TSTP Solution File: COL102-2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : COL102-2 : 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 : 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 : Fri Jul 15 00:34:51 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 59 ( 35 unt; 11 typ; 0 def)
% Number of atoms : 195 ( 52 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 938 ( 40 ~; 43 |; 0 &; 855 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-4 aty)
% Number of variables : 116 ( 0 ^ 116 !; 0 ?; 116 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Comb_Ocomb_Oop_A_D_D,type,
c_Comb_Ocomb_Oop_A_D_D: $i > $i > $i ).
thf(tp_c_Comb_Ocontract,type,
c_Comb_Ocontract: $i ).
thf(tp_c_Pair,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tp_c_Transitive__Closure_Ortrancl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_tc_Comb_Ocomb,type,
tc_Comb_Ocomb: $i ).
thf(tp_tc_prod,type,
tc_prod: $i > $i > $i ).
thf(tp_v_x,type,
v_x: $i ).
thf(tp_v_y,type,
v_y: $i ).
thf(tp_v_z,type,
v_z: $i ).
thf(tp_v_za,type,
v_za: $i ).
thf(1,axiom,
! [V_b: $i,V_c: $i,T_a: $i,V_r: $i,V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__trans_0) ).
thf(2,axiom,
! [V_p: $i,V_r: $i,T_a: $i] :
( ~ ( c_in @ V_p @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_p @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
thf(3,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ V_x @ V_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ V_y @ V_z ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Ocontract_OAp1_0) ).
thf(4,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(5,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,negated_conjecture,
~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ v_x @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_za @ v_z ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ ( c_Transitive__Closure_Ortrancl @ c_Comb_Ocontract @ tc_Comb_Ocomb ) @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(7,negated_conjecture,
c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ v_x @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_y @ v_z ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ ( c_Transitive__Closure_Ortrancl @ c_Comb_Ocontract @ tc_Comb_Ocomb ) @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(8,negated_conjecture,
c_in @ ( c_Pair @ v_y @ v_za @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(9,plain,
$false = $false,
inference(unfold_def,[status(thm)],[5]) ).
thf(10,plain,
( ( ! [V_b: $i,V_c: $i,T_a: $i,V_r: $i,V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [V_p: $i,V_r: $i,T_a: $i] :
( ~ ( c_in @ V_p @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_p @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ V_x @ V_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ V_y @ V_z ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ v_x @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_za @ v_z ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ ( c_Transitive__Closure_Ortrancl @ c_Comb_Ocontract @ tc_Comb_Ocomb ) @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(14,plain,
( ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ v_x @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_y @ v_z ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ ( c_Transitive__Closure_Ortrancl @ c_Comb_Ocontract @ tc_Comb_Ocomb ) @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(15,plain,
( ( c_in @ ( c_Pair @ v_y @ v_za @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [V_b: $i,V_c: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(18,plain,
( ( ! [V_x: $i,V_y: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ! [V_z: $i] : ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ V_x @ V_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ V_y @ V_z ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(19,plain,
( ( c_in @ ( c_Pair @ v_y @ v_za @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(20,plain,
( ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ v_x @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_y @ v_z ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ ( c_Transitive__Closure_Ortrancl @ c_Comb_Ocontract @ tc_Comb_Ocomb ) @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(21,plain,
( ( ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ v_x @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_za @ v_z ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ ( c_Transitive__Closure_Ortrancl @ c_Comb_Ocontract @ tc_Comb_Ocomb ) @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(22,plain,
( ( ! [V_x: $i,V_y: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ! [V_z: $i] : ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ V_x @ V_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ V_y @ V_z ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(23,plain,
( ( ! [V_p: $i,V_r: $i,T_a: $i] :
( ~ ( c_in @ V_p @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_p @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(24,plain,
( ( ! [V_b: $i,V_c: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(25,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(26,plain,
( ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ v_x @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_za @ v_z ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ ( c_Transitive__Closure_Ortrancl @ c_Comb_Ocontract @ tc_Comb_Ocomb ) @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV1: $i] :
( ( ! [SY11: $i] :
( ~ ( c_in @ ( c_Pair @ SV1 @ SY11 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ! [SY12: $i] : ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ SV1 @ SY12 ) @ ( c_Comb_Ocomb_Oop_A_D_D @ SY11 @ SY12 ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV2: $i] :
( ( ! [SY13: $i,SY14: $i] :
( ~ ( c_in @ SV2 @ SY13 @ ( tc_prod @ SY14 @ SY14 ) )
| ( c_in @ SV2 @ ( c_Transitive__Closure_Ortrancl @ SY13 @ SY14 ) @ ( tc_prod @ SY14 @ SY14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV3: $i] :
( ( ! [SY15: $i,SY16: $i,SY17: $i] :
( ~ ( c_in @ ( c_Pair @ SV3 @ SY15 @ SY16 @ SY16 ) @ ( c_Transitive__Closure_Ortrancl @ SY17 @ SY16 ) @ ( tc_prod @ SY16 @ SY16 ) )
| ! [SY18: $i] :
( ~ ( c_in @ ( c_Pair @ SY18 @ SV3 @ SY16 @ SY16 ) @ ( c_Transitive__Closure_Ortrancl @ SY17 @ SY16 ) @ ( tc_prod @ SY16 @ SY16 ) )
| ( c_in @ ( c_Pair @ SY18 @ SY15 @ SY16 @ SY16 ) @ ( c_Transitive__Closure_Ortrancl @ SY17 @ SY16 ) @ ( tc_prod @ SY16 @ SY16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(30,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(31,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV1 @ SV4 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ! [SY19: $i] : ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ SV1 @ SY19 ) @ ( c_Comb_Ocomb_Oop_A_D_D @ SV4 @ SY19 ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV5: $i,SV2: $i] :
( ( ! [SY20: $i] :
( ~ ( c_in @ SV2 @ SV5 @ ( tc_prod @ SY20 @ SY20 ) )
| ( c_in @ SV2 @ ( c_Transitive__Closure_Ortrancl @ SV5 @ SY20 ) @ ( tc_prod @ SY20 @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV6: $i,SV3: $i] :
( ( ! [SY21: $i,SY22: $i] :
( ~ ( c_in @ ( c_Pair @ SV3 @ SV6 @ SY21 @ SY21 ) @ ( c_Transitive__Closure_Ortrancl @ SY22 @ SY21 ) @ ( tc_prod @ SY21 @ SY21 ) )
| ! [SY23: $i] :
( ~ ( c_in @ ( c_Pair @ SY23 @ SV3 @ SY21 @ SY21 ) @ ( c_Transitive__Closure_Ortrancl @ SY22 @ SY21 ) @ ( tc_prod @ SY21 @ SY21 ) )
| ( c_in @ ( c_Pair @ SY23 @ SV6 @ SY21 @ SY21 ) @ ( c_Transitive__Closure_Ortrancl @ SY22 @ SY21 ) @ ( tc_prod @ SY21 @ SY21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1 @ SV4 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
= $true )
| ( ( ! [SY19: $i] : ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ SV1 @ SY19 ) @ ( c_Comb_Ocomb_Oop_A_D_D @ SV4 @ SY19 ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ~ ( c_in @ SV2 @ SV5 @ ( tc_prod @ SV7 @ SV7 ) )
| ( c_in @ SV2 @ ( c_Transitive__Closure_Ortrancl @ SV5 @ SV7 ) @ ( tc_prod @ SV7 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ! [SY24: $i] :
( ~ ( c_in @ ( c_Pair @ SV3 @ SV6 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SY24 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
| ! [SY25: $i] :
( ~ ( c_in @ ( c_Pair @ SY25 @ SV3 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SY24 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
| ( c_in @ ( c_Pair @ SY25 @ SV6 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SY24 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV4: $i,SV1: $i] :
( ( ( c_in @ ( c_Pair @ SV1 @ SV4 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $false )
| ( ( ! [SY19: $i] : ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ SV1 @ SY19 ) @ ( c_Comb_Ocomb_Oop_A_D_D @ SV4 @ SY19 ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ( ~ ( c_in @ SV2 @ SV5 @ ( tc_prod @ SV7 @ SV7 ) ) )
= $true )
| ( ( c_in @ SV2 @ ( c_Transitive__Closure_Ortrancl @ SV5 @ SV7 ) @ ( tc_prod @ SV7 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV9: $i,SV8: $i,SV6: $i,SV3: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV3 @ SV6 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV9 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
| ! [SY26: $i] :
( ~ ( c_in @ ( c_Pair @ SY26 @ SV3 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV9 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
| ( c_in @ ( c_Pair @ SY26 @ SV6 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV9 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV4: $i,SV10: $i,SV1: $i] :
( ( ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ SV1 @ SV10 ) @ ( c_Comb_Ocomb_Oop_A_D_D @ SV4 @ SV10 ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1 @ SV4 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ( c_in @ SV2 @ SV5 @ ( tc_prod @ SV7 @ SV7 ) )
= $false )
| ( ( c_in @ SV2 @ ( c_Transitive__Closure_Ortrancl @ SV5 @ SV7 ) @ ( tc_prod @ SV7 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV9: $i,SV8: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV3 @ SV6 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV9 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) ) )
= $true )
| ( ( ! [SY26: $i] :
( ~ ( c_in @ ( c_Pair @ SY26 @ SV3 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV9 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
| ( c_in @ ( c_Pair @ SY26 @ SV6 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV9 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV9: $i,SV8: $i,SV6: $i,SV3: $i] :
( ( ( c_in @ ( c_Pair @ SV3 @ SV6 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV9 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
= $false )
| ( ( ! [SY26: $i] :
( ~ ( c_in @ ( c_Pair @ SY26 @ SV3 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV9 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
| ( c_in @ ( c_Pair @ SY26 @ SV6 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV9 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(44,plain,
! [SV6: $i,SV9: $i,SV8: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV11 @ SV3 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV9 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
| ( c_in @ ( c_Pair @ SV11 @ SV6 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV9 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV3 @ SV6 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV9 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(45,plain,
! [SV6: $i,SV9: $i,SV8: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV11 @ SV3 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV9 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV11 @ SV6 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV9 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV3 @ SV6 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV9 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(46,plain,
! [SV6: $i,SV9: $i,SV8: $i,SV3: $i,SV11: $i] :
( ( ( c_in @ ( c_Pair @ SV11 @ SV3 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV9 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV11 @ SV6 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV9 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV3 @ SV6 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV9 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(47,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,46,41,40,30,26,20]) ).
thf(48,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COL102-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue May 31 09:30:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 6
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.35 (rf:0,axioms:6,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:8,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.20/0.42
% 0.20/0.42 ********************************
% 0.20/0.42 * All subproblems solved! *
% 0.20/0.42 ********************************
% 0.20/0.42 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,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:47,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.42
% 0.20/0.42 %**** Beginning of derivation protocol ****
% 0.20/0.42 % SZS output start CNFRefutation
% See solution above
% 0.20/0.42
% 0.20/0.42 %**** End of derivation protocol ****
% 0.20/0.42 %**** no. of clauses in derivation: 48 ****
% 0.20/0.42 %**** clause counter: 47 ****
% 0.20/0.42
% 0.20/0.42 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,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:47,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------