%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWX207-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 11:02:33 AM UTC 2026
% Result : Unsatisfiable 64.32s 13.16s
% Output : CNFRefutation 64.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 50
% Syntax : Number of formulae : 228 ( 208 unt; 0 typ; 0 def)
% Number of atoms : 654 ( 453 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 1114 ( 36 ~; 40 |; 0 &;1038 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 10 con; 0-2 aty)
% Number of variables : 360 ( 0 ^; 360 !; 0 ?; 360 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_aP,type,
aP: $i > $i ).
thf(tp_append,type,
append: $i > $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_bP,type,
bP: $i > $i ).
thf(tp_bfalse,type,
bfalse: $i ).
thf(tp_btrue,type,
btrue: $i ).
thf(tp_c2,type,
c2: $i > $i > $i ).
thf(tp_cons,type,
cons: $i > $i > $i ).
thf(tp_eq,type,
eq: $i > $i > $i ).
thf(tp_eq2,type,
eq2: $i > $i > $i ).
thf(tp_eq3,type,
eq3: $i > $i > $i ).
thf(tp_eq4,type,
eq4: $i > $i > $i ).
thf(tp_eq5,type,
eq5: $i > $i > $i ).
thf(tp_impl,type,
impl: $i > $i > $i ).
thf(tp_linC,type,
linC: $i > $i ).
thf(tp_linP,type,
linP: $i > $i ).
thf(tp_nil,type,
nil: $i ).
thf(tp_pA,type,
pA: $i ).
thf(tp_pB,type,
pB: $i ).
thf(tp_pE,type,
pE: $i ).
thf(tp_unambig,type,
unambig: $i > $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( eq @ ( cons @ X @ Y ) @ nil )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_047) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( eq @ nil @ ( cons @ X @ Y ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_046) ).
thf(3,axiom,
! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= btrue )
| ( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= ( eq @ Y @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_045) ).
thf(4,axiom,
! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= bfalse )
| ( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= bfalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_044) ).
thf(5,axiom,
! [X: $i] :
( ( eq5 @ X @ X )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_043) ).
thf(6,axiom,
! [X: $i] :
( ( eq4 @ X @ X )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_042) ).
thf(7,axiom,
! [X: $i] :
( ( eq3 @ X @ X )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_041) ).
thf(8,axiom,
! [X: $i] :
( ( eq2 @ X @ X )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_040) ).
thf(9,axiom,
! [X: $i] :
( ( eq @ X @ X )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_039) ).
thf(10,axiom,
! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq3 @ X @ Z )
!= btrue )
| ( ( eq4 @ ( c2 @ X @ Y ) @ ( c2 @ Z @ X2 ) )
= ( eq3 @ Y @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_038) ).
thf(11,axiom,
! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq3 @ X @ Z )
!= bfalse )
| ( ( eq4 @ ( c2 @ X @ Y ) @ ( c2 @ Z @ X2 ) )
= bfalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_037) ).
thf(12,axiom,
! [X: $i] :
( ( eq3 @ pE @ ( bP @ X ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_036) ).
thf(13,axiom,
! [X: $i] :
( ( eq3 @ pE @ ( aP @ X ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_035) ).
thf(14,axiom,
! [X: $i] :
( ( eq3 @ pB @ ( bP @ X ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_034) ).
thf(15,axiom,
! [X: $i] :
( ( eq3 @ pB @ ( aP @ X ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_033) ).
thf(16,axiom,
! [X: $i] :
( ( eq3 @ pA @ ( bP @ X ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_032) ).
thf(17,axiom,
! [X: $i] :
( ( eq3 @ pA @ ( aP @ X ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_031) ).
thf(18,axiom,
! [X: $i] :
( ( eq3 @ ( bP @ X ) @ pE )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_030) ).
thf(19,axiom,
! [X: $i] :
( ( eq3 @ ( bP @ X ) @ pB )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
thf(20,axiom,
! [X: $i] :
( ( eq3 @ ( bP @ X ) @ pA )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_028) ).
thf(21,axiom,
! [X: $i,Y: $i] :
( ( eq3 @ ( bP @ X ) @ ( aP @ Y ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
thf(22,axiom,
! [X: $i] :
( ( eq3 @ ( aP @ X ) @ pE )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
thf(23,axiom,
! [X: $i] :
( ( eq3 @ ( aP @ X ) @ pB )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_025) ).
thf(24,axiom,
! [X: $i] :
( ( eq3 @ ( aP @ X ) @ pA )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
thf(25,axiom,
! [X: $i,Y: $i] :
( ( eq3 @ ( aP @ X ) @ ( bP @ Y ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_023) ).
thf(26,axiom,
! [X: $i,Y: $i] :
( ( eq3 @ ( bP @ X ) @ ( bP @ Y ) )
= ( eq3 @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_022) ).
thf(27,axiom,
! [X: $i,Y: $i] :
( ( eq3 @ ( aP @ X ) @ ( aP @ Y ) )
= ( eq3 @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
thf(28,axiom,
( ( eq5 @ btrue @ bfalse )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
thf(29,axiom,
( ( eq5 @ bfalse @ btrue )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
thf(30,axiom,
( ( eq3 @ pE @ pB )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
thf(31,axiom,
( ( eq3 @ pE @ pA )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
thf(32,axiom,
( ( eq3 @ pB @ pE )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
thf(33,axiom,
( ( eq3 @ pB @ pA )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
thf(34,axiom,
( ( eq3 @ pA @ pE )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
thf(35,axiom,
( ( eq3 @ pA @ pB )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
thf(36,axiom,
( ( eq2 @ b @ a )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
thf(37,axiom,
( ( eq2 @ a @ b )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
thf(38,axiom,
! [X: $i,Y: $i] :
( ( unambig @ X @ Y )
= ( impl @ ( eq @ ( linC @ X ) @ ( linC @ Y ) ) @ ( eq4 @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
thf(39,axiom,
! [P: $i,Q: $i] :
( ( linC @ ( c2 @ P @ Q ) )
= ( append @ ( linP @ P ) @ ( linP @ Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
thf(40,axiom,
( ( linP @ pE )
= nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
thf(41,axiom,
( ( linP @ pB )
= ( cons @ b @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
thf(42,axiom,
( ( linP @ pA )
= ( cons @ a @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
thf(43,axiom,
! [Q: $i] :
( ( linP @ ( bP @ Q ) )
= ( append @ ( cons @ b @ nil ) @ ( append @ ( linP @ Q ) @ ( cons @ b @ nil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
thf(44,axiom,
! [P: $i] :
( ( linP @ ( aP @ P ) )
= ( append @ ( cons @ a @ nil ) @ ( append @ ( linP @ P ) @ ( cons @ a @ nil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
thf(45,axiom,
! [Z: $i,Xs: $i,Y: $i] :
( ( append @ ( cons @ Z @ Xs ) @ Y )
= ( cons @ Z @ ( append @ Xs @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
thf(46,axiom,
! [Y: $i] :
( ( append @ nil @ Y )
= Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
thf(47,axiom,
! [Q: $i] :
( ( impl @ bfalse @ Q )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
thf(48,axiom,
! [Q: $i] :
( ( impl @ btrue @ Q )
= Q ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
thf(49,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(50,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[49]) ).
thf(51,negated_conjecture,
! [X: $i,Y: $i] :
( ( eq5 @ ( unambig @ X @ Y ) @ bfalse )
!= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
thf(52,plain,
$false = $false,
inference(unfold_def,[status(thm)],[50]) ).
thf(53,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ ( cons @ X @ Y ) @ nil )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(54,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ nil @ ( cons @ X @ Y ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(55,plain,
( ( ! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= btrue )
| ( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= ( eq @ Y @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(56,plain,
( ( ! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= bfalse )
| ( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= bfalse ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(57,plain,
( ( ! [X: $i] :
( ( eq5 @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(58,plain,
( ( ! [X: $i] :
( ( eq4 @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(59,plain,
( ( ! [X: $i] :
( ( eq3 @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(60,plain,
( ( ! [X: $i] :
( ( eq2 @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(61,plain,
( ( ! [X: $i] :
( ( eq @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(62,plain,
( ( ! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq3 @ X @ Z )
!= btrue )
| ( ( eq4 @ ( c2 @ X @ Y ) @ ( c2 @ Z @ X2 ) )
= ( eq3 @ Y @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(63,plain,
( ( ! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq3 @ X @ Z )
!= bfalse )
| ( ( eq4 @ ( c2 @ X @ Y ) @ ( c2 @ Z @ X2 ) )
= bfalse ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(64,plain,
( ( ! [X: $i] :
( ( eq3 @ pE @ ( bP @ X ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(65,plain,
( ( ! [X: $i] :
( ( eq3 @ pE @ ( aP @ X ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(66,plain,
( ( ! [X: $i] :
( ( eq3 @ pB @ ( bP @ X ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(67,plain,
( ( ! [X: $i] :
( ( eq3 @ pB @ ( aP @ X ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(68,plain,
( ( ! [X: $i] :
( ( eq3 @ pA @ ( bP @ X ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(69,plain,
( ( ! [X: $i] :
( ( eq3 @ pA @ ( aP @ X ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(70,plain,
( ( ! [X: $i] :
( ( eq3 @ ( bP @ X ) @ pE )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(71,plain,
( ( ! [X: $i] :
( ( eq3 @ ( bP @ X ) @ pB )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(72,plain,
( ( ! [X: $i] :
( ( eq3 @ ( bP @ X ) @ pA )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(73,plain,
( ( ! [X: $i,Y: $i] :
( ( eq3 @ ( bP @ X ) @ ( aP @ Y ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(74,plain,
( ( ! [X: $i] :
( ( eq3 @ ( aP @ X ) @ pE )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(75,plain,
( ( ! [X: $i] :
( ( eq3 @ ( aP @ X ) @ pB )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(76,plain,
( ( ! [X: $i] :
( ( eq3 @ ( aP @ X ) @ pA )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(77,plain,
( ( ! [X: $i,Y: $i] :
( ( eq3 @ ( aP @ X ) @ ( bP @ Y ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(78,plain,
( ( ! [X: $i,Y: $i] :
( ( eq3 @ ( bP @ X ) @ ( bP @ Y ) )
= ( eq3 @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(79,plain,
( ( ! [X: $i,Y: $i] :
( ( eq3 @ ( aP @ X ) @ ( aP @ Y ) )
= ( eq3 @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(80,plain,
( ( ( eq5 @ btrue @ bfalse )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(81,plain,
( ( ( eq5 @ bfalse @ btrue )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(82,plain,
( ( ( eq3 @ pE @ pB )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(83,plain,
( ( ( eq3 @ pE @ pA )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(84,plain,
( ( ( eq3 @ pB @ pE )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(85,plain,
( ( ( eq3 @ pB @ pA )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(86,plain,
( ( ( eq3 @ pA @ pE )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(87,plain,
( ( ( eq3 @ pA @ pB )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(88,plain,
( ( ( eq2 @ b @ a )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(89,plain,
( ( ( eq2 @ a @ b )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(90,plain,
( ( ! [X: $i,Y: $i] :
( ( unambig @ X @ Y )
= ( impl @ ( eq @ ( linC @ X ) @ ( linC @ Y ) ) @ ( eq4 @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(91,plain,
( ( ! [P: $i,Q: $i] :
( ( linC @ ( c2 @ P @ Q ) )
= ( append @ ( linP @ P ) @ ( linP @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(92,plain,
( ( ( linP @ pE )
= nil )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(93,plain,
( ( ( linP @ pB )
= ( cons @ b @ nil ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(94,plain,
( ( ( linP @ pA )
= ( cons @ a @ nil ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(95,plain,
( ( ! [Q: $i] :
( ( linP @ ( bP @ Q ) )
= ( append @ ( cons @ b @ nil ) @ ( append @ ( linP @ Q ) @ ( cons @ b @ nil ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(96,plain,
( ( ! [P: $i] :
( ( linP @ ( aP @ P ) )
= ( append @ ( cons @ a @ nil ) @ ( append @ ( linP @ P ) @ ( cons @ a @ nil ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(97,plain,
( ( ! [Z: $i,Xs: $i,Y: $i] :
( ( append @ ( cons @ Z @ Xs ) @ Y )
= ( cons @ Z @ ( append @ Xs @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(98,plain,
( ( ! [Y: $i] :
( ( append @ nil @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(99,plain,
( ( ! [Q: $i] :
( ( impl @ bfalse @ Q )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(100,plain,
( ( ! [Q: $i] :
( ( impl @ btrue @ Q )
= Q ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(101,plain,
( ( ! [X: $i,Y: $i] :
( ( eq5 @ ( unambig @ X @ Y ) @ bfalse )
!= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(102,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[52]) ).
thf(103,plain,
( ( ! [X: $i,Z: $i] :
( ( ( eq2 @ X @ Z )
!= btrue )
| ! [Y: $i,X2: $i] :
( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= ( eq @ Y @ X2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(104,plain,
( ( ! [X: $i,Z: $i] :
( ( ( eq2 @ X @ Z )
!= bfalse )
| ! [Y: $i,X2: $i] :
( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(105,plain,
( ( ! [X: $i,Z: $i] :
( ( ( eq3 @ X @ Z )
!= btrue )
| ! [Y: $i,X2: $i] :
( ( eq4 @ ( c2 @ X @ Y ) @ ( c2 @ Z @ X2 ) )
= ( eq3 @ Y @ X2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(106,plain,
( ( ! [X: $i,Z: $i] :
( ( ( eq3 @ X @ Z )
!= bfalse )
| ! [Y: $i,X2: $i] :
( ( eq4 @ ( c2 @ X @ Y ) @ ( c2 @ Z @ X2 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(107,plain,
( ( ! [X: $i,Y: $i] :
( ( eq5 @ ( unambig @ X @ Y ) @ bfalse )
!= btrue ) )
= $true ),
inference(extcnf_combined,[status(esa)],[101]) ).
thf(108,plain,
( ( ! [X: $i,Y: $i] :
( ( eq5 @ ( unambig @ X @ Y ) @ bfalse )
!= btrue ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(109,plain,
( ( ! [Q: $i] :
( ( impl @ btrue @ Q )
= Q ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(110,plain,
( ( ! [Q: $i] :
( ( impl @ bfalse @ Q )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(111,plain,
( ( ! [Y: $i] :
( ( append @ nil @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(112,plain,
( ( ! [Z: $i,Xs: $i,Y: $i] :
( ( append @ ( cons @ Z @ Xs ) @ Y )
= ( cons @ Z @ ( append @ Xs @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(113,plain,
( ( ! [P: $i] :
( ( linP @ ( aP @ P ) )
= ( append @ ( cons @ a @ nil ) @ ( append @ ( linP @ P ) @ ( cons @ a @ nil ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(114,plain,
( ( ! [Q: $i] :
( ( linP @ ( bP @ Q ) )
= ( append @ ( cons @ b @ nil ) @ ( append @ ( linP @ Q ) @ ( cons @ b @ nil ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(115,plain,
( ( ( linP @ pA )
= ( cons @ a @ nil ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(116,plain,
( ( ( linP @ pB )
= ( cons @ b @ nil ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(117,plain,
( ( ( linP @ pE )
= nil )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(118,plain,
( ( ! [P: $i,Q: $i] :
( ( linC @ ( c2 @ P @ Q ) )
= ( append @ ( linP @ P ) @ ( linP @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(119,plain,
( ( ! [X: $i,Y: $i] :
( ( unambig @ X @ Y )
= ( impl @ ( eq @ ( linC @ X ) @ ( linC @ Y ) ) @ ( eq4 @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(120,plain,
( ( ( eq2 @ a @ b )
= bfalse )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(121,plain,
( ( ( eq2 @ b @ a )
= bfalse )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(122,plain,
( ( ( eq3 @ pA @ pB )
= bfalse )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(123,plain,
( ( ( eq3 @ pA @ pE )
= bfalse )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(124,plain,
( ( ( eq3 @ pB @ pA )
= bfalse )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(125,plain,
( ( ( eq3 @ pB @ pE )
= bfalse )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(126,plain,
( ( ( eq3 @ pE @ pA )
= bfalse )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(127,plain,
( ( ( eq3 @ pE @ pB )
= bfalse )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(128,plain,
( ( ( eq5 @ bfalse @ btrue )
= bfalse )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(129,plain,
( ( ( eq5 @ btrue @ bfalse )
= bfalse )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(130,plain,
( ( ! [X: $i,Y: $i] :
( ( eq3 @ ( aP @ X ) @ ( aP @ Y ) )
= ( eq3 @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(131,plain,
( ( ! [X: $i,Y: $i] :
( ( eq3 @ ( bP @ X ) @ ( bP @ Y ) )
= ( eq3 @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(132,plain,
( ( ! [X: $i,Y: $i] :
( ( eq3 @ ( aP @ X ) @ ( bP @ Y ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(133,plain,
( ( ! [X: $i] :
( ( eq3 @ ( aP @ X ) @ pA )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(134,plain,
( ( ! [X: $i] :
( ( eq3 @ ( aP @ X ) @ pB )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(135,plain,
( ( ! [X: $i] :
( ( eq3 @ ( aP @ X ) @ pE )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(136,plain,
( ( ! [X: $i,Y: $i] :
( ( eq3 @ ( bP @ X ) @ ( aP @ Y ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(137,plain,
( ( ! [X: $i] :
( ( eq3 @ ( bP @ X ) @ pA )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(138,plain,
( ( ! [X: $i] :
( ( eq3 @ ( bP @ X ) @ pB )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(139,plain,
( ( ! [X: $i] :
( ( eq3 @ ( bP @ X ) @ pE )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(140,plain,
( ( ! [X: $i] :
( ( eq3 @ pA @ ( aP @ X ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(141,plain,
( ( ! [X: $i] :
( ( eq3 @ pA @ ( bP @ X ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(142,plain,
( ( ! [X: $i] :
( ( eq3 @ pB @ ( aP @ X ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(143,plain,
( ( ! [X: $i] :
( ( eq3 @ pB @ ( bP @ X ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(144,plain,
( ( ! [X: $i] :
( ( eq3 @ pE @ ( aP @ X ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(145,plain,
( ( ! [X: $i] :
( ( eq3 @ pE @ ( bP @ X ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(146,plain,
( ( ! [X: $i,Z: $i] :
( ( ( eq3 @ X @ Z )
!= bfalse )
| ! [Y: $i,X2: $i] :
( ( eq4 @ ( c2 @ X @ Y ) @ ( c2 @ Z @ X2 ) )
= bfalse ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(147,plain,
( ( ! [X: $i,Z: $i] :
( ( ( eq3 @ X @ Z )
!= btrue )
| ! [Y: $i,X2: $i] :
( ( eq4 @ ( c2 @ X @ Y ) @ ( c2 @ Z @ X2 ) )
= ( eq3 @ Y @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(148,plain,
( ( ! [X: $i] :
( ( eq @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(149,plain,
( ( ! [X: $i] :
( ( eq2 @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(150,plain,
( ( ! [X: $i] :
( ( eq3 @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(151,plain,
( ( ! [X: $i] :
( ( eq4 @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(152,plain,
( ( ! [X: $i] :
( ( eq5 @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(153,plain,
( ( ! [X: $i,Z: $i] :
( ( ( eq2 @ X @ Z )
!= bfalse )
| ! [Y: $i,X2: $i] :
( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= bfalse ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(154,plain,
( ( ! [X: $i,Z: $i] :
( ( ( eq2 @ X @ Z )
!= btrue )
| ! [Y: $i,X2: $i] :
( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= ( eq @ Y @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(155,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ nil @ ( cons @ X @ Y ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(156,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ ( cons @ X @ Y ) @ nil )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(157,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[102]) ).
thf(158,plain,
! [SV1: $i] :
( ( ! [SY59: $i] :
( ( eq5 @ ( unambig @ SV1 @ SY59 ) @ bfalse )
!= btrue ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(159,plain,
! [SV2: $i] :
( ( ( impl @ btrue @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(160,plain,
! [SV3: $i] :
( ( ( impl @ bfalse @ SV3 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(161,plain,
! [SV4: $i] :
( ( ( append @ nil @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(162,plain,
! [SV5: $i] :
( ( ! [SY60: $i,SY61: $i] :
( ( append @ ( cons @ SV5 @ SY60 ) @ SY61 )
= ( cons @ SV5 @ ( append @ SY60 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(163,plain,
! [SV6: $i] :
( ( ( linP @ ( aP @ SV6 ) )
= ( append @ ( cons @ a @ nil ) @ ( append @ ( linP @ SV6 ) @ ( cons @ a @ nil ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(164,plain,
! [SV7: $i] :
( ( ( linP @ ( bP @ SV7 ) )
= ( append @ ( cons @ b @ nil ) @ ( append @ ( linP @ SV7 ) @ ( cons @ b @ nil ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(165,plain,
! [SV8: $i] :
( ( ! [SY62: $i] :
( ( linC @ ( c2 @ SV8 @ SY62 ) )
= ( append @ ( linP @ SV8 ) @ ( linP @ SY62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(166,plain,
! [SV9: $i] :
( ( ! [SY63: $i] :
( ( unambig @ SV9 @ SY63 )
= ( impl @ ( eq @ ( linC @ SV9 ) @ ( linC @ SY63 ) ) @ ( eq4 @ SV9 @ SY63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(167,plain,
! [SV10: $i] :
( ( ! [SY64: $i] :
( ( eq3 @ ( aP @ SV10 ) @ ( aP @ SY64 ) )
= ( eq3 @ SV10 @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(168,plain,
! [SV11: $i] :
( ( ! [SY65: $i] :
( ( eq3 @ ( bP @ SV11 ) @ ( bP @ SY65 ) )
= ( eq3 @ SV11 @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(169,plain,
! [SV12: $i] :
( ( ! [SY66: $i] :
( ( eq3 @ ( aP @ SV12 ) @ ( bP @ SY66 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(170,plain,
! [SV13: $i] :
( ( ( eq3 @ ( aP @ SV13 ) @ pA )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(171,plain,
! [SV14: $i] :
( ( ( eq3 @ ( aP @ SV14 ) @ pB )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(172,plain,
! [SV15: $i] :
( ( ( eq3 @ ( aP @ SV15 ) @ pE )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(173,plain,
! [SV16: $i] :
( ( ! [SY67: $i] :
( ( eq3 @ ( bP @ SV16 ) @ ( aP @ SY67 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(174,plain,
! [SV17: $i] :
( ( ( eq3 @ ( bP @ SV17 ) @ pA )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(175,plain,
! [SV18: $i] :
( ( ( eq3 @ ( bP @ SV18 ) @ pB )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(176,plain,
! [SV19: $i] :
( ( ( eq3 @ ( bP @ SV19 ) @ pE )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(177,plain,
! [SV20: $i] :
( ( ( eq3 @ pA @ ( aP @ SV20 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(178,plain,
! [SV21: $i] :
( ( ( eq3 @ pA @ ( bP @ SV21 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(179,plain,
! [SV22: $i] :
( ( ( eq3 @ pB @ ( aP @ SV22 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(180,plain,
! [SV23: $i] :
( ( ( eq3 @ pB @ ( bP @ SV23 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(181,plain,
! [SV24: $i] :
( ( ( eq3 @ pE @ ( aP @ SV24 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(182,plain,
! [SV25: $i] :
( ( ( eq3 @ pE @ ( bP @ SV25 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(183,plain,
! [SV26: $i] :
( ( ! [SY68: $i] :
( ( ( eq3 @ SV26 @ SY68 )
!= bfalse )
| ! [SY69: $i,SY70: $i] :
( ( eq4 @ ( c2 @ SV26 @ SY69 ) @ ( c2 @ SY68 @ SY70 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(184,plain,
! [SV27: $i] :
( ( ! [SY71: $i] :
( ( ( eq3 @ SV27 @ SY71 )
!= btrue )
| ! [SY72: $i,SY73: $i] :
( ( eq4 @ ( c2 @ SV27 @ SY72 ) @ ( c2 @ SY71 @ SY73 ) )
= ( eq3 @ SY72 @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(185,plain,
! [SV28: $i] :
( ( ( eq @ SV28 @ SV28 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(186,plain,
! [SV29: $i] :
( ( ( eq2 @ SV29 @ SV29 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(187,plain,
! [SV30: $i] :
( ( ( eq3 @ SV30 @ SV30 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(188,plain,
! [SV31: $i] :
( ( ( eq4 @ SV31 @ SV31 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(189,plain,
! [SV32: $i] :
( ( ( eq5 @ SV32 @ SV32 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(190,plain,
! [SV33: $i] :
( ( ! [SY74: $i] :
( ( ( eq2 @ SV33 @ SY74 )
!= bfalse )
| ! [SY75: $i,SY76: $i] :
( ( eq @ ( cons @ SV33 @ SY75 ) @ ( cons @ SY74 @ SY76 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(191,plain,
! [SV34: $i] :
( ( ! [SY77: $i] :
( ( ( eq2 @ SV34 @ SY77 )
!= btrue )
| ! [SY78: $i,SY79: $i] :
( ( eq @ ( cons @ SV34 @ SY78 ) @ ( cons @ SY77 @ SY79 ) )
= ( eq @ SY78 @ SY79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(192,plain,
! [SV35: $i] :
( ( ! [SY80: $i] :
( ( eq @ nil @ ( cons @ SV35 @ SY80 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(193,plain,
! [SV36: $i] :
( ( ! [SY81: $i] :
( ( eq @ ( cons @ SV36 @ SY81 ) @ nil )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(194,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(195,plain,
! [SV37: $i,SV1: $i] :
( ( ( eq5 @ ( unambig @ SV1 @ SV37 ) @ bfalse )
!= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(196,plain,
! [SV38: $i,SV5: $i] :
( ( ! [SY82: $i] :
( ( append @ ( cons @ SV5 @ SV38 ) @ SY82 )
= ( cons @ SV5 @ ( append @ SV38 @ SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(197,plain,
! [SV39: $i,SV8: $i] :
( ( ( linC @ ( c2 @ SV8 @ SV39 ) )
= ( append @ ( linP @ SV8 ) @ ( linP @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(198,plain,
! [SV40: $i,SV9: $i] :
( ( ( unambig @ SV9 @ SV40 )
= ( impl @ ( eq @ ( linC @ SV9 ) @ ( linC @ SV40 ) ) @ ( eq4 @ SV9 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(199,plain,
! [SV41: $i,SV10: $i] :
( ( ( eq3 @ ( aP @ SV10 ) @ ( aP @ SV41 ) )
= ( eq3 @ SV10 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(200,plain,
! [SV42: $i,SV11: $i] :
( ( ( eq3 @ ( bP @ SV11 ) @ ( bP @ SV42 ) )
= ( eq3 @ SV11 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(201,plain,
! [SV43: $i,SV12: $i] :
( ( ( eq3 @ ( aP @ SV12 ) @ ( bP @ SV43 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(202,plain,
! [SV44: $i,SV16: $i] :
( ( ( eq3 @ ( bP @ SV16 ) @ ( aP @ SV44 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(203,plain,
! [SV45: $i,SV26: $i] :
( ( ( ( eq3 @ SV26 @ SV45 )
!= bfalse )
| ! [SY83: $i,SY84: $i] :
( ( eq4 @ ( c2 @ SV26 @ SY83 ) @ ( c2 @ SV45 @ SY84 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(204,plain,
! [SV46: $i,SV27: $i] :
( ( ( ( eq3 @ SV27 @ SV46 )
!= btrue )
| ! [SY85: $i,SY86: $i] :
( ( eq4 @ ( c2 @ SV27 @ SY85 ) @ ( c2 @ SV46 @ SY86 ) )
= ( eq3 @ SY85 @ SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(205,plain,
! [SV47: $i,SV33: $i] :
( ( ( ( eq2 @ SV33 @ SV47 )
!= bfalse )
| ! [SY87: $i,SY88: $i] :
( ( eq @ ( cons @ SV33 @ SY87 ) @ ( cons @ SV47 @ SY88 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(206,plain,
! [SV48: $i,SV34: $i] :
( ( ( ( eq2 @ SV34 @ SV48 )
!= btrue )
| ! [SY89: $i,SY90: $i] :
( ( eq @ ( cons @ SV34 @ SY89 ) @ ( cons @ SV48 @ SY90 ) )
= ( eq @ SY89 @ SY90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(207,plain,
! [SV49: $i,SV35: $i] :
( ( ( eq @ nil @ ( cons @ SV35 @ SV49 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(208,plain,
! [SV50: $i,SV36: $i] :
( ( ( eq @ ( cons @ SV36 @ SV50 ) @ nil )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(209,plain,
! [SV37: $i,SV1: $i] :
( ( ( eq5 @ ( unambig @ SV1 @ SV37 ) @ bfalse )
= btrue )
= $false ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(210,plain,
! [SV51: $i,SV38: $i,SV5: $i] :
( ( ( append @ ( cons @ SV5 @ SV38 ) @ SV51 )
= ( cons @ SV5 @ ( append @ SV38 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(211,plain,
! [SV45: $i,SV26: $i] :
( ( ( ( eq3 @ SV26 @ SV45 )
!= bfalse )
= $true )
| ( ( ! [SY83: $i,SY84: $i] :
( ( eq4 @ ( c2 @ SV26 @ SY83 ) @ ( c2 @ SV45 @ SY84 ) )
= bfalse ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(212,plain,
! [SV46: $i,SV27: $i] :
( ( ( ( eq3 @ SV27 @ SV46 )
!= btrue )
= $true )
| ( ( ! [SY85: $i,SY86: $i] :
( ( eq4 @ ( c2 @ SV27 @ SY85 ) @ ( c2 @ SV46 @ SY86 ) )
= ( eq3 @ SY85 @ SY86 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(213,plain,
! [SV47: $i,SV33: $i] :
( ( ( ( eq2 @ SV33 @ SV47 )
!= bfalse )
= $true )
| ( ( ! [SY87: $i,SY88: $i] :
( ( eq @ ( cons @ SV33 @ SY87 ) @ ( cons @ SV47 @ SY88 ) )
= bfalse ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(214,plain,
! [SV48: $i,SV34: $i] :
( ( ( ( eq2 @ SV34 @ SV48 )
!= btrue )
= $true )
| ( ( ! [SY89: $i,SY90: $i] :
( ( eq @ ( cons @ SV34 @ SY89 ) @ ( cons @ SV48 @ SY90 ) )
= ( eq @ SY89 @ SY90 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(215,plain,
! [SV45: $i,SV26: $i] :
( ( ( ( eq3 @ SV26 @ SV45 )
= bfalse )
= $false )
| ( ( ! [SY83: $i,SY84: $i] :
( ( eq4 @ ( c2 @ SV26 @ SY83 ) @ ( c2 @ SV45 @ SY84 ) )
= bfalse ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(216,plain,
! [SV46: $i,SV27: $i] :
( ( ( ( eq3 @ SV27 @ SV46 )
= btrue )
= $false )
| ( ( ! [SY85: $i,SY86: $i] :
( ( eq4 @ ( c2 @ SV27 @ SY85 ) @ ( c2 @ SV46 @ SY86 ) )
= ( eq3 @ SY85 @ SY86 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(217,plain,
! [SV47: $i,SV33: $i] :
( ( ( ( eq2 @ SV33 @ SV47 )
= bfalse )
= $false )
| ( ( ! [SY87: $i,SY88: $i] :
( ( eq @ ( cons @ SV33 @ SY87 ) @ ( cons @ SV47 @ SY88 ) )
= bfalse ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(218,plain,
! [SV48: $i,SV34: $i] :
( ( ( ( eq2 @ SV34 @ SV48 )
= btrue )
= $false )
| ( ( ! [SY89: $i,SY90: $i] :
( ( eq @ ( cons @ SV34 @ SY89 ) @ ( cons @ SV48 @ SY90 ) )
= ( eq @ SY89 @ SY90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(219,plain,
! [SV45: $i,SV52: $i,SV26: $i] :
( ( ( ! [SY91: $i] :
( ( eq4 @ ( c2 @ SV26 @ SV52 ) @ ( c2 @ SV45 @ SY91 ) )
= bfalse ) )
= $true )
| ( ( ( eq3 @ SV26 @ SV45 )
= bfalse )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(220,plain,
! [SV46: $i,SV53: $i,SV27: $i] :
( ( ( ! [SY92: $i] :
( ( eq4 @ ( c2 @ SV27 @ SV53 ) @ ( c2 @ SV46 @ SY92 ) )
= ( eq3 @ SV53 @ SY92 ) ) )
= $true )
| ( ( ( eq3 @ SV27 @ SV46 )
= btrue )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(221,plain,
! [SV47: $i,SV54: $i,SV33: $i] :
( ( ( ! [SY93: $i] :
( ( eq @ ( cons @ SV33 @ SV54 ) @ ( cons @ SV47 @ SY93 ) )
= bfalse ) )
= $true )
| ( ( ( eq2 @ SV33 @ SV47 )
= bfalse )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(222,plain,
! [SV48: $i,SV55: $i,SV34: $i] :
( ( ( ! [SY94: $i] :
( ( eq @ ( cons @ SV34 @ SV55 ) @ ( cons @ SV48 @ SY94 ) )
= ( eq @ SV55 @ SY94 ) ) )
= $true )
| ( ( ( eq2 @ SV34 @ SV48 )
= btrue )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(223,plain,
! [SV56: $i,SV45: $i,SV52: $i,SV26: $i] :
( ( ( ( eq4 @ ( c2 @ SV26 @ SV52 ) @ ( c2 @ SV45 @ SV56 ) )
= bfalse )
= $true )
| ( ( ( eq3 @ SV26 @ SV45 )
= bfalse )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(224,plain,
! [SV57: $i,SV46: $i,SV53: $i,SV27: $i] :
( ( ( ( eq4 @ ( c2 @ SV27 @ SV53 ) @ ( c2 @ SV46 @ SV57 ) )
= ( eq3 @ SV53 @ SV57 ) )
= $true )
| ( ( ( eq3 @ SV27 @ SV46 )
= btrue )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(225,plain,
! [SV58: $i,SV47: $i,SV54: $i,SV33: $i] :
( ( ( ( eq @ ( cons @ SV33 @ SV54 ) @ ( cons @ SV47 @ SV58 ) )
= bfalse )
= $true )
| ( ( ( eq2 @ SV33 @ SV47 )
= bfalse )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(226,plain,
! [SV59: $i,SV48: $i,SV55: $i,SV34: $i] :
( ( ( ( eq @ ( cons @ SV34 @ SV55 ) @ ( cons @ SV48 @ SV59 ) )
= ( eq @ SV55 @ SV59 ) )
= $true )
| ( ( ( eq2 @ SV34 @ SV48 )
= btrue )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(227,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[115,226,225,224,223,210,209,208,207,202,201,200,199,198,197,194,189,188,187,186,185,182,181,180,179,178,177,176,175,174,172,171,170,164,163,161,160,159,129,128,127,126,125,124,123,122,121,120,117,116]) ).
thf(228,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWX207-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Oct 6 17:11:00 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 64.32/13.16
% 64.32/13.16 No.of.Axioms: 49
% 64.32/13.16
% 64.32/13.16 Length.of.Defs: 0
% 64.32/13.16
% 64.32/13.16 Contains.Choice.Funs: false
% 64.32/13.16 ......
% 64.32/13.16
% 64.32/13.16 ********************************
% 64.32/13.16 * All subproblems solved! *
% 64.32/13.16 ********************************
% 64.32/13.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:49,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:227,loop_count:0,foatp_calls:1,translation:fof_full)
% 64.32/13.16
% 64.32/13.16 %**** Beginning of derivation protocol ****
% 64.32/13.16 % SZS output start CNFRefutation
% See solution above
% 64.32/13.16
% 64.32/13.16 %**** End of derivation protocol ****
% 64.32/13.16 %**** no. of clauses in derivation: 228 ****
% 64.32/13.16 %**** clause counter: 227 ****
% 64.32/13.16
% 64.32/13.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:49,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:227,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------