TSTP Solution File: SYN065-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN065-1 : 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 : n017.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 : Thu Jul 21 08:23:13 EDT 2022
% Result : Unsatisfiable 0.20s 0.39s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 71 ( 41 unt; 6 typ; 0 def)
% Number of atoms : 321 ( 84 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 460 ( 74 ~; 88 |; 0 &; 298 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 145 ( 0 ^ 145 !; 0 ?; 145 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_big_f,type,
big_f: $i > $i > $o ).
thf(tp_big_g,type,
big_g: $i > $i > $o ).
thf(tp_big_h,type,
big_h: $i > $i > $o ).
thf(tp_f,type,
f: $i > $i ).
thf(tp_g,type,
g: $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( big_g @ X @ Y )
| ~ ( big_g @ Y @ Z )
| ( big_h @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
thf(2,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( big_g @ X @ Y )
| ~ ( big_f @ Y @ Z )
| ( big_h @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( big_f @ X @ Y )
| ~ ( big_g @ Y @ Z )
| ( big_h @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
thf(4,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( big_f @ X @ Y )
| ~ ( big_f @ Y @ Z )
| ( big_h @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
thf(5,axiom,
! [X: $i] : ( big_g @ X @ ( g @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
thf(6,axiom,
! [X: $i] : ( big_f @ X @ ( f @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
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,
! [X: $i] :
~ ( big_h @ a @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
thf(10,plain,
$false = $false,
inference(unfold_def,[status(thm)],[8]) ).
thf(11,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( big_g @ X @ Y )
| ~ ( big_g @ Y @ Z )
| ( big_h @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( big_g @ X @ Y )
| ~ ( big_f @ Y @ Z )
| ( big_h @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( big_f @ X @ Y )
| ~ ( big_g @ Y @ Z )
| ( big_h @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( big_f @ X @ Y )
| ~ ( big_f @ Y @ Z )
| ( big_h @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(15,plain,
( ( ! [X: $i] : ( big_g @ X @ ( g @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(16,plain,
( ( ! [X: $i] : ( big_f @ X @ ( f @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(17,plain,
( ( ! [X: $i] :
~ ( big_h @ a @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(18,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( big_g @ X @ Y )
| ! [Z: $i] :
( ~ ( big_g @ Y @ Z )
| ( big_h @ X @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(20,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( big_g @ X @ Y )
| ! [Z: $i] :
( ~ ( big_f @ Y @ Z )
| ( big_h @ X @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( big_f @ X @ Y )
| ! [Z: $i] :
( ~ ( big_g @ Y @ Z )
| ( big_h @ X @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(22,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( big_f @ X @ Y )
| ! [Z: $i] :
( ~ ( big_f @ Y @ Z )
| ( big_h @ X @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(23,plain,
( ( ! [X: $i] :
~ ( big_h @ a @ X ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(24,plain,
( ( ! [X: $i] : ( big_f @ X @ ( f @ X ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(25,plain,
( ( ! [X: $i] : ( big_g @ X @ ( g @ X ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(26,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( big_f @ X @ Y )
| ! [Z: $i] :
( ~ ( big_f @ Y @ Z )
| ( big_h @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( big_f @ X @ Y )
| ! [Z: $i] :
( ~ ( big_g @ Y @ Z )
| ( big_h @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( big_g @ X @ Y )
| ! [Z: $i] :
( ~ ( big_f @ Y @ Z )
| ( big_h @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( big_g @ X @ Y )
| ! [Z: $i] :
( ~ ( big_g @ Y @ Z )
| ( big_h @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(30,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(31,plain,
! [SV1: $i] :
( ( ~ ( big_h @ a @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(32,plain,
! [SV2: $i] :
( ( big_f @ SV2 @ ( f @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(33,plain,
! [SV3: $i] :
( ( big_g @ SV3 @ ( g @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(34,plain,
! [SV4: $i] :
( ( ! [SY15: $i] :
( ~ ( big_f @ SV4 @ SY15 )
| ! [SY16: $i] :
( ~ ( big_f @ SY15 @ SY16 )
| ( big_h @ SV4 @ SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(35,plain,
! [SV5: $i] :
( ( ! [SY17: $i] :
( ~ ( big_f @ SV5 @ SY17 )
| ! [SY18: $i] :
( ~ ( big_g @ SY17 @ SY18 )
| ( big_h @ SV5 @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(36,plain,
! [SV6: $i] :
( ( ! [SY19: $i] :
( ~ ( big_g @ SV6 @ SY19 )
| ! [SY20: $i] :
( ~ ( big_f @ SY19 @ SY20 )
| ( big_h @ SV6 @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(37,plain,
! [SV7: $i] :
( ( ! [SY21: $i] :
( ~ ( big_g @ SV7 @ SY21 )
| ! [SY22: $i] :
( ~ ( big_g @ SY21 @ SY22 )
| ( big_h @ SV7 @ SY22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(38,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(39,plain,
! [SV1: $i] :
( ( big_h @ a @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(40,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ( big_f @ SV4 @ SV8 )
| ! [SY23: $i] :
( ~ ( big_f @ SV8 @ SY23 )
| ( big_h @ SV4 @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV9: $i,SV5: $i] :
( ( ~ ( big_f @ SV5 @ SV9 )
| ! [SY24: $i] :
( ~ ( big_g @ SV9 @ SY24 )
| ( big_h @ SV5 @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(42,plain,
! [SV10: $i,SV6: $i] :
( ( ~ ( big_g @ SV6 @ SV10 )
| ! [SY25: $i] :
( ~ ( big_f @ SV10 @ SY25 )
| ( big_h @ SV6 @ SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(43,plain,
! [SV11: $i,SV7: $i] :
( ( ~ ( big_g @ SV7 @ SV11 )
| ! [SY26: $i] :
( ~ ( big_g @ SV11 @ SY26 )
| ( big_h @ SV7 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( big_f @ SV4 @ SV8 ) )
= $true )
| ( ( ! [SY23: $i] :
( ~ ( big_f @ SV8 @ SY23 )
| ( big_h @ SV4 @ SY23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV9: $i,SV5: $i] :
( ( ( ~ ( big_f @ SV5 @ SV9 ) )
= $true )
| ( ( ! [SY24: $i] :
( ~ ( big_g @ SV9 @ SY24 )
| ( big_h @ SV5 @ SY24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV10: $i,SV6: $i] :
( ( ( ~ ( big_g @ SV6 @ SV10 ) )
= $true )
| ( ( ! [SY25: $i] :
( ~ ( big_f @ SV10 @ SY25 )
| ( big_h @ SV6 @ SY25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV11: $i,SV7: $i] :
( ( ( ~ ( big_g @ SV7 @ SV11 ) )
= $true )
| ( ( ! [SY26: $i] :
( ~ ( big_g @ SV11 @ SY26 )
| ( big_h @ SV7 @ SY26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV8: $i,SV4: $i] :
( ( ( big_f @ SV4 @ SV8 )
= $false )
| ( ( ! [SY23: $i] :
( ~ ( big_f @ SV8 @ SY23 )
| ( big_h @ SV4 @ SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV9: $i,SV5: $i] :
( ( ( big_f @ SV5 @ SV9 )
= $false )
| ( ( ! [SY24: $i] :
( ~ ( big_g @ SV9 @ SY24 )
| ( big_h @ SV5 @ SY24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV10: $i,SV6: $i] :
( ( ( big_g @ SV6 @ SV10 )
= $false )
| ( ( ! [SY25: $i] :
( ~ ( big_f @ SV10 @ SY25 )
| ( big_h @ SV6 @ SY25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV11: $i,SV7: $i] :
( ( ( big_g @ SV7 @ SV11 )
= $false )
| ( ( ! [SY26: $i] :
( ~ ( big_g @ SV11 @ SY26 )
| ( big_h @ SV7 @ SY26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV4: $i,SV12: $i,SV8: $i] :
( ( ( ~ ( big_f @ SV8 @ SV12 )
| ( big_h @ SV4 @ SV12 ) )
= $true )
| ( ( big_f @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV5: $i,SV13: $i,SV9: $i] :
( ( ( ~ ( big_g @ SV9 @ SV13 )
| ( big_h @ SV5 @ SV13 ) )
= $true )
| ( ( big_f @ SV5 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV6: $i,SV14: $i,SV10: $i] :
( ( ( ~ ( big_f @ SV10 @ SV14 )
| ( big_h @ SV6 @ SV14 ) )
= $true )
| ( ( big_g @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV7: $i,SV15: $i,SV11: $i] :
( ( ( ~ ( big_g @ SV11 @ SV15 )
| ( big_h @ SV7 @ SV15 ) )
= $true )
| ( ( big_g @ SV7 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV4: $i,SV12: $i,SV8: $i] :
( ( ( ~ ( big_f @ SV8 @ SV12 ) )
= $true )
| ( ( big_h @ SV4 @ SV12 )
= $true )
| ( ( big_f @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV5: $i,SV13: $i,SV9: $i] :
( ( ( ~ ( big_g @ SV9 @ SV13 ) )
= $true )
| ( ( big_h @ SV5 @ SV13 )
= $true )
| ( ( big_f @ SV5 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV6: $i,SV14: $i,SV10: $i] :
( ( ( ~ ( big_f @ SV10 @ SV14 ) )
= $true )
| ( ( big_h @ SV6 @ SV14 )
= $true )
| ( ( big_g @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(59,plain,
! [SV7: $i,SV15: $i,SV11: $i] :
( ( ( ~ ( big_g @ SV11 @ SV15 ) )
= $true )
| ( ( big_h @ SV7 @ SV15 )
= $true )
| ( ( big_g @ SV7 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(60,plain,
! [SV4: $i,SV12: $i,SV8: $i] :
( ( ( big_f @ SV8 @ SV12 )
= $false )
| ( ( big_h @ SV4 @ SV12 )
= $true )
| ( ( big_f @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV5: $i,SV13: $i,SV9: $i] :
( ( ( big_g @ SV9 @ SV13 )
= $false )
| ( ( big_h @ SV5 @ SV13 )
= $true )
| ( ( big_f @ SV5 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV6: $i,SV14: $i,SV10: $i] :
( ( ( big_f @ SV10 @ SV14 )
= $false )
| ( ( big_h @ SV6 @ SV14 )
= $true )
| ( ( big_g @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV7: $i,SV15: $i,SV11: $i] :
( ( ( big_g @ SV11 @ SV15 )
= $false )
| ( ( big_h @ SV7 @ SV15 )
= $true )
| ( ( big_g @ SV7 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(64,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[32,63,62,61,60,39,38,33]) ).
thf(65,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN065-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 11 21:53:49 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35
% 0.14/0.35 No.of.Axioms: 7
% 0.14/0.35
% 0.14/0.35 Length.of.Defs: 0
% 0.14/0.35
% 0.14/0.35 Contains.Choice.Funs: false
% 0.14/0.35 (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)...
% 0.20/0.39
% 0.20/0.39 ********************************
% 0.20/0.39 * All subproblems solved! *
% 0.20/0.39 ********************************
% 0.20/0.39 % 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:64,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.39
% 0.20/0.39 %**** Beginning of derivation protocol ****
% 0.20/0.39 % SZS output start CNFRefutation
% See solution above
% 0.20/0.39
% 0.20/0.39 %**** End of derivation protocol ****
% 0.20/0.39 %**** no. of clauses in derivation: 65 ****
% 0.20/0.39 %**** clause counter: 64 ****
% 0.20/0.39
% 0.20/0.39 % 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:64,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------