TSTP Solution File: COL121-2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : COL121-2 : 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 00:34:55 EDT 2022
% Result : Unsatisfiable 0.47s 0.65s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 24
% Syntax : Number of formulae : 100 ( 50 unt; 13 typ; 0 def)
% Number of atoms : 472 ( 121 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 2361 ( 117 ~; 143 |; 0 &;2101 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 258 ( 0 ^ 258 !; 0 ?; 258 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Comb_Odiamond,type,
c_Comb_Odiamond: $i > $i > $o ).
thf(tp_c_Comb_Odiamond__strip__lemmaE__1,type,
c_Comb_Odiamond__strip__lemmaE__1: $i > $i > $i > $i > $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_t_a,type,
t_a: $i ).
thf(tp_tc_prod,type,
tc_prod: $i > $i > $i ).
thf(tp_v_r,type,
v_r: $i ).
thf(tp_v_x,type,
v_x: $i > $i ).
thf(tp_v_xaa,type,
v_xaa: $i ).
thf(tp_v_y,type,
v_y: $i ).
thf(tp_v_ya,type,
v_ya: $i ).
thf(tp_v_z,type,
v_z: $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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
thf(3,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_y_H: $i,V_y: $i] :
( ~ ( c_Comb_Odiamond @ V_r @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y_H @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_y @ ( c_Comb_Odiamond__strip__lemmaE__1 @ V_r @ V_y @ V_y_H @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Odiamond__strip__lemmaE_1) ).
thf(4,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_y_H: $i,V_y: $i] :
( ~ ( c_Comb_Odiamond @ V_r @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y_H @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_y_H @ ( c_Comb_Odiamond__strip__lemmaE__1 @ V_r @ V_y @ V_y_H @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Odiamond__strip__lemmaE_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,
! [V_U: $i] :
( ~ ( c_in @ ( c_Pair @ v_xaa @ V_U @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_z @ V_U @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(8,negated_conjecture,
! [V_U: $i] :
( ( c_in @ ( c_Pair @ V_U @ ( v_x @ V_U ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_y @ V_U @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(9,negated_conjecture,
! [V_U: $i] :
( ( c_in @ ( c_Pair @ v_ya @ ( v_x @ V_U ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_y @ V_U @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(10,negated_conjecture,
c_in @ ( c_Pair @ v_y @ v_xaa @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(11,negated_conjecture,
c_in @ ( c_Pair @ v_ya @ v_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(12,negated_conjecture,
c_Comb_Odiamond @ v_r @ t_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(13,plain,
$false = $false,
inference(unfold_def,[status(thm)],[6]) ).
thf(14,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(15,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(16,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y_H: $i,V_y: $i] :
( ~ ( c_Comb_Odiamond @ V_r @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y_H @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_y @ ( c_Comb_Odiamond__strip__lemmaE__1 @ V_r @ V_y @ V_y_H @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y_H: $i,V_y: $i] :
( ~ ( c_Comb_Odiamond @ V_r @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y_H @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_y_H @ ( c_Comb_Odiamond__strip__lemmaE__1 @ V_r @ V_y @ V_y_H @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(18,plain,
( ( ! [V_U: $i] :
( ~ ( c_in @ ( c_Pair @ v_xaa @ V_U @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_z @ V_U @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(19,plain,
( ( ! [V_U: $i] :
( ( c_in @ ( c_Pair @ V_U @ ( v_x @ V_U ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_y @ V_U @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(20,plain,
( ( ! [V_U: $i] :
( ( c_in @ ( c_Pair @ v_ya @ ( v_x @ V_U ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_y @ V_U @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(21,plain,
( ( c_in @ ( c_Pair @ v_y @ v_xaa @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(22,plain,
( ( c_in @ ( c_Pair @ v_ya @ v_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(23,plain,
( ( c_Comb_Odiamond @ v_r @ t_a )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(24,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(25,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)],[14]) ).
thf(26,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] :
( ~ ( c_Comb_Odiamond @ V_r @ T_a )
| ! [V_y_H: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y_H @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_y: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_y @ ( c_Comb_Odiamond__strip__lemmaE__1 @ V_r @ V_y @ V_y_H @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(27,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] :
( ~ ( c_Comb_Odiamond @ V_r @ T_a )
| ! [V_y_H: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y_H @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_y: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_y_H @ ( c_Comb_Odiamond__strip__lemmaE__1 @ V_r @ V_y @ V_y_H @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(28,plain,
( ( c_Comb_Odiamond @ v_r @ t_a )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(29,plain,
( ( c_in @ ( c_Pair @ v_ya @ v_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(30,plain,
( ( c_in @ ( c_Pair @ v_y @ v_xaa @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(31,plain,
( ( ! [V_U: $i] :
( ( c_in @ ( c_Pair @ v_ya @ ( v_x @ V_U ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_y @ V_U @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(32,plain,
( ( ! [V_U: $i] :
( ( c_in @ ( c_Pair @ V_U @ ( v_x @ V_U ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_y @ V_U @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(33,plain,
( ( ! [V_U: $i] :
( ~ ( c_in @ ( c_Pair @ v_xaa @ V_U @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_z @ V_U @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(34,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] :
( ~ ( c_Comb_Odiamond @ V_r @ T_a )
| ! [V_y_H: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y_H @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_y: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_y_H @ ( c_Comb_Odiamond__strip__lemmaE__1 @ V_r @ V_y @ V_y_H @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(35,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] :
( ~ ( c_Comb_Odiamond @ V_r @ T_a )
| ! [V_y_H: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y_H @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_y: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_y @ ( c_Comb_Odiamond__strip__lemmaE__1 @ V_r @ V_y @ V_y_H @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(36,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)],[15]) ).
thf(37,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)],[25]) ).
thf(38,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(39,plain,
! [SV1: $i] :
( ( ( c_in @ ( c_Pair @ v_ya @ ( v_x @ SV1 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_y @ SV1 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(40,plain,
! [SV2: $i] :
( ( ( c_in @ ( c_Pair @ SV2 @ ( v_x @ SV2 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_y @ SV2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(41,plain,
! [SV3: $i] :
( ( ~ ( c_in @ ( c_Pair @ v_xaa @ SV3 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_z @ SV3 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(42,plain,
! [SV4: $i] :
( ( ! [SY21: $i,SY22: $i] :
( ~ ( c_Comb_Odiamond @ SV4 @ SY21 )
| ! [SY23: $i] :
( ~ ( c_in @ ( c_Pair @ SY22 @ SY23 @ SY21 @ SY21 ) @ SV4 @ ( tc_prod @ SY21 @ SY21 ) )
| ! [SY24: $i] :
( ~ ( c_in @ ( c_Pair @ SY22 @ SY24 @ SY21 @ SY21 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SY21 ) @ ( tc_prod @ SY21 @ SY21 ) )
| ( c_in @ ( c_Pair @ SY23 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV4 @ SY24 @ SY23 @ SY21 ) @ SY21 @ SY21 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SY21 ) @ ( tc_prod @ SY21 @ SY21 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(43,plain,
! [SV5: $i] :
( ( ! [SY25: $i,SY26: $i] :
( ~ ( c_Comb_Odiamond @ SV5 @ SY25 )
| ! [SY27: $i] :
( ~ ( c_in @ ( c_Pair @ SY26 @ SY27 @ SY25 @ SY25 ) @ SV5 @ ( tc_prod @ SY25 @ SY25 ) )
| ! [SY28: $i] :
( ~ ( c_in @ ( c_Pair @ SY26 @ SY28 @ SY25 @ SY25 ) @ ( c_Transitive__Closure_Ortrancl @ SV5 @ SY25 ) @ ( tc_prod @ SY25 @ SY25 ) )
| ( c_in @ ( c_Pair @ SY28 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV5 @ SY28 @ SY27 @ SY25 ) @ SY25 @ SY25 ) @ SV5 @ ( tc_prod @ SY25 @ SY25 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(44,plain,
! [SV6: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ~ ( c_in @ SV6 @ SY29 @ ( tc_prod @ SY30 @ SY30 ) )
| ( c_in @ SV6 @ ( c_Transitive__Closure_Ortrancl @ SY29 @ SY30 ) @ ( tc_prod @ SY30 @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(45,plain,
! [SV7: $i] :
( ( ! [SY31: $i,SY32: $i,SY33: $i] :
( ~ ( c_in @ ( c_Pair @ SV7 @ SY31 @ SY32 @ SY32 ) @ ( c_Transitive__Closure_Ortrancl @ SY33 @ SY32 ) @ ( tc_prod @ SY32 @ SY32 ) )
| ! [SY34: $i] :
( ~ ( c_in @ ( c_Pair @ SY34 @ SV7 @ SY32 @ SY32 ) @ ( c_Transitive__Closure_Ortrancl @ SY33 @ SY32 ) @ ( tc_prod @ SY32 @ SY32 ) )
| ( c_in @ ( c_Pair @ SY34 @ SY31 @ SY32 @ SY32 ) @ ( c_Transitive__Closure_Ortrancl @ SY33 @ SY32 ) @ ( tc_prod @ SY32 @ SY32 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(46,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(47,plain,
! [SV1: $i] :
( ( ( c_in @ ( c_Pair @ v_ya @ ( v_x @ SV1 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ v_y @ SV1 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(48,plain,
! [SV2: $i] :
( ( ( c_in @ ( c_Pair @ SV2 @ ( v_x @ SV2 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ v_y @ SV2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(49,plain,
! [SV3: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ v_xaa @ SV3 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ v_z @ SV3 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(50,plain,
! [SV8: $i,SV4: $i] :
( ( ! [SY35: $i] :
( ~ ( c_Comb_Odiamond @ SV4 @ SV8 )
| ! [SY36: $i] :
( ~ ( c_in @ ( c_Pair @ SY35 @ SY36 @ SV8 @ SV8 ) @ SV4 @ ( tc_prod @ SV8 @ SV8 ) )
| ! [SY37: $i] :
( ~ ( c_in @ ( c_Pair @ SY35 @ SY37 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
| ( c_in @ ( c_Pair @ SY36 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV4 @ SY37 @ SY36 @ SV8 ) @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(51,plain,
! [SV9: $i,SV5: $i] :
( ( ! [SY38: $i] :
( ~ ( c_Comb_Odiamond @ SV5 @ SV9 )
| ! [SY39: $i] :
( ~ ( c_in @ ( c_Pair @ SY38 @ SY39 @ SV9 @ SV9 ) @ SV5 @ ( tc_prod @ SV9 @ SV9 ) )
| ! [SY40: $i] :
( ~ ( c_in @ ( c_Pair @ SY38 @ SY40 @ SV9 @ SV9 ) @ ( c_Transitive__Closure_Ortrancl @ SV5 @ SV9 ) @ ( tc_prod @ SV9 @ SV9 ) )
| ( c_in @ ( c_Pair @ SY40 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV5 @ SY40 @ SY39 @ SV9 ) @ SV9 @ SV9 ) @ SV5 @ ( tc_prod @ SV9 @ SV9 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(52,plain,
! [SV10: $i,SV6: $i] :
( ( ! [SY41: $i] :
( ~ ( c_in @ SV6 @ SV10 @ ( tc_prod @ SY41 @ SY41 ) )
| ( c_in @ SV6 @ ( c_Transitive__Closure_Ortrancl @ SV10 @ SY41 ) @ ( tc_prod @ SY41 @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(53,plain,
! [SV11: $i,SV7: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ~ ( c_in @ ( c_Pair @ SV7 @ SV11 @ SY42 @ SY42 ) @ ( c_Transitive__Closure_Ortrancl @ SY43 @ SY42 ) @ ( tc_prod @ SY42 @ SY42 ) )
| ! [SY44: $i] :
( ~ ( c_in @ ( c_Pair @ SY44 @ SV7 @ SY42 @ SY42 ) @ ( c_Transitive__Closure_Ortrancl @ SY43 @ SY42 ) @ ( tc_prod @ SY42 @ SY42 ) )
| ( c_in @ ( c_Pair @ SY44 @ SV11 @ SY42 @ SY42 ) @ ( c_Transitive__Closure_Ortrancl @ SY43 @ SY42 ) @ ( tc_prod @ SY42 @ SY42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(54,plain,
! [SV1: $i] :
( ( ( c_in @ ( c_Pair @ v_y @ SV1 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ v_ya @ ( v_x @ SV1 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(55,plain,
! [SV2: $i] :
( ( ( c_in @ ( c_Pair @ v_y @ SV2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2 @ ( v_x @ SV2 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(56,plain,
! [SV3: $i] :
( ( ( c_in @ ( c_Pair @ v_xaa @ SV3 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ v_z @ SV3 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(57,plain,
! [SV12: $i,SV8: $i,SV4: $i] :
( ( ~ ( c_Comb_Odiamond @ SV4 @ SV8 )
| ! [SY45: $i] :
( ~ ( c_in @ ( c_Pair @ SV12 @ SY45 @ SV8 @ SV8 ) @ SV4 @ ( tc_prod @ SV8 @ SV8 ) )
| ! [SY46: $i] :
( ~ ( c_in @ ( c_Pair @ SV12 @ SY46 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
| ( c_in @ ( c_Pair @ SY45 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV4 @ SY46 @ SY45 @ SV8 ) @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(58,plain,
! [SV13: $i,SV9: $i,SV5: $i] :
( ( ~ ( c_Comb_Odiamond @ SV5 @ SV9 )
| ! [SY47: $i] :
( ~ ( c_in @ ( c_Pair @ SV13 @ SY47 @ SV9 @ SV9 ) @ SV5 @ ( tc_prod @ SV9 @ SV9 ) )
| ! [SY48: $i] :
( ~ ( c_in @ ( c_Pair @ SV13 @ SY48 @ SV9 @ SV9 ) @ ( c_Transitive__Closure_Ortrancl @ SV5 @ SV9 ) @ ( tc_prod @ SV9 @ SV9 ) )
| ( c_in @ ( c_Pair @ SY48 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV5 @ SY48 @ SY47 @ SV9 ) @ SV9 @ SV9 ) @ SV5 @ ( tc_prod @ SV9 @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(59,plain,
! [SV14: $i,SV10: $i,SV6: $i] :
( ( ~ ( c_in @ SV6 @ SV10 @ ( tc_prod @ SV14 @ SV14 ) )
| ( c_in @ SV6 @ ( c_Transitive__Closure_Ortrancl @ SV10 @ SV14 ) @ ( tc_prod @ SV14 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(60,plain,
! [SV15: $i,SV11: $i,SV7: $i] :
( ( ! [SY49: $i] :
( ~ ( c_in @ ( c_Pair @ SV7 @ SV11 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SY49 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) )
| ! [SY50: $i] :
( ~ ( c_in @ ( c_Pair @ SY50 @ SV7 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SY49 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) )
| ( c_in @ ( c_Pair @ SY50 @ SV11 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SY49 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(61,plain,
! [SV3: $i] :
( ( ( c_in @ ( c_Pair @ v_z @ SV3 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ v_xaa @ SV3 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV12: $i,SV8: $i,SV4: $i] :
( ( ( ~ ( c_Comb_Odiamond @ SV4 @ SV8 ) )
= $true )
| ( ( ! [SY45: $i] :
( ~ ( c_in @ ( c_Pair @ SV12 @ SY45 @ SV8 @ SV8 ) @ SV4 @ ( tc_prod @ SV8 @ SV8 ) )
| ! [SY46: $i] :
( ~ ( c_in @ ( c_Pair @ SV12 @ SY46 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
| ( c_in @ ( c_Pair @ SY45 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV4 @ SY46 @ SY45 @ SV8 ) @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(63,plain,
! [SV13: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( c_Comb_Odiamond @ SV5 @ SV9 ) )
= $true )
| ( ( ! [SY47: $i] :
( ~ ( c_in @ ( c_Pair @ SV13 @ SY47 @ SV9 @ SV9 ) @ SV5 @ ( tc_prod @ SV9 @ SV9 ) )
| ! [SY48: $i] :
( ~ ( c_in @ ( c_Pair @ SV13 @ SY48 @ SV9 @ SV9 ) @ ( c_Transitive__Closure_Ortrancl @ SV5 @ SV9 ) @ ( tc_prod @ SV9 @ SV9 ) )
| ( c_in @ ( c_Pair @ SY48 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV5 @ SY48 @ SY47 @ SV9 ) @ SV9 @ SV9 ) @ SV5 @ ( tc_prod @ SV9 @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(64,plain,
! [SV14: $i,SV10: $i,SV6: $i] :
( ( ( ~ ( c_in @ SV6 @ SV10 @ ( tc_prod @ SV14 @ SV14 ) ) )
= $true )
| ( ( c_in @ SV6 @ ( c_Transitive__Closure_Ortrancl @ SV10 @ SV14 ) @ ( tc_prod @ SV14 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(65,plain,
! [SV16: $i,SV15: $i,SV11: $i,SV7: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV7 @ SV11 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SV16 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) )
| ! [SY51: $i] :
( ~ ( c_in @ ( c_Pair @ SY51 @ SV7 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SV16 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) )
| ( c_in @ ( c_Pair @ SY51 @ SV11 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SV16 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(66,plain,
! [SV12: $i,SV8: $i,SV4: $i] :
( ( ( c_Comb_Odiamond @ SV4 @ SV8 )
= $false )
| ( ( ! [SY45: $i] :
( ~ ( c_in @ ( c_Pair @ SV12 @ SY45 @ SV8 @ SV8 ) @ SV4 @ ( tc_prod @ SV8 @ SV8 ) )
| ! [SY46: $i] :
( ~ ( c_in @ ( c_Pair @ SV12 @ SY46 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
| ( c_in @ ( c_Pair @ SY45 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV4 @ SY46 @ SY45 @ SV8 ) @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV13: $i,SV9: $i,SV5: $i] :
( ( ( c_Comb_Odiamond @ SV5 @ SV9 )
= $false )
| ( ( ! [SY47: $i] :
( ~ ( c_in @ ( c_Pair @ SV13 @ SY47 @ SV9 @ SV9 ) @ SV5 @ ( tc_prod @ SV9 @ SV9 ) )
| ! [SY48: $i] :
( ~ ( c_in @ ( c_Pair @ SV13 @ SY48 @ SV9 @ SV9 ) @ ( c_Transitive__Closure_Ortrancl @ SV5 @ SV9 ) @ ( tc_prod @ SV9 @ SV9 ) )
| ( c_in @ ( c_Pair @ SY48 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV5 @ SY48 @ SY47 @ SV9 ) @ SV9 @ SV9 ) @ SV5 @ ( tc_prod @ SV9 @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV14: $i,SV10: $i,SV6: $i] :
( ( ( c_in @ SV6 @ SV10 @ ( tc_prod @ SV14 @ SV14 ) )
= $false )
| ( ( c_in @ SV6 @ ( c_Transitive__Closure_Ortrancl @ SV10 @ SV14 ) @ ( tc_prod @ SV14 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV16: $i,SV15: $i,SV11: $i,SV7: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV7 @ SV11 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SV16 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) ) )
= $true )
| ( ( ! [SY51: $i] :
( ~ ( c_in @ ( c_Pair @ SY51 @ SV7 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SV16 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) )
| ( c_in @ ( c_Pair @ SY51 @ SV11 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SV16 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV4: $i,SV8: $i,SV17: $i,SV12: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV12 @ SV17 @ SV8 @ SV8 ) @ SV4 @ ( tc_prod @ SV8 @ SV8 ) )
| ! [SY52: $i] :
( ~ ( c_in @ ( c_Pair @ SV12 @ SY52 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
| ( c_in @ ( c_Pair @ SV17 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV4 @ SY52 @ SV17 @ SV8 ) @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) ) ) )
= $true )
| ( ( c_Comb_Odiamond @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(71,plain,
! [SV5: $i,SV9: $i,SV18: $i,SV13: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV13 @ SV18 @ SV9 @ SV9 ) @ SV5 @ ( tc_prod @ SV9 @ SV9 ) )
| ! [SY53: $i] :
( ~ ( c_in @ ( c_Pair @ SV13 @ SY53 @ SV9 @ SV9 ) @ ( c_Transitive__Closure_Ortrancl @ SV5 @ SV9 ) @ ( tc_prod @ SV9 @ SV9 ) )
| ( c_in @ ( c_Pair @ SY53 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV5 @ SY53 @ SV18 @ SV9 ) @ SV9 @ SV9 ) @ SV5 @ ( tc_prod @ SV9 @ SV9 ) ) ) )
= $true )
| ( ( c_Comb_Odiamond @ SV5 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(72,plain,
! [SV16: $i,SV15: $i,SV11: $i,SV7: $i] :
( ( ( c_in @ ( c_Pair @ SV7 @ SV11 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SV16 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) )
= $false )
| ( ( ! [SY51: $i] :
( ~ ( c_in @ ( c_Pair @ SY51 @ SV7 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SV16 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) )
| ( c_in @ ( c_Pair @ SY51 @ SV11 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SV16 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(73,plain,
! [SV4: $i,SV8: $i,SV17: $i,SV12: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV12 @ SV17 @ SV8 @ SV8 ) @ SV4 @ ( tc_prod @ SV8 @ SV8 ) ) )
= $true )
| ( ( ! [SY52: $i] :
( ~ ( c_in @ ( c_Pair @ SV12 @ SY52 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
| ( c_in @ ( c_Pair @ SV17 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV4 @ SY52 @ SV17 @ SV8 ) @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) ) ) )
= $true )
| ( ( c_Comb_Odiamond @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(74,plain,
! [SV5: $i,SV9: $i,SV18: $i,SV13: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV13 @ SV18 @ SV9 @ SV9 ) @ SV5 @ ( tc_prod @ SV9 @ SV9 ) ) )
= $true )
| ( ( ! [SY53: $i] :
( ~ ( c_in @ ( c_Pair @ SV13 @ SY53 @ SV9 @ SV9 ) @ ( c_Transitive__Closure_Ortrancl @ SV5 @ SV9 ) @ ( tc_prod @ SV9 @ SV9 ) )
| ( c_in @ ( c_Pair @ SY53 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV5 @ SY53 @ SV18 @ SV9 ) @ SV9 @ SV9 ) @ SV5 @ ( tc_prod @ SV9 @ SV9 ) ) ) )
= $true )
| ( ( c_Comb_Odiamond @ SV5 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(75,plain,
! [SV11: $i,SV16: $i,SV15: $i,SV7: $i,SV19: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV19 @ SV7 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SV16 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) )
| ( c_in @ ( c_Pair @ SV19 @ SV11 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SV16 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV7 @ SV11 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SV16 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(76,plain,
! [SV4: $i,SV8: $i,SV17: $i,SV12: $i] :
( ( ( c_in @ ( c_Pair @ SV12 @ SV17 @ SV8 @ SV8 ) @ SV4 @ ( tc_prod @ SV8 @ SV8 ) )
= $false )
| ( ( ! [SY52: $i] :
( ~ ( c_in @ ( c_Pair @ SV12 @ SY52 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
| ( c_in @ ( c_Pair @ SV17 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV4 @ SY52 @ SV17 @ SV8 ) @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) ) ) )
= $true )
| ( ( c_Comb_Odiamond @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(77,plain,
! [SV5: $i,SV9: $i,SV18: $i,SV13: $i] :
( ( ( c_in @ ( c_Pair @ SV13 @ SV18 @ SV9 @ SV9 ) @ SV5 @ ( tc_prod @ SV9 @ SV9 ) )
= $false )
| ( ( ! [SY53: $i] :
( ~ ( c_in @ ( c_Pair @ SV13 @ SY53 @ SV9 @ SV9 ) @ ( c_Transitive__Closure_Ortrancl @ SV5 @ SV9 ) @ ( tc_prod @ SV9 @ SV9 ) )
| ( c_in @ ( c_Pair @ SY53 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV5 @ SY53 @ SV18 @ SV9 ) @ SV9 @ SV9 ) @ SV5 @ ( tc_prod @ SV9 @ SV9 ) ) ) )
= $true )
| ( ( c_Comb_Odiamond @ SV5 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(78,plain,
! [SV11: $i,SV16: $i,SV15: $i,SV7: $i,SV19: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV19 @ SV7 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SV16 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV19 @ SV11 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SV16 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV7 @ SV11 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SV16 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(79,plain,
! [SV17: $i,SV4: $i,SV8: $i,SV20: $i,SV12: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV12 @ SV20 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
| ( c_in @ ( c_Pair @ SV17 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV4 @ SV20 @ SV17 @ SV8 ) @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV12 @ SV17 @ SV8 @ SV8 ) @ SV4 @ ( tc_prod @ SV8 @ SV8 ) )
= $false )
| ( ( c_Comb_Odiamond @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(80,plain,
! [SV18: $i,SV5: $i,SV9: $i,SV21: $i,SV13: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV13 @ SV21 @ SV9 @ SV9 ) @ ( c_Transitive__Closure_Ortrancl @ SV5 @ SV9 ) @ ( tc_prod @ SV9 @ SV9 ) )
| ( c_in @ ( c_Pair @ SV21 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV5 @ SV21 @ SV18 @ SV9 ) @ SV9 @ SV9 ) @ SV5 @ ( tc_prod @ SV9 @ SV9 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV13 @ SV18 @ SV9 @ SV9 ) @ SV5 @ ( tc_prod @ SV9 @ SV9 ) )
= $false )
| ( ( c_Comb_Odiamond @ SV5 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(81,plain,
! [SV11: $i,SV16: $i,SV15: $i,SV7: $i,SV19: $i] :
( ( ( c_in @ ( c_Pair @ SV19 @ SV7 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SV16 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV19 @ SV11 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SV16 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV7 @ SV11 @ SV15 @ SV15 ) @ ( c_Transitive__Closure_Ortrancl @ SV16 @ SV15 ) @ ( tc_prod @ SV15 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(82,plain,
! [SV17: $i,SV4: $i,SV8: $i,SV20: $i,SV12: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV12 @ SV20 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV17 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV4 @ SV20 @ SV17 @ SV8 ) @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV12 @ SV17 @ SV8 @ SV8 ) @ SV4 @ ( tc_prod @ SV8 @ SV8 ) )
= $false )
| ( ( c_Comb_Odiamond @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(83,plain,
! [SV18: $i,SV5: $i,SV9: $i,SV21: $i,SV13: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV13 @ SV21 @ SV9 @ SV9 ) @ ( c_Transitive__Closure_Ortrancl @ SV5 @ SV9 ) @ ( tc_prod @ SV9 @ SV9 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV21 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV5 @ SV21 @ SV18 @ SV9 ) @ SV9 @ SV9 ) @ SV5 @ ( tc_prod @ SV9 @ SV9 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV13 @ SV18 @ SV9 @ SV9 ) @ SV5 @ ( tc_prod @ SV9 @ SV9 ) )
= $false )
| ( ( c_Comb_Odiamond @ SV5 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(84,plain,
! [SV17: $i,SV4: $i,SV8: $i,SV20: $i,SV12: $i] :
( ( ( c_in @ ( c_Pair @ SV12 @ SV20 @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV17 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV4 @ SV20 @ SV17 @ SV8 ) @ SV8 @ SV8 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV8 ) @ ( tc_prod @ SV8 @ SV8 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV12 @ SV17 @ SV8 @ SV8 ) @ SV4 @ ( tc_prod @ SV8 @ SV8 ) )
= $false )
| ( ( c_Comb_Odiamond @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(85,plain,
! [SV18: $i,SV5: $i,SV9: $i,SV21: $i,SV13: $i] :
( ( ( c_in @ ( c_Pair @ SV13 @ SV21 @ SV9 @ SV9 ) @ ( c_Transitive__Closure_Ortrancl @ SV5 @ SV9 ) @ ( tc_prod @ SV9 @ SV9 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV21 @ ( c_Comb_Odiamond__strip__lemmaE__1 @ SV5 @ SV21 @ SV18 @ SV9 ) @ SV9 @ SV9 ) @ SV5 @ ( tc_prod @ SV9 @ SV9 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV13 @ SV18 @ SV9 @ SV9 ) @ SV5 @ ( tc_prod @ SV9 @ SV9 ) )
= $false )
| ( ( c_Comb_Odiamond @ SV5 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(86,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,85,84,81,68,61,55,54,46,30,29]) ).
thf(87,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : COL121-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue May 31 15:09:26 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.38
% 0.14/0.38 No.of.Axioms: 10
% 0.14/0.38
% 0.14/0.38 Length.of.Defs: 0
% 0.14/0.38
% 0.14/0.38 Contains.Choice.Funs: false
% 0.14/0.40 (rf:0,axioms:10,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:12,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.47/0.65
% 0.47/0.65 ********************************
% 0.47/0.65 * All subproblems solved! *
% 0.47/0.65 ********************************
% 0.47/0.65 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,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:86,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.47/0.65
% 0.47/0.65 %**** Beginning of derivation protocol ****
% 0.47/0.65 % SZS output start CNFRefutation
% See solution above
% 0.47/0.65
% 0.47/0.65 %**** End of derivation protocol ****
% 0.47/0.65 %**** no. of clauses in derivation: 87 ****
% 0.47/0.65 %**** clause counter: 86 ****
% 0.47/0.65
% 0.47/0.65 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,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:86,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------