TSTP Solution File: LCL109-5 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LCL109-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n025.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 : Sun Jul 17 12:20:43 EDT 2022
% Result : Unsatisfiable 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 26
% Syntax : Number of formulae : 122 ( 94 unt; 8 typ; 0 def)
% Number of atoms : 381 ( 181 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 861 ( 47 ~; 49 |; 0 &; 765 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 250 ( 0 ^ 250 !; 0 ?; 250 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_big_V,type,
big_V: $i > $i > $i ).
thf(tp_big_hat,type,
big_hat: $i > $i > $i ).
thf(tp_implies,type,
implies: $i > $i > $i ).
thf(tp_not,type,
not: $i > $i ).
thf(tp_ordered,type,
ordered: $i > $i > $o ).
thf(tp_truth,type,
truth: $i ).
thf(tp_x,type,
x: $i ).
thf(tp_y,type,
y: $i ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( implies @ X @ ( big_hat @ Y @ Z ) )
= ( big_hat @ ( implies @ X @ Y ) @ ( implies @ X @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_7) ).
thf(2,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( implies @ ( big_V @ X @ Y ) @ Z )
= ( big_hat @ ( implies @ X @ Z ) @ ( implies @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_6) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( not @ ( big_hat @ X @ Y ) )
= ( big_V @ ( not @ X ) @ ( not @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_5) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ( not @ ( big_V @ X @ Y ) )
= ( big_hat @ ( not @ X ) @ ( not @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_4) ).
thf(5,axiom,
! [Y: $i,X: $i,Z: $i] :
( ~ ( ordered @ Y @ ( implies @ X @ Z ) )
| ( ordered @ X @ ( implies @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_3_2) ).
thf(6,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( ordered @ X @ ( implies @ Y @ Z ) )
| ( ordered @ Y @ ( implies @ X @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_3_1) ).
thf(7,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( ordered @ X @ Y )
| ( ordered @ ( implies @ Z @ X ) @ ( implies @ Z @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_2) ).
thf(8,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( ordered @ X @ Y )
| ( ordered @ ( implies @ X @ Z ) @ ( implies @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1) ).
thf(9,axiom,
! [X: $i,Y: $i] :
( ( ( implies @ X @ Y )
!= truth )
| ( ordered @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partial_order_definition2) ).
thf(10,axiom,
! [X: $i,Y: $i] :
( ~ ( ordered @ X @ Y )
| ( ( implies @ X @ Y )
= truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partial_order_definition1) ).
thf(11,axiom,
! [X: $i,Y: $i] :
( ( big_hat @ X @ Y )
= ( not @ ( big_V @ ( not @ X ) @ ( not @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',big_hat_definition) ).
thf(12,axiom,
! [X: $i,Y: $i] :
( ( big_V @ X @ Y )
= ( implies @ ( implies @ X @ Y ) @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',big_V_definition) ).
thf(13,axiom,
! [X: $i,Y: $i] :
( ( implies @ ( implies @ ( not @ X ) @ ( not @ Y ) ) @ ( implies @ Y @ X ) )
= truth ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_4) ).
thf(14,axiom,
! [X: $i,Y: $i] :
( ( implies @ ( implies @ X @ Y ) @ Y )
= ( implies @ ( implies @ Y @ X ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_3) ).
thf(15,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) )
= truth ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_2) ).
thf(16,axiom,
! [X: $i] :
( ( implies @ truth @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_1) ).
thf(17,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(18,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[17]) ).
thf(19,negated_conjecture,
( big_V @ ( implies @ x @ y ) @ ( implies @ y @ x ) )
!= truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_mv_4) ).
thf(20,plain,
$false = $false,
inference(unfold_def,[status(thm)],[18]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( implies @ X @ ( big_hat @ Y @ Z ) )
= ( big_hat @ ( implies @ X @ Y ) @ ( implies @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(22,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( implies @ ( big_V @ X @ Y ) @ Z )
= ( big_hat @ ( implies @ X @ Z ) @ ( implies @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i] :
( ( not @ ( big_hat @ X @ Y ) )
= ( big_V @ ( not @ X ) @ ( not @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i] :
( ( not @ ( big_V @ X @ Y ) )
= ( big_hat @ ( not @ X ) @ ( not @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(25,plain,
( ( ! [Y: $i,X: $i,Z: $i] :
( ~ ( ordered @ Y @ ( implies @ X @ Z ) )
| ( ordered @ X @ ( implies @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(26,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( ordered @ X @ ( implies @ Y @ Z ) )
| ( ordered @ Y @ ( implies @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( ordered @ X @ Y )
| ( ordered @ ( implies @ Z @ X ) @ ( implies @ Z @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( ordered @ X @ Y )
| ( ordered @ ( implies @ X @ Z ) @ ( implies @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i] :
( ( ( implies @ X @ Y )
!= truth )
| ( ordered @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( ordered @ X @ Y )
| ( ( implies @ X @ Y )
= truth ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i] :
( ( big_hat @ X @ Y )
= ( not @ ( big_V @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i] :
( ( big_V @ X @ Y )
= ( implies @ ( implies @ X @ Y ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i] :
( ( implies @ ( implies @ ( not @ X ) @ ( not @ Y ) ) @ ( implies @ Y @ X ) )
= truth ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(34,plain,
( ( ! [X: $i,Y: $i] :
( ( implies @ ( implies @ X @ Y ) @ Y )
= ( implies @ ( implies @ Y @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(35,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) )
= truth ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(36,plain,
( ( ! [X: $i] :
( ( implies @ truth @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(37,plain,
( ( ( ( big_V @ ( implies @ x @ y ) @ ( implies @ y @ x ) )
!= truth ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(38,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[20]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( ordered @ X @ Y )
| ! [Z: $i] : ( ordered @ ( implies @ Z @ X ) @ ( implies @ Z @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( ordered @ X @ Y )
| ! [Z: $i] : ( ordered @ ( implies @ X @ Z ) @ ( implies @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(41,plain,
( ( ! [X: $i,Y: $i] :
( ( ( implies @ X @ Y )
!= truth )
| ( ordered @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(42,plain,
( ( ( ( big_V @ ( implies @ x @ y ) @ ( implies @ y @ x ) )
!= truth ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(43,plain,
( ( ( ( big_V @ ( implies @ x @ y ) @ ( implies @ y @ x ) )
!= truth ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(44,plain,
( ( ! [X: $i] :
( ( implies @ truth @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(45,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) )
= truth ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i] :
( ( implies @ ( implies @ X @ Y ) @ Y )
= ( implies @ ( implies @ Y @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(47,plain,
( ( ! [X: $i,Y: $i] :
( ( implies @ ( implies @ ( not @ X ) @ ( not @ Y ) ) @ ( implies @ Y @ X ) )
= truth ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i] :
( ( big_V @ X @ Y )
= ( implies @ ( implies @ X @ Y ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(49,plain,
( ( ! [X: $i,Y: $i] :
( ( big_hat @ X @ Y )
= ( not @ ( big_V @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(50,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( ordered @ X @ Y )
| ( ( implies @ X @ Y )
= truth ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(51,plain,
( ( ! [X: $i,Y: $i] :
( ( ( implies @ X @ Y )
!= truth )
| ( ordered @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(52,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( ordered @ X @ Y )
| ! [Z: $i] : ( ordered @ ( implies @ X @ Z ) @ ( implies @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(53,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( ordered @ X @ Y )
| ! [Z: $i] : ( ordered @ ( implies @ Z @ X ) @ ( implies @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(54,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( ordered @ X @ ( implies @ Y @ Z ) )
| ( ordered @ Y @ ( implies @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(55,plain,
( ( ! [Y: $i,X: $i,Z: $i] :
( ~ ( ordered @ Y @ ( implies @ X @ Z ) )
| ( ordered @ X @ ( implies @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i] :
( ( not @ ( big_V @ X @ Y ) )
= ( big_hat @ ( not @ X ) @ ( not @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(57,plain,
( ( ! [X: $i,Y: $i] :
( ( not @ ( big_hat @ X @ Y ) )
= ( big_V @ ( not @ X ) @ ( not @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(58,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( implies @ ( big_V @ X @ Y ) @ Z )
= ( big_hat @ ( implies @ X @ Z ) @ ( implies @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( implies @ X @ ( big_hat @ Y @ Z ) )
= ( big_hat @ ( implies @ X @ Y ) @ ( implies @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(60,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(61,plain,
( ( ( big_V @ ( implies @ x @ y ) @ ( implies @ y @ x ) )
= truth )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(62,plain,
! [SV1: $i] :
( ( ( implies @ truth @ SV1 )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(63,plain,
! [SV2: $i] :
( ( ! [SY38: $i,SY39: $i] :
( ( implies @ ( implies @ SV2 @ SY38 ) @ ( implies @ ( implies @ SY38 @ SY39 ) @ ( implies @ SV2 @ SY39 ) ) )
= truth ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(64,plain,
! [SV3: $i] :
( ( ! [SY40: $i] :
( ( implies @ ( implies @ SV3 @ SY40 ) @ SY40 )
= ( implies @ ( implies @ SY40 @ SV3 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(65,plain,
! [SV4: $i] :
( ( ! [SY41: $i] :
( ( implies @ ( implies @ ( not @ SV4 ) @ ( not @ SY41 ) ) @ ( implies @ SY41 @ SV4 ) )
= truth ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(66,plain,
! [SV5: $i] :
( ( ! [SY42: $i] :
( ( big_V @ SV5 @ SY42 )
= ( implies @ ( implies @ SV5 @ SY42 ) @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(67,plain,
! [SV6: $i] :
( ( ! [SY43: $i] :
( ( big_hat @ SV6 @ SY43 )
= ( not @ ( big_V @ ( not @ SV6 ) @ ( not @ SY43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(68,plain,
! [SV7: $i] :
( ( ! [SY44: $i] :
( ~ ( ordered @ SV7 @ SY44 )
| ( ( implies @ SV7 @ SY44 )
= truth ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(69,plain,
! [SV8: $i] :
( ( ! [SY45: $i] :
( ( ( implies @ SV8 @ SY45 )
!= truth )
| ( ordered @ SV8 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(70,plain,
! [SV9: $i] :
( ( ! [SY46: $i] :
( ~ ( ordered @ SV9 @ SY46 )
| ! [SY47: $i] : ( ordered @ ( implies @ SV9 @ SY47 ) @ ( implies @ SY46 @ SY47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(71,plain,
! [SV10: $i] :
( ( ! [SY48: $i] :
( ~ ( ordered @ SV10 @ SY48 )
| ! [SY49: $i] : ( ordered @ ( implies @ SY49 @ SV10 ) @ ( implies @ SY49 @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(72,plain,
! [SV11: $i] :
( ( ! [SY50: $i,SY51: $i] :
( ~ ( ordered @ SV11 @ ( implies @ SY50 @ SY51 ) )
| ( ordered @ SY50 @ ( implies @ SV11 @ SY51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(73,plain,
! [SV12: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ~ ( ordered @ SV12 @ ( implies @ SY52 @ SY53 ) )
| ( ordered @ SY52 @ ( implies @ SV12 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(74,plain,
! [SV13: $i] :
( ( ! [SY54: $i] :
( ( not @ ( big_V @ SV13 @ SY54 ) )
= ( big_hat @ ( not @ SV13 ) @ ( not @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(75,plain,
! [SV14: $i] :
( ( ! [SY55: $i] :
( ( not @ ( big_hat @ SV14 @ SY55 ) )
= ( big_V @ ( not @ SV14 ) @ ( not @ SY55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(76,plain,
! [SV15: $i] :
( ( ! [SY56: $i,SY57: $i] :
( ( implies @ ( big_V @ SV15 @ SY56 ) @ SY57 )
= ( big_hat @ ( implies @ SV15 @ SY57 ) @ ( implies @ SY56 @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(77,plain,
! [SV16: $i] :
( ( ! [SY58: $i,SY59: $i] :
( ( implies @ SV16 @ ( big_hat @ SY58 @ SY59 ) )
= ( big_hat @ ( implies @ SV16 @ SY58 ) @ ( implies @ SV16 @ SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(78,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(79,plain,
! [SV17: $i,SV2: $i] :
( ( ! [SY60: $i] :
( ( implies @ ( implies @ SV2 @ SV17 ) @ ( implies @ ( implies @ SV17 @ SY60 ) @ ( implies @ SV2 @ SY60 ) ) )
= truth ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(80,plain,
! [SV18: $i,SV3: $i] :
( ( ( implies @ ( implies @ SV3 @ SV18 ) @ SV18 )
= ( implies @ ( implies @ SV18 @ SV3 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(81,plain,
! [SV19: $i,SV4: $i] :
( ( ( implies @ ( implies @ ( not @ SV4 ) @ ( not @ SV19 ) ) @ ( implies @ SV19 @ SV4 ) )
= truth )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(82,plain,
! [SV20: $i,SV5: $i] :
( ( ( big_V @ SV5 @ SV20 )
= ( implies @ ( implies @ SV5 @ SV20 ) @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(83,plain,
! [SV21: $i,SV6: $i] :
( ( ( big_hat @ SV6 @ SV21 )
= ( not @ ( big_V @ ( not @ SV6 ) @ ( not @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(84,plain,
! [SV22: $i,SV7: $i] :
( ( ~ ( ordered @ SV7 @ SV22 )
| ( ( implies @ SV7 @ SV22 )
= truth ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(85,plain,
! [SV23: $i,SV8: $i] :
( ( ( ( implies @ SV8 @ SV23 )
!= truth )
| ( ordered @ SV8 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(86,plain,
! [SV24: $i,SV9: $i] :
( ( ~ ( ordered @ SV9 @ SV24 )
| ! [SY61: $i] : ( ordered @ ( implies @ SV9 @ SY61 ) @ ( implies @ SV24 @ SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(87,plain,
! [SV25: $i,SV10: $i] :
( ( ~ ( ordered @ SV10 @ SV25 )
| ! [SY62: $i] : ( ordered @ ( implies @ SY62 @ SV10 ) @ ( implies @ SY62 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(88,plain,
! [SV26: $i,SV11: $i] :
( ( ! [SY63: $i] :
( ~ ( ordered @ SV11 @ ( implies @ SV26 @ SY63 ) )
| ( ordered @ SV26 @ ( implies @ SV11 @ SY63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(89,plain,
! [SV27: $i,SV12: $i] :
( ( ! [SY64: $i] :
( ~ ( ordered @ SV12 @ ( implies @ SV27 @ SY64 ) )
| ( ordered @ SV27 @ ( implies @ SV12 @ SY64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(90,plain,
! [SV28: $i,SV13: $i] :
( ( ( not @ ( big_V @ SV13 @ SV28 ) )
= ( big_hat @ ( not @ SV13 ) @ ( not @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(91,plain,
! [SV29: $i,SV14: $i] :
( ( ( not @ ( big_hat @ SV14 @ SV29 ) )
= ( big_V @ ( not @ SV14 ) @ ( not @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(92,plain,
! [SV30: $i,SV15: $i] :
( ( ! [SY65: $i] :
( ( implies @ ( big_V @ SV15 @ SV30 ) @ SY65 )
= ( big_hat @ ( implies @ SV15 @ SY65 ) @ ( implies @ SV30 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(93,plain,
! [SV31: $i,SV16: $i] :
( ( ! [SY66: $i] :
( ( implies @ SV16 @ ( big_hat @ SV31 @ SY66 ) )
= ( big_hat @ ( implies @ SV16 @ SV31 ) @ ( implies @ SV16 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(94,plain,
! [SV32: $i,SV17: $i,SV2: $i] :
( ( ( implies @ ( implies @ SV2 @ SV17 ) @ ( implies @ ( implies @ SV17 @ SV32 ) @ ( implies @ SV2 @ SV32 ) ) )
= truth )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(95,plain,
! [SV22: $i,SV7: $i] :
( ( ( ~ ( ordered @ SV7 @ SV22 ) )
= $true )
| ( ( ( implies @ SV7 @ SV22 )
= truth )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(96,plain,
! [SV23: $i,SV8: $i] :
( ( ( ( ( implies @ SV8 @ SV23 )
!= truth ) )
= $true )
| ( ( ordered @ SV8 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(97,plain,
! [SV24: $i,SV9: $i] :
( ( ( ~ ( ordered @ SV9 @ SV24 ) )
= $true )
| ( ( ! [SY61: $i] : ( ordered @ ( implies @ SV9 @ SY61 ) @ ( implies @ SV24 @ SY61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(98,plain,
! [SV25: $i,SV10: $i] :
( ( ( ~ ( ordered @ SV10 @ SV25 ) )
= $true )
| ( ( ! [SY62: $i] : ( ordered @ ( implies @ SY62 @ SV10 ) @ ( implies @ SY62 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(99,plain,
! [SV33: $i,SV26: $i,SV11: $i] :
( ( ~ ( ordered @ SV11 @ ( implies @ SV26 @ SV33 ) )
| ( ordered @ SV26 @ ( implies @ SV11 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(100,plain,
! [SV34: $i,SV27: $i,SV12: $i] :
( ( ~ ( ordered @ SV12 @ ( implies @ SV27 @ SV34 ) )
| ( ordered @ SV27 @ ( implies @ SV12 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(101,plain,
! [SV35: $i,SV30: $i,SV15: $i] :
( ( ( implies @ ( big_V @ SV15 @ SV30 ) @ SV35 )
= ( big_hat @ ( implies @ SV15 @ SV35 ) @ ( implies @ SV30 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(102,plain,
! [SV36: $i,SV31: $i,SV16: $i] :
( ( ( implies @ SV16 @ ( big_hat @ SV31 @ SV36 ) )
= ( big_hat @ ( implies @ SV16 @ SV31 ) @ ( implies @ SV16 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(103,plain,
! [SV22: $i,SV7: $i] :
( ( ( ordered @ SV7 @ SV22 )
= $false )
| ( ( ( implies @ SV7 @ SV22 )
= truth )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(104,plain,
! [SV23: $i,SV8: $i] :
( ( ( ( implies @ SV8 @ SV23 )
= truth )
= $false )
| ( ( ordered @ SV8 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(105,plain,
! [SV24: $i,SV9: $i] :
( ( ( ordered @ SV9 @ SV24 )
= $false )
| ( ( ! [SY61: $i] : ( ordered @ ( implies @ SV9 @ SY61 ) @ ( implies @ SV24 @ SY61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(106,plain,
! [SV25: $i,SV10: $i] :
( ( ( ordered @ SV10 @ SV25 )
= $false )
| ( ( ! [SY62: $i] : ( ordered @ ( implies @ SY62 @ SV10 ) @ ( implies @ SY62 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(107,plain,
! [SV33: $i,SV26: $i,SV11: $i] :
( ( ( ~ ( ordered @ SV11 @ ( implies @ SV26 @ SV33 ) ) )
= $true )
| ( ( ordered @ SV26 @ ( implies @ SV11 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(108,plain,
! [SV34: $i,SV27: $i,SV12: $i] :
( ( ( ~ ( ordered @ SV12 @ ( implies @ SV27 @ SV34 ) ) )
= $true )
| ( ( ordered @ SV27 @ ( implies @ SV12 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(109,plain,
! [SV24: $i,SV37: $i,SV9: $i] :
( ( ( ordered @ ( implies @ SV9 @ SV37 ) @ ( implies @ SV24 @ SV37 ) )
= $true )
| ( ( ordered @ SV9 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(110,plain,
! [SV25: $i,SV10: $i,SV38: $i] :
( ( ( ordered @ ( implies @ SV38 @ SV10 ) @ ( implies @ SV38 @ SV25 ) )
= $true )
| ( ( ordered @ SV10 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(111,plain,
! [SV33: $i,SV26: $i,SV11: $i] :
( ( ( ordered @ SV11 @ ( implies @ SV26 @ SV33 ) )
= $false )
| ( ( ordered @ SV26 @ ( implies @ SV11 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV34: $i,SV27: $i,SV12: $i] :
( ( ( ordered @ SV12 @ ( implies @ SV27 @ SV34 ) )
= $false )
| ( ( ordered @ SV27 @ ( implies @ SV12 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(113,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[61,112,111,110,109,104,103,102,101,94,91,90,83,82,81,80,78,62]) ).
thf(114,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL109-5 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 2 09:55:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 17
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 0
% 0.12/0.35
% 0.12/0.35 Contains.Choice.Funs: false
% 0.12/0.36 (rf:0,axioms:17,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:19,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.18/0.47
% 0.18/0.47 ********************************
% 0.18/0.47 * All subproblems solved! *
% 0.18/0.47 ********************************
% 0.18/0.47 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:17,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:113,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.47
% 0.18/0.47 %**** Beginning of derivation protocol ****
% 0.18/0.47 % SZS output start CNFRefutation
% See solution above
% 0.18/0.47
% 0.18/0.47 %**** End of derivation protocol ****
% 0.18/0.47 %**** no. of clauses in derivation: 114 ****
% 0.18/0.47 %**** clause counter: 113 ****
% 0.18/0.47
% 0.18/0.47 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:17,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:113,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------