%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV252-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:56:39 AM UTC 2026
% Result : Unsatisfiable 7.02s 1.49s
% Output : CNFRefutation 7.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 20
% Syntax : Number of formulae : 142 ( 100 unt; 0 typ; 0 def)
% Number of atoms : 591 ( 192 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1577 ( 115 ~; 133 |; 0 &;1329 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 380 ( 0 ^; 380 !; 0 ?; 380 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Message_Oanalz,type,
c_Message_Oanalz: $i > $i ).
thf(tp_c_Message_Oparts,type,
c_Message_Oparts: $i > $i ).
thf(tp_c_Message_Osynth,type,
c_Message_Osynth: $i > $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_insert,type,
c_insert: $i > $i > $i > $i ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_c_minus,type,
c_minus: $i > $i > $i > $i ).
thf(tp_c_union,type,
c_union: $i > $i > $i > $i ).
thf(tp_class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
thf(tp_tc_Message_Omsg,type,
tc_Message_Omsg: $i ).
thf(tp_tc_set,type,
tc_set: $i > $i ).
thf(tp_v_H,type,
v_H: $i ).
thf(tp_v_X,type,
v_X: $i ).
thf(1,axiom,
! [T_1: $i] : ( class_Orderings_Oorder @ ( tc_set @ T_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).
thf(2,axiom,
! [V_B: $i,V_A: $i,T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( V_A = V_B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(3,axiom,
! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ~ ( c_in @ V_x @ V_B @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_lessequals @ ( c_insert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
thf(4,axiom,
! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ~ ( c_lessequals @ ( c_insert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).
thf(5,axiom,
! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ~ ( c_lessequals @ ( c_insert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_set @ T_a ) )
| ( c_in @ V_x @ V_B @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).
thf(6,axiom,
! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ~ ( c_lessequals @ V_B @ V_C @ ( tc_set @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
thf(7,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ~ ( c_lessequals @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_B @ V_C @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
thf(8,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ~ ( c_lessequals @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_A @ V_C @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
thf(9,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_union @ V_A @ ( c_minus @ V_B @ V_A @ ( tc_set @ T_a ) ) @ T_a )
= ( c_union @ V_A @ V_B @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
thf(10,axiom,
! [V_B: $i,V_A: $i,T_a: $i] :
( ( c_union @ ( c_minus @ V_B @ V_A @ ( tc_set @ T_a ) ) @ V_A @ T_a )
= ( c_union @ V_B @ V_A @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
thf(11,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
thf(12,axiom,
! [V_H: $i] :
( ( c_Message_Oparts @ ( c_Message_Osynth @ V_H ) )
= ( c_union @ ( c_Message_Oparts @ V_H ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__synth_0) ).
thf(13,axiom,
! [V_G: $i,V_H: $i] :
( ~ ( c_lessequals @ V_G @ ( c_Message_Oparts @ V_H ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oparts @ V_G ) @ ( c_Message_Oparts @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_1) ).
thf(14,axiom,
! [V_G: $i,V_H: $i] :
( ~ ( c_lessequals @ ( c_Message_Oparts @ V_G ) @ ( c_Message_Oparts @ V_H ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ V_G @ ( c_Message_Oparts @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_0) ).
thf(15,axiom,
! [V_H: $i] :
( ( c_Message_Oparts @ ( c_Message_Oanalz @ V_H ) )
= ( c_Message_Oparts @ V_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__analz_0) ).
thf(16,axiom,
! [V_G: $i,V_H: $i] :
( ~ ( c_lessequals @ ( c_Message_Oanalz @ V_G ) @ ( c_Message_Oanalz @ V_H ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ V_G @ ( c_Message_Oanalz @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__iff_0) ).
thf(17,axiom,
! [V_H: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oparts @ V_H ) )
= ( c_Message_Oparts @ V_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__parts_0) ).
thf(18,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(19,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[18]) ).
thf(20,negated_conjecture,
~ ( c_lessequals @ ( c_Message_Oparts @ ( c_insert @ v_X @ v_H @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_H ) ) @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(21,negated_conjecture,
c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_H ) ) @ tc_Message_Omsg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(22,plain,
$false = $false,
inference(unfold_def,[status(thm)],[19]) ).
thf(23,plain,
( ( ! [T_1: $i] : ( class_Orderings_Oorder @ ( tc_set @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(24,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( V_A = V_B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(25,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ~ ( c_in @ V_x @ V_B @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_lessequals @ ( c_insert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(26,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ~ ( c_lessequals @ ( c_insert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(27,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ~ ( c_lessequals @ ( c_insert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_set @ T_a ) )
| ( c_in @ V_x @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(28,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ~ ( c_lessequals @ V_B @ V_C @ ( tc_set @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(29,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ~ ( c_lessequals @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_B @ V_C @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(30,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ~ ( c_lessequals @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_A @ V_C @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(31,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_union @ V_A @ ( c_minus @ V_B @ V_A @ ( tc_set @ T_a ) ) @ T_a )
= ( c_union @ V_A @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(32,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] :
( ( c_union @ ( c_minus @ V_B @ V_A @ ( tc_set @ T_a ) ) @ V_A @ T_a )
= ( c_union @ V_B @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(33,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(34,plain,
( ( ! [V_H: $i] :
( ( c_Message_Oparts @ ( c_Message_Osynth @ V_H ) )
= ( c_union @ ( c_Message_Oparts @ V_H ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(35,plain,
( ( ! [V_G: $i,V_H: $i] :
( ~ ( c_lessequals @ V_G @ ( c_Message_Oparts @ V_H ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oparts @ V_G ) @ ( c_Message_Oparts @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(36,plain,
( ( ! [V_G: $i,V_H: $i] :
( ~ ( c_lessequals @ ( c_Message_Oparts @ V_G ) @ ( c_Message_Oparts @ V_H ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ V_G @ ( c_Message_Oparts @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(37,plain,
( ( ! [V_H: $i] :
( ( c_Message_Oparts @ ( c_Message_Oanalz @ V_H ) )
= ( c_Message_Oparts @ V_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(38,plain,
( ( ! [V_G: $i,V_H: $i] :
( ~ ( c_lessequals @ ( c_Message_Oanalz @ V_G ) @ ( c_Message_Oanalz @ V_H ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ V_G @ ( c_Message_Oanalz @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(39,plain,
( ( ! [V_H: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oparts @ V_H ) )
= ( c_Message_Oparts @ V_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(40,plain,
( ( ~ ( c_lessequals @ ( c_Message_Oparts @ ( c_insert @ v_X @ v_H @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_H ) ) @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(41,plain,
( ( c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_H ) ) @ tc_Message_Omsg )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(42,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(43,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_lessequals @ ( c_insert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(44,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_C @ ( tc_set @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_lessequals @ V_A @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(45,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(46,plain,
( ( c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_H ) ) @ tc_Message_Omsg )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(47,plain,
( ( ~ ( c_lessequals @ ( c_Message_Oparts @ ( c_insert @ v_X @ v_H @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_H ) ) @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(48,plain,
( ( ! [V_H: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oparts @ V_H ) )
= ( c_Message_Oparts @ V_H ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(49,plain,
( ( ! [V_G: $i,V_H: $i] :
( ~ ( c_lessequals @ ( c_Message_Oanalz @ V_G ) @ ( c_Message_Oanalz @ V_H ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ V_G @ ( c_Message_Oanalz @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(50,plain,
( ( ! [V_H: $i] :
( ( c_Message_Oparts @ ( c_Message_Oanalz @ V_H ) )
= ( c_Message_Oparts @ V_H ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(51,plain,
( ( ! [V_G: $i,V_H: $i] :
( ~ ( c_lessequals @ ( c_Message_Oparts @ V_G ) @ ( c_Message_Oparts @ V_H ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ V_G @ ( c_Message_Oparts @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(52,plain,
( ( ! [V_G: $i,V_H: $i] :
( ~ ( c_lessequals @ V_G @ ( c_Message_Oparts @ V_H ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oparts @ V_G ) @ ( c_Message_Oparts @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(53,plain,
( ( ! [V_H: $i] :
( ( c_Message_Oparts @ ( c_Message_Osynth @ V_H ) )
= ( c_union @ ( c_Message_Oparts @ V_H ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(54,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(55,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] :
( ( c_union @ ( c_minus @ V_B @ V_A @ ( tc_set @ T_a ) ) @ V_A @ T_a )
= ( c_union @ V_B @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(56,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_union @ V_A @ ( c_minus @ V_B @ V_A @ ( tc_set @ T_a ) ) @ T_a )
= ( c_union @ V_A @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(57,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ~ ( c_lessequals @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_A @ V_C @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(58,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ~ ( c_lessequals @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_B @ V_C @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(59,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_C @ ( tc_set @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_lessequals @ V_A @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ ( c_union @ V_A @ V_B @ T_a ) @ V_C @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(60,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ~ ( c_lessequals @ ( c_insert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_set @ T_a ) )
| ( c_in @ V_x @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(61,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ~ ( c_lessequals @ ( c_insert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(62,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_lessequals @ ( c_insert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(63,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( V_A = V_B ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(64,plain,
( ( ! [T_1: $i] : ( class_Orderings_Oorder @ ( tc_set @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(65,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[42]) ).
thf(66,plain,
( ( c_lessequals @ ( c_Message_Oparts @ ( c_insert @ v_X @ v_H @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_H ) ) @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(67,plain,
! [SV1: $i] :
( ( ( c_Message_Oanalz @ ( c_Message_Oparts @ SV1 ) )
= ( c_Message_Oparts @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(68,plain,
! [SV2: $i] :
( ( ! [SY45: $i] :
( ~ ( c_lessequals @ ( c_Message_Oanalz @ SV2 ) @ ( c_Message_Oanalz @ SY45 ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ SV2 @ ( c_Message_Oanalz @ SY45 ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(69,plain,
! [SV3: $i] :
( ( ( c_Message_Oparts @ ( c_Message_Oanalz @ SV3 ) )
= ( c_Message_Oparts @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(70,plain,
! [SV4: $i] :
( ( ! [SY46: $i] :
( ~ ( c_lessequals @ ( c_Message_Oparts @ SV4 ) @ ( c_Message_Oparts @ SY46 ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ SV4 @ ( c_Message_Oparts @ SY46 ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(71,plain,
! [SV5: $i] :
( ( ! [SY47: $i] :
( ~ ( c_lessequals @ SV5 @ ( c_Message_Oparts @ SY47 ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oparts @ SV5 ) @ ( c_Message_Oparts @ SY47 ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(72,plain,
! [SV6: $i] :
( ( ( c_Message_Oparts @ ( c_Message_Osynth @ SV6 ) )
= ( c_union @ ( c_Message_Oparts @ SV6 ) @ ( c_Message_Osynth @ SV6 ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(73,plain,
! [SV7: $i] :
( ( ~ ( class_Orderings_Oorder @ SV7 )
| ! [SY48: $i] : ( c_lessequals @ SY48 @ SY48 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(74,plain,
! [SV8: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ( c_union @ ( c_minus @ SV8 @ SY49 @ ( tc_set @ SY50 ) ) @ SY49 @ SY50 )
= ( c_union @ SV8 @ SY49 @ SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(75,plain,
! [SV9: $i] :
( ( ! [SY51: $i,SY52: $i] :
( ( c_union @ SV9 @ ( c_minus @ SY51 @ SV9 @ ( tc_set @ SY52 ) ) @ SY52 )
= ( c_union @ SV9 @ SY51 @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(76,plain,
! [SV10: $i] :
( ( ! [SY53: $i,SY54: $i,SY55: $i] :
( ~ ( c_lessequals @ ( c_union @ SV10 @ SY53 @ SY54 ) @ SY55 @ ( tc_set @ SY54 ) )
| ( c_lessequals @ SV10 @ SY55 @ ( tc_set @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(77,plain,
! [SV11: $i] :
( ( ! [SY56: $i,SY57: $i,SY58: $i] :
( ~ ( c_lessequals @ ( c_union @ SV11 @ SY56 @ SY57 ) @ SY58 @ ( tc_set @ SY57 ) )
| ( c_lessequals @ SY56 @ SY58 @ ( tc_set @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(78,plain,
! [SV12: $i] :
( ( ! [SY59: $i,SY60: $i] :
( ~ ( c_lessequals @ SV12 @ SY59 @ ( tc_set @ SY60 ) )
| ! [SY61: $i] :
( ~ ( c_lessequals @ SY61 @ SY59 @ ( tc_set @ SY60 ) )
| ( c_lessequals @ ( c_union @ SY61 @ SV12 @ SY60 ) @ SY59 @ ( tc_set @ SY60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(79,plain,
! [SV13: $i] :
( ( ! [SY62: $i,SY63: $i,SY64: $i] :
( ~ ( c_lessequals @ ( c_insert @ SV13 @ SY62 @ SY63 ) @ SY64 @ ( tc_set @ SY63 ) )
| ( c_in @ SV13 @ SY64 @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(80,plain,
! [SV14: $i] :
( ( ! [SY65: $i,SY66: $i,SY67: $i] :
( ~ ( c_lessequals @ ( c_insert @ SV14 @ SY65 @ SY66 ) @ SY67 @ ( tc_set @ SY66 ) )
| ( c_lessequals @ SY65 @ SY67 @ ( tc_set @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(81,plain,
! [SV15: $i] :
( ( ! [SY68: $i,SY69: $i] :
( ~ ( c_in @ SV15 @ SY68 @ SY69 )
| ! [SY70: $i] :
( ~ ( c_lessequals @ SY70 @ SY68 @ ( tc_set @ SY69 ) )
| ( c_lessequals @ ( c_insert @ SV15 @ SY70 @ SY69 ) @ SY68 @ ( tc_set @ SY69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(82,plain,
! [SV16: $i] :
( ( ! [SY71: $i,SY72: $i] :
( ~ ( c_lessequals @ SV16 @ SY71 @ ( tc_set @ SY72 ) )
| ~ ( c_lessequals @ SY71 @ SV16 @ ( tc_set @ SY72 ) )
| ( SY71 = SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(83,plain,
! [SV17: $i] :
( ( class_Orderings_Oorder @ ( tc_set @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(84,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(85,plain,
! [SV18: $i,SV2: $i] :
( ( ~ ( c_lessequals @ ( c_Message_Oanalz @ SV2 ) @ ( c_Message_Oanalz @ SV18 ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ SV2 @ ( c_Message_Oanalz @ SV18 ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(86,plain,
! [SV19: $i,SV4: $i] :
( ( ~ ( c_lessequals @ ( c_Message_Oparts @ SV4 ) @ ( c_Message_Oparts @ SV19 ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ SV4 @ ( c_Message_Oparts @ SV19 ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(87,plain,
! [SV20: $i,SV5: $i] :
( ( ~ ( c_lessequals @ SV5 @ ( c_Message_Oparts @ SV20 ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oparts @ SV5 ) @ ( c_Message_Oparts @ SV20 ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(88,plain,
! [SV7: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV7 ) )
= $true )
| ( ( ! [SY48: $i] : ( c_lessequals @ SY48 @ SY48 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(89,plain,
! [SV21: $i,SV8: $i] :
( ( ! [SY73: $i] :
( ( c_union @ ( c_minus @ SV8 @ SV21 @ ( tc_set @ SY73 ) ) @ SV21 @ SY73 )
= ( c_union @ SV8 @ SV21 @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(90,plain,
! [SV22: $i,SV9: $i] :
( ( ! [SY74: $i] :
( ( c_union @ SV9 @ ( c_minus @ SV22 @ SV9 @ ( tc_set @ SY74 ) ) @ SY74 )
= ( c_union @ SV9 @ SV22 @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(91,plain,
! [SV23: $i,SV10: $i] :
( ( ! [SY75: $i,SY76: $i] :
( ~ ( c_lessequals @ ( c_union @ SV10 @ SV23 @ SY75 ) @ SY76 @ ( tc_set @ SY75 ) )
| ( c_lessequals @ SV10 @ SY76 @ ( tc_set @ SY75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(92,plain,
! [SV24: $i,SV11: $i] :
( ( ! [SY77: $i,SY78: $i] :
( ~ ( c_lessequals @ ( c_union @ SV11 @ SV24 @ SY77 ) @ SY78 @ ( tc_set @ SY77 ) )
| ( c_lessequals @ SV24 @ SY78 @ ( tc_set @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(93,plain,
! [SV25: $i,SV12: $i] :
( ( ! [SY79: $i] :
( ~ ( c_lessequals @ SV12 @ SV25 @ ( tc_set @ SY79 ) )
| ! [SY80: $i] :
( ~ ( c_lessequals @ SY80 @ SV25 @ ( tc_set @ SY79 ) )
| ( c_lessequals @ ( c_union @ SY80 @ SV12 @ SY79 ) @ SV25 @ ( tc_set @ SY79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(94,plain,
! [SV26: $i,SV13: $i] :
( ( ! [SY81: $i,SY82: $i] :
( ~ ( c_lessequals @ ( c_insert @ SV13 @ SV26 @ SY81 ) @ SY82 @ ( tc_set @ SY81 ) )
| ( c_in @ SV13 @ SY82 @ SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(95,plain,
! [SV27: $i,SV14: $i] :
( ( ! [SY83: $i,SY84: $i] :
( ~ ( c_lessequals @ ( c_insert @ SV14 @ SV27 @ SY83 ) @ SY84 @ ( tc_set @ SY83 ) )
| ( c_lessequals @ SV27 @ SY84 @ ( tc_set @ SY83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(96,plain,
! [SV28: $i,SV15: $i] :
( ( ! [SY85: $i] :
( ~ ( c_in @ SV15 @ SV28 @ SY85 )
| ! [SY86: $i] :
( ~ ( c_lessequals @ SY86 @ SV28 @ ( tc_set @ SY85 ) )
| ( c_lessequals @ ( c_insert @ SV15 @ SY86 @ SY85 ) @ SV28 @ ( tc_set @ SY85 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(97,plain,
! [SV29: $i,SV16: $i] :
( ( ! [SY87: $i] :
( ~ ( c_lessequals @ SV16 @ SV29 @ ( tc_set @ SY87 ) )
| ~ ( c_lessequals @ SV29 @ SV16 @ ( tc_set @ SY87 ) )
| ( SV29 = SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(98,plain,
! [SV18: $i,SV2: $i] :
( ( ( ~ ( c_lessequals @ ( c_Message_Oanalz @ SV2 ) @ ( c_Message_Oanalz @ SV18 ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true )
| ( ( c_lessequals @ SV2 @ ( c_Message_Oanalz @ SV18 ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(99,plain,
! [SV19: $i,SV4: $i] :
( ( ( ~ ( c_lessequals @ ( c_Message_Oparts @ SV4 ) @ ( c_Message_Oparts @ SV19 ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true )
| ( ( c_lessequals @ SV4 @ ( c_Message_Oparts @ SV19 ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(100,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ( c_lessequals @ SV5 @ ( c_Message_Oparts @ SV20 ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true )
| ( ( c_lessequals @ ( c_Message_Oparts @ SV5 ) @ ( c_Message_Oparts @ SV20 ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(101,plain,
! [SV7: $i] :
( ( ( class_Orderings_Oorder @ SV7 )
= $false )
| ( ( ! [SY48: $i] : ( c_lessequals @ SY48 @ SY48 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(102,plain,
! [SV30: $i,SV21: $i,SV8: $i] :
( ( ( c_union @ ( c_minus @ SV8 @ SV21 @ ( tc_set @ SV30 ) ) @ SV21 @ SV30 )
= ( c_union @ SV8 @ SV21 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(103,plain,
! [SV31: $i,SV22: $i,SV9: $i] :
( ( ( c_union @ SV9 @ ( c_minus @ SV22 @ SV9 @ ( tc_set @ SV31 ) ) @ SV31 )
= ( c_union @ SV9 @ SV22 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(104,plain,
! [SV32: $i,SV23: $i,SV10: $i] :
( ( ! [SY88: $i] :
( ~ ( c_lessequals @ ( c_union @ SV10 @ SV23 @ SV32 ) @ SY88 @ ( tc_set @ SV32 ) )
| ( c_lessequals @ SV10 @ SY88 @ ( tc_set @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(105,plain,
! [SV33: $i,SV24: $i,SV11: $i] :
( ( ! [SY89: $i] :
( ~ ( c_lessequals @ ( c_union @ SV11 @ SV24 @ SV33 ) @ SY89 @ ( tc_set @ SV33 ) )
| ( c_lessequals @ SV24 @ SY89 @ ( tc_set @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(106,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ~ ( c_lessequals @ SV12 @ SV25 @ ( tc_set @ SV34 ) )
| ! [SY90: $i] :
( ~ ( c_lessequals @ SY90 @ SV25 @ ( tc_set @ SV34 ) )
| ( c_lessequals @ ( c_union @ SY90 @ SV12 @ SV34 ) @ SV25 @ ( tc_set @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(107,plain,
! [SV35: $i,SV26: $i,SV13: $i] :
( ( ! [SY91: $i] :
( ~ ( c_lessequals @ ( c_insert @ SV13 @ SV26 @ SV35 ) @ SY91 @ ( tc_set @ SV35 ) )
| ( c_in @ SV13 @ SY91 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(108,plain,
! [SV36: $i,SV27: $i,SV14: $i] :
( ( ! [SY92: $i] :
( ~ ( c_lessequals @ ( c_insert @ SV14 @ SV27 @ SV36 ) @ SY92 @ ( tc_set @ SV36 ) )
| ( c_lessequals @ SV27 @ SY92 @ ( tc_set @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(109,plain,
! [SV37: $i,SV28: $i,SV15: $i] :
( ( ~ ( c_in @ SV15 @ SV28 @ SV37 )
| ! [SY93: $i] :
( ~ ( c_lessequals @ SY93 @ SV28 @ ( tc_set @ SV37 ) )
| ( c_lessequals @ ( c_insert @ SV15 @ SY93 @ SV37 ) @ SV28 @ ( tc_set @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(110,plain,
! [SV38: $i,SV29: $i,SV16: $i] :
( ( ~ ( c_lessequals @ SV16 @ SV29 @ ( tc_set @ SV38 ) )
| ~ ( c_lessequals @ SV29 @ SV16 @ ( tc_set @ SV38 ) )
| ( SV29 = SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(111,plain,
! [SV18: $i,SV2: $i] :
( ( ( c_lessequals @ ( c_Message_Oanalz @ SV2 ) @ ( c_Message_Oanalz @ SV18 ) @ ( tc_set @ tc_Message_Omsg ) )
= $false )
| ( ( c_lessequals @ SV2 @ ( c_Message_Oanalz @ SV18 ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(112,plain,
! [SV19: $i,SV4: $i] :
( ( ( c_lessequals @ ( c_Message_Oparts @ SV4 ) @ ( c_Message_Oparts @ SV19 ) @ ( tc_set @ tc_Message_Omsg ) )
= $false )
| ( ( c_lessequals @ SV4 @ ( c_Message_Oparts @ SV19 ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(113,plain,
! [SV20: $i,SV5: $i] :
( ( ( c_lessequals @ SV5 @ ( c_Message_Oparts @ SV20 ) @ ( tc_set @ tc_Message_Omsg ) )
= $false )
| ( ( c_lessequals @ ( c_Message_Oparts @ SV5 ) @ ( c_Message_Oparts @ SV20 ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(114,plain,
! [SV7: $i,SV39: $i] :
( ( ( c_lessequals @ SV39 @ SV39 @ SV7 )
= $true )
| ( ( class_Orderings_Oorder @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(115,plain,
! [SV40: $i,SV32: $i,SV23: $i,SV10: $i] :
( ( ~ ( c_lessequals @ ( c_union @ SV10 @ SV23 @ SV32 ) @ SV40 @ ( tc_set @ SV32 ) )
| ( c_lessequals @ SV10 @ SV40 @ ( tc_set @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(116,plain,
! [SV41: $i,SV33: $i,SV24: $i,SV11: $i] :
( ( ~ ( c_lessequals @ ( c_union @ SV11 @ SV24 @ SV33 ) @ SV41 @ ( tc_set @ SV33 ) )
| ( c_lessequals @ SV24 @ SV41 @ ( tc_set @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(117,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( c_lessequals @ SV12 @ SV25 @ ( tc_set @ SV34 ) ) )
= $true )
| ( ( ! [SY90: $i] :
( ~ ( c_lessequals @ SY90 @ SV25 @ ( tc_set @ SV34 ) )
| ( c_lessequals @ ( c_union @ SY90 @ SV12 @ SV34 ) @ SV25 @ ( tc_set @ SV34 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(118,plain,
! [SV42: $i,SV35: $i,SV26: $i,SV13: $i] :
( ( ~ ( c_lessequals @ ( c_insert @ SV13 @ SV26 @ SV35 ) @ SV42 @ ( tc_set @ SV35 ) )
| ( c_in @ SV13 @ SV42 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(119,plain,
! [SV43: $i,SV36: $i,SV27: $i,SV14: $i] :
( ( ~ ( c_lessequals @ ( c_insert @ SV14 @ SV27 @ SV36 ) @ SV43 @ ( tc_set @ SV36 ) )
| ( c_lessequals @ SV27 @ SV43 @ ( tc_set @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(120,plain,
! [SV37: $i,SV28: $i,SV15: $i] :
( ( ( ~ ( c_in @ SV15 @ SV28 @ SV37 ) )
= $true )
| ( ( ! [SY93: $i] :
( ~ ( c_lessequals @ SY93 @ SV28 @ ( tc_set @ SV37 ) )
| ( c_lessequals @ ( c_insert @ SV15 @ SY93 @ SV37 ) @ SV28 @ ( tc_set @ SV37 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(121,plain,
! [SV38: $i,SV29: $i,SV16: $i] :
( ( ( ~ ( c_lessequals @ SV16 @ SV29 @ ( tc_set @ SV38 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV29 @ SV16 @ ( tc_set @ SV38 ) )
| ( SV29 = SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(122,plain,
! [SV40: $i,SV32: $i,SV23: $i,SV10: $i] :
( ( ( ~ ( c_lessequals @ ( c_union @ SV10 @ SV23 @ SV32 ) @ SV40 @ ( tc_set @ SV32 ) ) )
= $true )
| ( ( c_lessequals @ SV10 @ SV40 @ ( tc_set @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(123,plain,
! [SV41: $i,SV33: $i,SV24: $i,SV11: $i] :
( ( ( ~ ( c_lessequals @ ( c_union @ SV11 @ SV24 @ SV33 ) @ SV41 @ ( tc_set @ SV33 ) ) )
= $true )
| ( ( c_lessequals @ SV24 @ SV41 @ ( tc_set @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(124,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ( c_lessequals @ SV12 @ SV25 @ ( tc_set @ SV34 ) )
= $false )
| ( ( ! [SY90: $i] :
( ~ ( c_lessequals @ SY90 @ SV25 @ ( tc_set @ SV34 ) )
| ( c_lessequals @ ( c_union @ SY90 @ SV12 @ SV34 ) @ SV25 @ ( tc_set @ SV34 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(125,plain,
! [SV42: $i,SV35: $i,SV26: $i,SV13: $i] :
( ( ( ~ ( c_lessequals @ ( c_insert @ SV13 @ SV26 @ SV35 ) @ SV42 @ ( tc_set @ SV35 ) ) )
= $true )
| ( ( c_in @ SV13 @ SV42 @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(126,plain,
! [SV43: $i,SV36: $i,SV27: $i,SV14: $i] :
( ( ( ~ ( c_lessequals @ ( c_insert @ SV14 @ SV27 @ SV36 ) @ SV43 @ ( tc_set @ SV36 ) ) )
= $true )
| ( ( c_lessequals @ SV27 @ SV43 @ ( tc_set @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(127,plain,
! [SV37: $i,SV28: $i,SV15: $i] :
( ( ( c_in @ SV15 @ SV28 @ SV37 )
= $false )
| ( ( ! [SY93: $i] :
( ~ ( c_lessequals @ SY93 @ SV28 @ ( tc_set @ SV37 ) )
| ( c_lessequals @ ( c_insert @ SV15 @ SY93 @ SV37 ) @ SV28 @ ( tc_set @ SV37 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(128,plain,
! [SV38: $i,SV29: $i,SV16: $i] :
( ( ( c_lessequals @ SV16 @ SV29 @ ( tc_set @ SV38 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV29 @ SV16 @ ( tc_set @ SV38 ) )
| ( SV29 = SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(129,plain,
! [SV40: $i,SV32: $i,SV23: $i,SV10: $i] :
( ( ( c_lessequals @ ( c_union @ SV10 @ SV23 @ SV32 ) @ SV40 @ ( tc_set @ SV32 ) )
= $false )
| ( ( c_lessequals @ SV10 @ SV40 @ ( tc_set @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(130,plain,
! [SV41: $i,SV33: $i,SV24: $i,SV11: $i] :
( ( ( c_lessequals @ ( c_union @ SV11 @ SV24 @ SV33 ) @ SV41 @ ( tc_set @ SV33 ) )
= $false )
| ( ( c_lessequals @ SV24 @ SV41 @ ( tc_set @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(131,plain,
! [SV12: $i,SV34: $i,SV25: $i,SV44: $i] :
( ( ( ~ ( c_lessequals @ SV44 @ SV25 @ ( tc_set @ SV34 ) )
| ( c_lessequals @ ( c_union @ SV44 @ SV12 @ SV34 ) @ SV25 @ ( tc_set @ SV34 ) ) )
= $true )
| ( ( c_lessequals @ SV12 @ SV25 @ ( tc_set @ SV34 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(132,plain,
! [SV42: $i,SV35: $i,SV26: $i,SV13: $i] :
( ( ( c_lessequals @ ( c_insert @ SV13 @ SV26 @ SV35 ) @ SV42 @ ( tc_set @ SV35 ) )
= $false )
| ( ( c_in @ SV13 @ SV42 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(133,plain,
! [SV43: $i,SV36: $i,SV27: $i,SV14: $i] :
( ( ( c_lessequals @ ( c_insert @ SV14 @ SV27 @ SV36 ) @ SV43 @ ( tc_set @ SV36 ) )
= $false )
| ( ( c_lessequals @ SV27 @ SV43 @ ( tc_set @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(134,plain,
! [SV15: $i,SV37: $i,SV28: $i,SV45: $i] :
( ( ( ~ ( c_lessequals @ SV45 @ SV28 @ ( tc_set @ SV37 ) )
| ( c_lessequals @ ( c_insert @ SV15 @ SV45 @ SV37 ) @ SV28 @ ( tc_set @ SV37 ) ) )
= $true )
| ( ( c_in @ SV15 @ SV28 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(135,plain,
! [SV38: $i,SV16: $i,SV29: $i] :
( ( ( ~ ( c_lessequals @ SV29 @ SV16 @ ( tc_set @ SV38 ) ) )
= $true )
| ( ( SV29 = SV16 )
= $true )
| ( ( c_lessequals @ SV16 @ SV29 @ ( tc_set @ SV38 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(136,plain,
! [SV12: $i,SV34: $i,SV25: $i,SV44: $i] :
( ( ( ~ ( c_lessequals @ SV44 @ SV25 @ ( tc_set @ SV34 ) ) )
= $true )
| ( ( c_lessequals @ ( c_union @ SV44 @ SV12 @ SV34 ) @ SV25 @ ( tc_set @ SV34 ) )
= $true )
| ( ( c_lessequals @ SV12 @ SV25 @ ( tc_set @ SV34 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(137,plain,
! [SV15: $i,SV37: $i,SV28: $i,SV45: $i] :
( ( ( ~ ( c_lessequals @ SV45 @ SV28 @ ( tc_set @ SV37 ) ) )
= $true )
| ( ( c_lessequals @ ( c_insert @ SV15 @ SV45 @ SV37 ) @ SV28 @ ( tc_set @ SV37 ) )
= $true )
| ( ( c_in @ SV15 @ SV28 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(138,plain,
! [SV38: $i,SV16: $i,SV29: $i] :
( ( ( c_lessequals @ SV29 @ SV16 @ ( tc_set @ SV38 ) )
= $false )
| ( ( SV29 = SV16 )
= $true )
| ( ( c_lessequals @ SV16 @ SV29 @ ( tc_set @ SV38 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(139,plain,
! [SV12: $i,SV34: $i,SV25: $i,SV44: $i] :
( ( ( c_lessequals @ SV44 @ SV25 @ ( tc_set @ SV34 ) )
= $false )
| ( ( c_lessequals @ ( c_union @ SV44 @ SV12 @ SV34 ) @ SV25 @ ( tc_set @ SV34 ) )
= $true )
| ( ( c_lessequals @ SV12 @ SV25 @ ( tc_set @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(140,plain,
! [SV15: $i,SV37: $i,SV28: $i,SV45: $i] :
( ( ( c_lessequals @ SV45 @ SV28 @ ( tc_set @ SV37 ) )
= $false )
| ( ( c_lessequals @ ( c_insert @ SV15 @ SV45 @ SV37 ) @ SV28 @ ( tc_set @ SV37 ) )
= $true )
| ( ( c_in @ SV15 @ SV28 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(141,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[46,140,139,138,133,132,130,129,114,113,112,111,103,102,84,83,72,69,67,66]) ).
thf(142,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV252-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.16 % Computer : n002.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Oct 6 16:24:27 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.02/1.49
% 7.02/1.49 No.of.Axioms: 19
% 7.02/1.49
% 7.02/1.49 Length.of.Defs: 0
% 7.02/1.49
% 7.02/1.49 Contains.Choice.Funs: false
% 7.02/1.49 ....
% 7.02/1.49
% 7.02/1.49 ********************************
% 7.02/1.49 * All subproblems solved! *
% 7.02/1.49 ********************************
% 7.02/1.49 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:19,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:141,loop_count:0,foatp_calls:1,translation:fof_full)
% 7.02/1.49
% 7.02/1.49 %**** Beginning of derivation protocol ****
% 7.02/1.49 % SZS output start CNFRefutation
% See solution above
% 7.02/1.50
% 7.02/1.50 %**** End of derivation protocol ****
% 7.02/1.50 %**** no. of clauses in derivation: 142 ****
% 7.02/1.50 %**** clause counter: 141 ****
% 7.02/1.50
% 7.02/1.50 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:19,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:141,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------