TSTP Solution File: SET907+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET907+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n022.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 : Tue Jul 19 03:06:07 EDT 2022
% Result : Theorem 0.12s 0.41s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 22
% Syntax : Number of formulae : 118 ( 83 unt; 10 typ; 0 def)
% Number of atoms : 458 ( 150 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 797 ( 120 ~; 88 |; 12 &; 561 @)
% ( 2 <=>; 14 =>; 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 : 13 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 232 ( 0 ^ 228 !; 4 ?; 232 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY24,type,
sK2_SY24: $i ).
thf(tp_sK3_SY26,type,
sK3_SY26: $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(3,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(4,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(5,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(12,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( in @ C @ B ) )
=> ( ( set_union2 @ ( unordered_pair @ A @ C ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_zfmisc_1) ).
thf(13,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( in @ C @ B ) )
=> ( ( set_union2 @ ( unordered_pair @ A @ C ) @ B )
= B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( in @ C @ B ) )
=> ( ( set_union2 @ ( unordered_pair @ A @ C ) @ B )
= B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(18,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(19,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(20,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(21,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(22,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(26,plain,
( ( ! [SY24: $i,SY25: $i] :
( ( ( in @ sK1_A @ SY24 )
& ( in @ SY25 @ SY24 ) )
=> ( ( set_union2 @ ( unordered_pair @ sK1_A @ SY25 ) @ SY24 )
= SY24 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(27,plain,
( ( ! [SY26: $i] :
( ( ( in @ sK1_A @ sK2_SY24 )
& ( in @ SY26 @ sK2_SY24 ) )
=> ( ( set_union2 @ ( unordered_pair @ sK1_A @ SY26 ) @ sK2_SY24 )
= sK2_SY24 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[26]) ).
thf(28,plain,
( ( ( ( in @ sK1_A @ sK2_SY24 )
& ( in @ sK3_SY26 @ sK2_SY24 ) )
=> ( ( set_union2 @ ( unordered_pair @ sK1_A @ sK3_SY26 ) @ sK2_SY24 )
= sK2_SY24 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(29,plain,
( ( in @ sK1_A @ sK2_SY24 )
= $true ),
inference(standard_cnf,[status(thm)],[28]) ).
thf(30,plain,
( ( in @ sK3_SY26 @ sK2_SY24 )
= $true ),
inference(standard_cnf,[status(thm)],[28]) ).
thf(31,plain,
( ( ( set_union2 @ ( unordered_pair @ sK1_A @ sK3_SY26 ) @ sK2_SY24 )
= sK2_SY24 )
= $false ),
inference(standard_cnf,[status(thm)],[28]) ).
thf(32,plain,
( ( ( ( set_union2 @ ( unordered_pair @ sK1_A @ sK3_SY26 ) @ sK2_SY24 )
!= sK2_SY24 ) )
= $true ),
inference(polarity_switch,[status(thm)],[31]) ).
thf(33,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(34,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(35,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(36,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(37,plain,
( ( empty @ sK5_A )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(38,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(39,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(40,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(45,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(46,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(47,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(48,plain,
( ( empty @ sK5_A )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(49,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(50,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(51,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(52,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(53,plain,
( ( in @ sK3_SY26 @ sK2_SY24 )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(54,plain,
( ( in @ sK1_A @ sK2_SY24 )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(55,plain,
( ( ( ( set_union2 @ ( unordered_pair @ sK1_A @ sK3_SY26 ) @ sK2_SY24 )
!= sK2_SY24 ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(56,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX2 )
| ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(57,plain,
! [SV1: $i] :
( ( ! [SY27: $i] :
( ~ ( in @ SV1 @ SY27 )
| ~ ( in @ SY27 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(58,plain,
! [SV2: $i] :
( ( ! [SY28: $i] :
( ( unordered_pair @ SV2 @ SY28 )
= ( unordered_pair @ SY28 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(59,plain,
! [SV3: $i] :
( ( ! [SY29: $i] :
( ( set_union2 @ SV3 @ SY29 )
= ( set_union2 @ SY29 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(60,plain,
! [SV4: $i] :
( ( ( empty @ SV4 )
| ! [SY30: $i] :
~ ( empty @ ( set_union2 @ SV4 @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(61,plain,
! [SV5: $i] :
( ( ( empty @ SV5 )
| ! [SY31: $i] :
~ ( empty @ ( set_union2 @ SY31 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(62,plain,
! [SV6: $i] :
( ( ( set_union2 @ SV6 @ SV6 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(63,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(64,plain,
! [SV7: $i] :
( ( subset @ SV7 @ SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(65,plain,
! [SV8: $i] :
( ( ! [SY32: $i] :
( ~ ( subset @ SV8 @ SY32 )
| ( ( set_union2 @ SV8 @ SY32 )
= SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(66,plain,
( ( ( set_union2 @ ( unordered_pair @ sK1_A @ sK3_SY26 ) @ sK2_SY24 )
= sK2_SY24 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(67,plain,
! [SV9: $i] :
( ( ~ ( ~ ! [SY33: $i,SY34: $i] :
( ~ ( in @ SV9 @ SY34 )
| ~ ( in @ SY33 @ SY34 )
| ( subset @ ( unordered_pair @ SV9 @ SY33 ) @ SY34 ) )
| ~ ~ ( ~ ! [SY35: $i,SY36: $i] :
( ~ ( subset @ ( unordered_pair @ SV9 @ SY35 ) @ SY36 )
| ( in @ SV9 @ SY36 ) )
| ~ ! [SY37: $i,SY38: $i] :
( ~ ( subset @ ( unordered_pair @ SV9 @ SY37 ) @ SY38 )
| ( in @ SY37 @ SY38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(68,plain,
! [SV10: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV10 )
| ~ ( in @ SV10 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(69,plain,
! [SV11: $i,SV2: $i] :
( ( ( unordered_pair @ SV2 @ SV11 )
= ( unordered_pair @ SV11 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(70,plain,
! [SV12: $i,SV3: $i] :
( ( ( set_union2 @ SV3 @ SV12 )
= ( set_union2 @ SV12 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(71,plain,
! [SV4: $i] :
( ( ( empty @ SV4 )
= $true )
| ( ( ! [SY30: $i] :
~ ( empty @ ( set_union2 @ SV4 @ SY30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(72,plain,
! [SV5: $i] :
( ( ( empty @ SV5 )
= $true )
| ( ( ! [SY31: $i] :
~ ( empty @ ( set_union2 @ SY31 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(73,plain,
! [SV13: $i,SV8: $i] :
( ( ~ ( subset @ SV8 @ SV13 )
| ( ( set_union2 @ SV8 @ SV13 )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(74,plain,
! [SV9: $i] :
( ( ~ ! [SY33: $i,SY34: $i] :
( ~ ( in @ SV9 @ SY34 )
| ~ ( in @ SY33 @ SY34 )
| ( subset @ ( unordered_pair @ SV9 @ SY33 ) @ SY34 ) )
| ~ ~ ( ~ ! [SY35: $i,SY36: $i] :
( ~ ( subset @ ( unordered_pair @ SV9 @ SY35 ) @ SY36 )
| ( in @ SV9 @ SY36 ) )
| ~ ! [SY37: $i,SY38: $i] :
( ~ ( subset @ ( unordered_pair @ SV9 @ SY37 ) @ SY38 )
| ( in @ SY37 @ SY38 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(75,plain,
! [SV10: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV10 ) )
= $true )
| ( ( ~ ( in @ SV10 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(76,plain,
! [SV14: $i,SV4: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV4 @ SV14 ) ) )
= $true )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(77,plain,
! [SV5: $i,SV15: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV15 @ SV5 ) ) )
= $true )
| ( ( empty @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(78,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV13 ) )
= $true )
| ( ( ( set_union2 @ SV8 @ SV13 )
= SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(79,plain,
! [SV9: $i] :
( ( ~ ! [SY33: $i,SY34: $i] :
( ~ ( in @ SV9 @ SY34 )
| ~ ( in @ SY33 @ SY34 )
| ( subset @ ( unordered_pair @ SV9 @ SY33 ) @ SY34 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(80,plain,
! [SV9: $i] :
( ( ~ ~ ( ~ ! [SY35: $i,SY36: $i] :
( ~ ( subset @ ( unordered_pair @ SV9 @ SY35 ) @ SY36 )
| ( in @ SV9 @ SY36 ) )
| ~ ! [SY37: $i,SY38: $i] :
( ~ ( subset @ ( unordered_pair @ SV9 @ SY37 ) @ SY38 )
| ( in @ SY37 @ SY38 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(81,plain,
! [SV10: $i,SV1: $i] :
( ( ( in @ SV1 @ SV10 )
= $false )
| ( ( ~ ( in @ SV10 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(82,plain,
! [SV14: $i,SV4: $i] :
( ( ( empty @ ( set_union2 @ SV4 @ SV14 ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(83,plain,
! [SV5: $i,SV15: $i] :
( ( ( empty @ ( set_union2 @ SV15 @ SV5 ) )
= $false )
| ( ( empty @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(84,plain,
! [SV13: $i,SV8: $i] :
( ( ( subset @ SV8 @ SV13 )
= $false )
| ( ( ( set_union2 @ SV8 @ SV13 )
= SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(85,plain,
! [SV9: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ~ ( in @ SV9 @ SY34 )
| ~ ( in @ SY33 @ SY34 )
| ( subset @ ( unordered_pair @ SV9 @ SY33 ) @ SY34 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(86,plain,
! [SV9: $i] :
( ( ~ ( ~ ! [SY35: $i,SY36: $i] :
( ~ ( subset @ ( unordered_pair @ SV9 @ SY35 ) @ SY36 )
| ( in @ SV9 @ SY36 ) )
| ~ ! [SY37: $i,SY38: $i] :
( ~ ( subset @ ( unordered_pair @ SV9 @ SY37 ) @ SY38 )
| ( in @ SY37 @ SY38 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(87,plain,
! [SV1: $i,SV10: $i] :
( ( ( in @ SV10 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(88,plain,
! [SV16: $i,SV9: $i] :
( ( ! [SY39: $i] :
( ~ ( in @ SV9 @ SY39 )
| ~ ( in @ SV16 @ SY39 )
| ( subset @ ( unordered_pair @ SV9 @ SV16 ) @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(89,plain,
! [SV9: $i] :
( ( ~ ! [SY35: $i,SY36: $i] :
( ~ ( subset @ ( unordered_pair @ SV9 @ SY35 ) @ SY36 )
| ( in @ SV9 @ SY36 ) )
| ~ ! [SY37: $i,SY38: $i] :
( ~ ( subset @ ( unordered_pair @ SV9 @ SY37 ) @ SY38 )
| ( in @ SY37 @ SY38 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(90,plain,
! [SV16: $i,SV17: $i,SV9: $i] :
( ( ~ ( in @ SV9 @ SV17 )
| ~ ( in @ SV16 @ SV17 )
| ( subset @ ( unordered_pair @ SV9 @ SV16 ) @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(91,plain,
! [SV9: $i] :
( ( ~ ! [SY35: $i,SY36: $i] :
( ~ ( subset @ ( unordered_pair @ SV9 @ SY35 ) @ SY36 )
| ( in @ SV9 @ SY36 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(92,plain,
! [SV9: $i] :
( ( ~ ! [SY37: $i,SY38: $i] :
( ~ ( subset @ ( unordered_pair @ SV9 @ SY37 ) @ SY38 )
| ( in @ SY37 @ SY38 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(93,plain,
! [SV16: $i,SV17: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV17 )
| ~ ( in @ SV16 @ SV17 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV9 @ SV16 ) @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(94,plain,
! [SV9: $i] :
( ( ! [SY35: $i,SY36: $i] :
( ~ ( subset @ ( unordered_pair @ SV9 @ SY35 ) @ SY36 )
| ( in @ SV9 @ SY36 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(95,plain,
! [SV9: $i] :
( ( ! [SY37: $i,SY38: $i] :
( ~ ( subset @ ( unordered_pair @ SV9 @ SY37 ) @ SY38 )
| ( in @ SY37 @ SY38 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(96,plain,
! [SV16: $i,SV17: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV17 ) )
= $true )
| ( ( ~ ( in @ SV16 @ SV17 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV9 @ SV16 ) @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(97,plain,
! [SV18: $i,SV9: $i] :
( ( ! [SY40: $i] :
( ~ ( subset @ ( unordered_pair @ SV9 @ SV18 ) @ SY40 )
| ( in @ SV9 @ SY40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(98,plain,
! [SV19: $i,SV9: $i] :
( ( ! [SY41: $i] :
( ~ ( subset @ ( unordered_pair @ SV9 @ SV19 ) @ SY41 )
| ( in @ SV19 @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(99,plain,
! [SV16: $i,SV17: $i,SV9: $i] :
( ( ( in @ SV9 @ SV17 )
= $false )
| ( ( ~ ( in @ SV16 @ SV17 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV9 @ SV16 ) @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(100,plain,
! [SV20: $i,SV18: $i,SV9: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV9 @ SV18 ) @ SV20 )
| ( in @ SV9 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(101,plain,
! [SV21: $i,SV19: $i,SV9: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV9 @ SV19 ) @ SV21 )
| ( in @ SV19 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(102,plain,
! [SV9: $i,SV17: $i,SV16: $i] :
( ( ( in @ SV16 @ SV17 )
= $false )
| ( ( in @ SV9 @ SV17 )
= $false )
| ( ( subset @ ( unordered_pair @ SV9 @ SV16 ) @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(103,plain,
! [SV20: $i,SV18: $i,SV9: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV9 @ SV18 ) @ SV20 ) )
= $true )
| ( ( in @ SV9 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(104,plain,
! [SV21: $i,SV19: $i,SV9: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV9 @ SV19 ) @ SV21 ) )
= $true )
| ( ( in @ SV19 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(105,plain,
! [SV20: $i,SV18: $i,SV9: $i] :
( ( ( subset @ ( unordered_pair @ SV9 @ SV18 ) @ SV20 )
= $false )
| ( ( in @ SV9 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(106,plain,
! [SV21: $i,SV19: $i,SV9: $i] :
( ( ( subset @ ( unordered_pair @ SV9 @ SV19 ) @ SV21 )
= $false )
| ( ( in @ SV19 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(107,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[48,106,105,102,87,84,83,82,70,69,66,64,63,62,54,53]) ).
thf(108,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET907+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n022.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 9 21:49:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 11
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:11,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:13,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.12/0.41
% 0.12/0.41 ********************************
% 0.12/0.41 * All subproblems solved! *
% 0.12/0.41 ********************************
% 0.12/0.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:13,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:107,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.41
% 0.18/0.41 %**** Beginning of derivation protocol ****
% 0.18/0.41 % SZS output start CNFRefutation
% See solution above
% 0.18/0.41
% 0.18/0.41 %**** End of derivation protocol ****
% 0.18/0.41 %**** no. of clauses in derivation: 108 ****
% 0.18/0.41 %**** clause counter: 107 ****
% 0.18/0.41
% 0.18/0.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:13,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:107,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------