f @ SV2 @ SY25 )
| ( cS @ SV7 @ SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(31,plain,
! [SV8: a,SV5: a] :
( ( ! [SY26: a] :
( ~ ( cR @ SV5 @ SV8 )
| ~ ( cR @ SY26 @ SV8 )
| ( cR @ SV5 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(32,plain,
( ( ~ ( ! [SX0: b] : ( f @ ( sK2_Xw @ SX0 ) @ SX0 )
| ~ ( cR @ sK1_Xx @ z ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(33,plain,
( ( ~ ! [SX0: b] :
~ ( f @ sK1_Xx @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(34,plain,
! [SV6: a,SV1: a] :
( ( ( ! [SY24: b] :
( ~ ( f @ SV1 @ SY24 )
| ~ ( f @ SV6 @ SY24 ) ) )
= $true )
| ( ( cR @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(35,plain,
! [SV9: b,SV7: b,SV2: a] :
( ( ~ ( f @ SV2 @ SV7 )
| ~ ( f @ SV2 @ SV9 )
| ( cS @ SV7 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(36,plain,
! [SV10: a,SV8: a,SV5: a] :
( ( ~ ( cR @ SV5 @ SV8 )
| ~ ( cR @ SV10 @ SV8 )
| ( cR @ SV5 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(37,plain,
( ( ! [SX0: b] : ( f @ ( sK2_Xw @ SX0 ) @ SX0 )
| ~ ( cR @ sK1_Xx @ z ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(38,plain,
( ( ! [SX0: b] :
~ ( f @ sK1_Xx @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(39,plain,
! [SV6: a,SV11: b,SV1: a] :
( ( ( ~ ( f @ SV1 @ SV11 )
| ~ ( f @ SV6 @ SV11 ) )
= $true )
| ( ( cR @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(40,plain,
! [SV9: b,SV7: b,SV2: a] :
( ( ( ~ ( f @ SV2 @ SV7 )
| ~ ( f @ SV2 @ SV9 ) )
= $true )
| ( ( cS @ SV7 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(41,plain,
! [SV10: a,SV8: a,SV5: a] :
( ( ( ~ ( cR @ SV5 @ SV8 )
| ~ ( cR @ SV10 @ SV8 ) )
= $true )
| ( ( cR @ SV5 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(42,plain,
( ( ( ! [SX0: b] : ( f @ ( sK2_Xw @ SX0 ) @ SX0 ) )
= $true )
| ( ( ~ ( cR @ sK1_Xx @ z ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV12: b] :
( ( ~ ( f @ sK1_Xx @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV6: a,SV11: b,SV1: a] :
( ( ( ~ ( f @ SV1 @ SV11 ) )
= $true )
| ( ( ~ ( f @ SV6 @ SV11 ) )
= $true )
| ( ( cR @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(45,plain,
! [SV9: b,SV7: b,SV2: a] :
( ( ( ~ ( f @ SV2 @ SV7 ) )
= $true )
| ( ( ~ ( f @ SV2 @ SV9 ) )
= $true )
| ( ( cS @ SV7 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(46,plain,
! [SV10: a,SV8: a,SV5: a] :
( ( ( ~ ( cR @ SV5 @ SV8 ) )
= $true )
| ( ( ~ ( cR @ SV10 @ SV8 ) )
= $true )
| ( ( cR @ SV5 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV13: b] :
( ( ( f @ ( sK2_Xw @ SV13 ) @ SV13 )
= $true )
| ( ( ~ ( cR @ sK1_Xx @ z ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV12: b] :
( ( f @ sK1_Xx @ SV12 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(49,plain,
! [SV6: a,SV11: b,SV1: a] :
( ( ( f @ SV1 @ SV11 )
= $false )
| ( ( ~ ( f @ SV6 @ SV11 ) )
= $true )
| ( ( cR @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(50,plain,
! [SV9: b,SV7: b,SV2: a] :
( ( ( f @ SV2 @ SV7 )
= $false )
| ( ( ~ ( f @ SV2 @ SV9 ) )
= $true )
| ( ( cS @ SV7 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV10: a,SV8: a,SV5: a] :
( ( ( cR @ SV5 @ SV8 )
= $false )
| ( ( ~ ( cR @ SV10 @ SV8 ) )
= $true )
| ( ( cR @ SV5 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV13: b] :
( ( ( cR @ sK1_Xx @ z )
= $false )
| ( ( f @ ( sK2_Xw @ SV13 ) @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV1: a,SV11: b,SV6: a] :
( ( ( f @ SV6 @ SV11 )
= $false )
| ( ( f @ SV1 @ SV11 )
= $false )
| ( ( cR @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV7: b,SV9: b,SV2: a] :
( ( ( f @ SV2 @ SV9 )
= $false )
| ( ( f @ SV2 @ SV7 )
= $false )
| ( ( cS @ SV7 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV5: a,SV8: a,SV10: a] :
( ( ( cR @ SV10 @ SV8 )
= $false )
| ( ( cR @ SV5 @ SV8 )
= $false )
| ( ( cR @ SV5 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(56,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,55,54,53,52,48,26]) ).
thf(57,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEV097^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 27 22:01:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 0
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.12/0.38
% 0.12/0.38 ********************************
% 0.12/0.38 * All subproblems solved! *
% 0.12/0.38 ********************************
% 0.12/0.39 % SZS status Theorem 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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:56,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.39
% 0.12/0.39 %**** Beginning of derivation protocol ****
% 0.12/0.39 % SZS output start CNFRefutation
% See solution above
% 0.12/0.39
% 0.12/0.39 %**** End of derivation protocol ****
% 0.12/0.39 %**** no. of clauses in derivation: 57 ****
% 0.12/0.39 %**** clause counter: 56 ****
% 0.12/0.39
% 0.12/0.39 % SZS status Theorem 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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:56,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------